# Exact Bounded Discrete Logistic Increment Models

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This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20261013-advance-20261021-r07-discrete-logistic-growth-foundations · 2026-10-13 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=0/5, rate=0/1, capacity=5/1. Give (current,rate,capacity,next).

View answer and explanation(0, 0, 5, 0)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 0, 5, 0).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0001/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 2. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=1/5, rate=1/4, capacity=6/1. Give (current,rate,capacity,next).

View answer and explanation(1/5, 1/4, 6, 149/600)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1/5, 1/4, 6, 149/600).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0002/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 3. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=2/5, rate=1/2, capacity=7/1. Give (current,rate,capacity,next).

View answer and explanation(2/5, 1/2, 7, 103/175)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2/5, 1/2, 7, 103/175).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0003/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 4. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=3/5, rate=3/4, capacity=8/1. Give (current,rate,capacity,next).

View answer and explanation(3/5, 3/4, 8, 813/800)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3/5, 3/4, 8, 813/800).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0004/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 5. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=4/5, rate=1/1, capacity=9/1. Give (current,rate,capacity,next).

View answer and explanation(4/5, 1, 9, 344/225)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (4/5, 1, 9, 344/225).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0005/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 6. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=5/5, rate=0/1, capacity=5/1. Give (current,rate,capacity,next).

View answer and explanation(1, 0, 5, 1)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 0, 5, 1).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0006/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 7. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=6/5, rate=1/4, capacity=6/1. Give (current,rate,capacity,next).

View answer and explanation(6/5, 1/4, 6, 36/25)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (6/5, 1/4, 6, 36/25).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0007/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 8. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=7/5, rate=1/2, capacity=7/1. Give (current,rate,capacity,next).

View answer and explanation(7/5, 1/2, 7, 49/25)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (7/5, 1/2, 7, 49/25).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0008/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 9. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=8/5, rate=3/4, capacity=8/1. Give (current,rate,capacity,next).

View answer and explanation(8/5, 3/4, 8, 64/25)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (8/5, 3/4, 8, 64/25).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0009/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 10. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=9/5, rate=1/1, capacity=9/1. Give (current,rate,capacity,next).

View answer and explanation(9/5, 1, 9, 81/25)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (9/5, 1, 9, 81/25).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0010/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 11. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=10/5, rate=0/1, capacity=5/1. Give (current,rate,capacity,next).

View answer and explanation(2, 0, 5, 2)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2, 0, 5, 2).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0011/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 12. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=11/5, rate=1/4, capacity=6/1. Give (current,rate,capacity,next).

View answer and explanation(11/5, 1/4, 6, 1529/600)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (11/5, 1/4, 6, 1529/600).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0012/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 13. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=12/5, rate=1/2, capacity=7/1. Give (current,rate,capacity,next).

View answer and explanation(12/5, 1/2, 7, 558/175)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (12/5, 1/2, 7, 558/175).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0013/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 14. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=13/5, rate=3/4, capacity=8/1. Give (current,rate,capacity,next).

View answer and explanation(13/5, 3/4, 8, 3133/800)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (13/5, 3/4, 8, 3133/800).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0014/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 15. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=14/5, rate=1/1, capacity=9/1. Give (current,rate,capacity,next).

View answer and explanation(14/5, 1, 9, 1064/225)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (14/5, 1, 9, 1064/225).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0015/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 16. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=15/5, rate=0/1, capacity=5/1. Give (current,rate,capacity,next).

View answer and explanation(3, 0, 5, 3)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3, 0, 5, 3).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0016/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 17. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=16/5, rate=1/4, capacity=6/1. Give (current,rate,capacity,next).

View answer and explanation(16/5, 1/4, 6, 268/75)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (16/5, 1/4, 6, 268/75).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0017/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 18. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=17/5, rate=1/2, capacity=7/1. Give (current,rate,capacity,next).

