Exact Bounded Discrete Logistic Increment Models
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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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Discrete logistic increment model · qf-app21-logistic-equilibrium-audit · candidate
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