View answer and explanation(17/5, 1/2, 7, 748/175)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (17/5, 1/2, 7, 748/175).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0018/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 19. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=18/5, rate=3/4, capacity=8/1. Give (current,rate,capacity,next).

View answer and explanation(18/5, 3/4, 8, 1017/200)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (18/5, 3/4, 8, 1017/200).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0019/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 20. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=19/5, rate=1/1, capacity=9/1. Give (current,rate,capacity,next).

View answer and explanation(19/5, 1, 9, 1349/225)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (19/5, 1, 9, 1349/225).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0020/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 21. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=20/5, rate=0/1, capacity=5/1. Give (current,rate,capacity,next).

View answer and explanation(4, 0, 5, 4)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (4, 0, 5, 4).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0021/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 22. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=21/5, rate=1/4, capacity=6/1. Give (current,rate,capacity,next).

View answer and explanation(21/5, 1/4, 6, 903/200)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21/5, 1/4, 6, 903/200).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0022/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 23. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=22/5, rate=1/2, capacity=7/1. Give (current,rate,capacity,next).

View answer and explanation(22/5, 1/2, 7, 913/175)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (22/5, 1/2, 7, 913/175).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0023/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 24. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=23/5, rate=3/4, capacity=8/1. Give (current,rate,capacity,next).

View answer and explanation(23/5, 3/4, 8, 4853/800)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (23/5, 3/4, 8, 4853/800).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0024/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 25. One Exact Capacity-Limited Discrete Increment

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=24/5, rate=1/1, capacity=9/1. Give (current,rate,capacity,next).

View answer and explanation(24/5, 1, 9, 176/25)

Compute the increment and add it to the current state; do not replace this model with r*x*(1−x/K). This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (24/5, 1, 9, 176/25).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0025/)

Discrete logistic increment model · qf-app21-logistic-single-step · candidate





## 26. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=0/25, rate=0/1, capacity=5/1, updates=2. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(0, 0, 5, 2, [0, 0, 0])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 0, 5, 2, [0, 0, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0026/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 27. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=1/25, rate=1/4, capacity=6/1, updates=1. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(1/25, 1/4, 6, 1, [1/25, 749/15000])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1/25, 1/4, 6, 1, [1/25, 749/15000]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0027/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 28. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=2/25, rate=1/2, capacity=7/1, updates=0. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(2/25, 1/2, 7, 0, [2/25])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2/25, 1/2, 7, 0, [2/25]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0028/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 29. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=3/25, rate=3/4, capacity=8/1, updates=1. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(3/25, 3/4, 8, 1, [3/25, 4173/20000])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3/25, 3/4, 8, 1, [3/25, 4173/20000]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0029/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 30. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=4/25, rate=1/1, capacity=9/1, updates=0. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(4/25, 1, 9, 0, [4/25])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (4/25, 1, 9, 0, [4/25]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0030/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 31. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=5/25, rate=0/1, capacity=5/1, updates=2. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(1/5, 0, 5, 2, [1/5, 1/5, 1/5])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1/5, 0, 5, 2, [1/5, 1/5, 1/5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0031/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 32. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=6/25, rate=1/4, capacity=6/1, updates=0. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(6/25, 1/4, 6, 0, [6/25])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (6/25, 1/4, 6, 0, [6/25]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0032/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 33. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=7/25, rate=1/2, capacity=7/1, updates=1. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(7/25, 1/2, 7, 1, [7/25, 259/625])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (7/25, 1/2, 7, 1, [7/25, 259/625]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0033/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 34. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=8/25, rate=3/4, capacity=8/1, updates=0. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(8/25, 3/4, 8, 0, [8/25])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (8/25, 3/4, 8, 0, [8/25]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0034/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 35. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=9/25, rate=1/1, capacity=9/1, updates=1. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(9/25, 1, 9, 1, [9/25, 441/625])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (9/25, 1, 9, 1, [9/25, 441/625]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0035/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 36. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=10/25, rate=0/1, capacity=5/1, updates=2. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(2/5, 0, 5, 2, [2/5, 2/5, 2/5])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2/5, 0, 5, 2, [2/5, 2/5, 2/5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0036/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 37. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=11/25, rate=1/4, capacity=6/1, updates=1. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(11/25, 1/4, 6, 1, [11/25, 8129/15000])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (11/25, 1/4, 6, 1, [11/25, 8129/15000]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0037/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 38. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=12/25, rate=1/2, capacity=7/1, updates=0. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(12/25, 1/2, 7, 0, [12/25])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (12/25, 1/2, 7, 0, [12/25]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0038/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 39. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=13/25, rate=3/4, capacity=8/1, updates=1. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(13/25, 3/4, 8, 1, [13/25, 17693/20000])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (13/25, 3/4, 8, 1, [13/25, 17693/20000]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0039/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 40. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=14/25, rate=1/1, capacity=9/1, updates=0. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(14/25, 1, 9, 0, [14/25])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (14/25, 1, 9, 0, [14/25]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0040/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 41. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=15/25, rate=0/1, capacity=5/1, updates=2. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(3/5, 0, 5, 2, [3/5, 3/5, 3/5])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3/5, 0, 5, 2, [3/5, 3/5, 3/5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0041/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 42. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=16/25, rate=1/4, capacity=6/1, updates=0. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(16/25, 1/4, 6, 0, [16/25])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (16/25, 1/4, 6, 0, [16/25]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0042/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 43. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=17/25, rate=1/2, capacity=7/1, updates=1. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(17/25, 1/2, 7, 1, [17/25, 4318/4375])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (17/25, 1/2, 7, 1, [17/25, 4318/4375]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0043/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 44. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=18/25, rate=3/4, capacity=8/1, updates=0. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(18/25, 3/4, 8, 0, [18/25])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (18/25, 3/4, 8, 0, [18/25]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0044/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 45. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=19/25, rate=1/1, capacity=9/1, updates=1. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(19/25, 1, 9, 1, [19/25, 8189/5625])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (19/25, 1, 9, 1, [19/25, 8189/5625]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0045/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 46. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=20/25, rate=0/1, capacity=5/1, updates=2. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(4/5, 0, 5, 2, [4/5, 4/5, 4/5])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (4/5, 0, 5, 2, [4/5, 4/5, 4/5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0046/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 47. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=21/25, rate=1/4, capacity=6/1, updates=1. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(21/25, 1/4, 6, 1, [21/25, 5103/5000])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21/25, 1/4, 6, 1, [21/25, 5103/5000]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0047/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 48. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=22/25, rate=1/2, capacity=7/1, updates=0. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(22/25, 1/2, 7, 0, [22/25])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (22/25, 1/2, 7, 0, [22/25]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0048/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 49. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=23/25, rate=3/4, capacity=8/1, updates=1. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(23/25, 3/4, 8, 1, [23/25, 30613/20000])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (23/25, 3/4, 8, 1, [23/25, 30613/20000]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0049/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 50. A Short Exact Orbit of the Specified Logistic Increment Model

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=24/25, rate=1/1, capacity=9/1, updates=0. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

View answer and explanation(24/25, 1, 9, 0, [24/25])

Reapply the same exact update, retaining all rational values without rounding. A short orbit is not a long-term stability or convergence proof. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (24/25, 1, 9, 0, [24/25]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0050/)

Discrete logistic increment model · qf-app21-logistic-orbit-prefix · candidate





## 51. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=0/5, rate=1/2, capacity=5/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(0, 1/2, 5, 0, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 1/2, 5, 0, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0051/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 52. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=1/5, rate=3/4, capacity=6/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(1/5, 3/4, 6, 69/200, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1/5, 3/4, 6, 69/200, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0052/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 53. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=2/5, rate=1/1, capacity=7/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(2/5, 1, 7, 136/175, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2/5, 1, 7, 136/175, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0053/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 54. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=3/5, rate=0/1, capacity=8/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(3/5, 0, 8, 3/5, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3/5, 0, 8, 3/5, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0054/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 55. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=4/5, rate=1/4, capacity=9/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(4/5, 1/4, 9, 221/225, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (4/5, 1/4, 9, 221/225, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0055/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 56. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=5/5, rate=1/2, capacity=5/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(1, 1/2, 5, 7/5, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 1/2, 5, 7/5, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0056/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 57. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=6/5, rate=3/4, capacity=6/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(6/5, 3/4, 6, 48/25, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (6/5, 3/4, 6, 48/25, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0057/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 58. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=7/5, rate=1/1, capacity=7/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(7/5, 1, 7, 63/25, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (7/5, 1, 7, 63/25, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0058/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 59. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=8/5, rate=0/1, capacity=8/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(8/5, 0, 8, 8/5, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (8/5, 0, 8, 8/5, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0059/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 60. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=9/5, rate=1/4, capacity=9/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(9/5, 1/4, 9, 54/25, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (9/5, 1/4, 9, 54/25, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0060/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 61. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=10/5, rate=1/2, capacity=5/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(2, 1/2, 5, 13/5, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2, 1/2, 5, 13/5, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0061/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 62. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=11/5, rate=3/4, capacity=6/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(11/5, 3/4, 6, 649/200, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (11/5, 3/4, 6, 649/200, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0062/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 63. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=12/5, rate=1/1, capacity=7/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(12/5, 1, 7, 696/175, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (12/5, 1, 7, 696/175, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0063/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 64. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=13/5, rate=0/1, capacity=8/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(13/5, 0, 8, 13/5, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (13/5, 0, 8, 13/5, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0064/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 65. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=14/5, rate=1/4, capacity=9/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(14/5, 1/4, 9, 1477/450, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (14/5, 1/4, 9, 1477/450, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0065/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 66. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=15/5, rate=1/2, capacity=5/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(3, 1/2, 5, 18/5, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3, 1/2, 5, 18/5, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0066/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 67. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=16/5, rate=3/4, capacity=6/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(16/5, 3/4, 6, 108/25, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (16/5, 3/4, 6, 108/25, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0067/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 68. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=17/5, rate=1/1, capacity=7/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(17/5, 1, 7, 901/175, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (17/5, 1, 7, 901/175, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0068/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 69. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=18/5, rate=0/1, capacity=8/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(18/5, 0, 8, 18/5, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (18/5, 0, 8, 18/5, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0069/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 70. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=19/5, rate=1/4, capacity=9/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(19/5, 1/4, 9, 1957/450, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (19/5, 1/4, 9, 1957/450, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0070/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 71. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=20/5, rate=1/2, capacity=5/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(4, 1/2, 5, 22/5, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (4, 1/2, 5, 22/5, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0071/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 72. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=21/5, rate=3/4, capacity=6/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(21/5, 3/4, 6, 1029/200, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21/5, 3/4, 6, 1029/200, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0072/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 73. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=22/5, rate=1/1, capacity=7/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(22/5, 1, 7, 1056/175, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (22/5, 1, 7, 1056/175, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0073/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 74. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=23/5, rate=0/1, capacity=8/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(23/5, 0, 8, 23/5, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (23/5, 0, 8, 23/5, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0074/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 75. One-Step Retention of the Declared Capacity Interval

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. current=24/5, rate=1/4, capacity=9/1. Give (current,rate,capacity,next,0≤next≤capacity?).

View answer and explanation(24/5, 1/4, 9, 134/25, Yes)

Evaluate the exact next state and both endpoint inequalities only in the qualified parameter domain; do not extrapolate to other logistic definitions or rates. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (24/5, 1/4, 9, 134/25, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0075/)

Discrete logistic increment model · qf-app21-logistic-capacity-interval-audit · candidate





## 76. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=0/1, rate=1/4, capacity=5/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(0, 1/4, 5, 0, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 1/4, 5, 0, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0076/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 77. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=6/1, rate=1/2, capacity=6/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(6, 1/2, 6, 6, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (6, 1/2, 6, 6, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0077/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 78. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=1/1, rate=3/4, capacity=7/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(1, 3/4, 7, 23/14, No)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 3/4, 7, 23/14, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0078/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 79. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=0/1, rate=1/1, capacity=8/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(0, 1, 8, 0, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 1, 8, 0, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0079/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 80. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=9/1, rate=0/1, capacity=9/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(9, 0, 9, 9, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (9, 0, 9, 9, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0080/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 81. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=1/1, rate=1/4, capacity=10/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(1, 1/4, 10, 49/40, No)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 1/4, 10, 49/40, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0081/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 82. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=0/1, rate=1/2, capacity=11/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(0, 1/2, 11, 0, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 1/2, 11, 0, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0082/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 83. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=12/1, rate=3/4, capacity=12/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(12, 3/4, 12, 12, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (12, 3/4, 12, 12, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0083/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 84. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=1/1, rate=1/1, capacity=13/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(1, 1, 13, 25/13, No)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 1, 13, 25/13, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0084/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 85. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=0/1, rate=0/1, capacity=14/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(0, 0, 14, 0, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 0, 14, 0, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0085/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 86. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=15/1, rate=1/4, capacity=15/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(15, 1/4, 15, 15, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (15, 1/4, 15, 15, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0086/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 87. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=1/1, rate=1/2, capacity=16/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(1, 1/2, 16, 47/32, No)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 1/2, 16, 47/32, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0087/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 88. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=0/1, rate=3/4, capacity=17/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(0, 3/4, 17, 0, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 3/4, 17, 0, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0088/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 89. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=18/1, rate=1/1, capacity=18/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(18, 1, 18, 18, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (18, 1, 18, 18, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0089/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 90. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=1/1, rate=0/1, capacity=19/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(1, 0, 19, 1, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 0, 19, 1, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0090/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 91. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=0/1, rate=1/4, capacity=20/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(0, 1/4, 20, 0, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 1/4, 20, 0, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0091/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 92. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=21/1, rate=1/2, capacity=21/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(21, 1/2, 21, 21, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21, 1/2, 21, 21, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0092/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 93. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=1/1, rate=3/4, capacity=22/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(1, 3/4, 22, 151/88, No)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 3/4, 22, 151/88, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0093/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 94. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=0/1, rate=1/1, capacity=23/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(0, 1, 23, 0, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 1, 23, 0, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0094/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 95. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=24/1, rate=0/1, capacity=24/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(24, 0, 24, 24, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (24, 0, 24, 24, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0095/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 96. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=1/1, rate=1/4, capacity=25/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(1, 1/4, 25, 31/25, No)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 1/4, 25, 31/25, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0096/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 97. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=0/1, rate=1/2, capacity=26/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(0, 1/2, 26, 0, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 1/2, 26, 0, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0097/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 98. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=27/1, rate=3/4, capacity=27/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(27, 3/4, 27, 27, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (27, 3/4, 27, 27, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0098/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 99. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=1/1, rate=1/1, capacity=28/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(1, 1, 28, 55/28, No)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 1, 28, 55/28, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0099/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate





## 100. A Fixed Candidate, Including the Zero-Rate Degeneracy

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. candidate=0/1, rate=0/1, capacity=29/1. Give (candidate,rate,capacity,next,next=candidate?). Both capacity endpoints are fixed; at rate=0 every allowed candidate is fixed.

View answer and explanation(0, 0, 29, 0, Yes)

Test exact equality after one update. Being fixed is separate from stability, attraction, convergence or empirical fit. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 0, 29, 0, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r07-discrete-logistic-growth-0100/)

Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261021-r07-discrete-logistic-growth-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261013-advance-20261021-r07-discrete-logistic-growth-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261021-r07-discrete-logistic-growth-foundations/validation-report.json)