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Question 1956: Highest Explicit Derivative Order, Not Candidate Polynomial Degree

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0002-01956 · q-20261013-advance-20261020-r02-ordinary-differential-equation-0006

Original question and givens

Derivative orders occurring in the specified relation are [1, 2], with 0 denoting y itself. Give (sorted distinct orders, highest order, does y occur?). A [0]-only list records the algebraic order-zero boundary, not evidence of a positive-order ODE.

  • G001 — Derivative orders occurring in the specified relation are [1, 2], with 0 denoting y itself. Give (sorted distinct orders, highest order, does y occur?). A [0]-only list records the algebraic order-zero boundary, not evidence of a positive-order ODE.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

Step-by-step derivation

S001 · implies

Before

[1, 2]

After

distinct actual derivative orders=[1, 2]

Conditions: none

Classify using the explicitly present derivative orders;sorting and deduplication add no derivative terms.

Step identifiers and dependencies

Rule: derivative_order_list · Uses: G001

S002 · implies

Before

[1, 2]

After

highest listed order=2

Conditions: none

Take the highest order,not the number of entries in the list.

Step identifiers and dependencies

Rule: highest_derivative_order · Uses: G001, S001

S003 · implies

Before

0 in orders: No

After

order0 denotes the undifferentiated y term

Conditions: none

The third flag asks whether y itself occurs;its presence does not make the whole equation order0.

Step identifiers and dependencies

Rule: includes_y_flag · Uses: G001, S002

S004 · implies

Before

highest=2; includes_y=No

After

classification assumes the listed terms survive simplification

Conditions: none

A list containing only0 is the algebraic boundary;this classification proves no existence,uniqueness or candidate-solution claim.

Step identifiers and dependencies

Rule: order_not_existence_theorem · Uses: G001, S003

Reverse checks

  • S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

([1, 2], 2, No)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: 2afe5033a9b085b09ab36b49a24b85307cfd72d345ec49f37df35bf89ee064d3
  • candidate record SHA-256: 54ea77451677e58b96045c54abd288e2c723b915f5729dd87b357ae3c0178947
  • semantic review receipt SHA-256: 340d74dcc6e37df6249594a0b79a9ee2af804337b7847478b3c1342af9722861
  • question-first witness SHA-256: 9a06233d190d31a16f13fb03b6c3ceba4cbb748fff6c997941f66ab1888dcca8
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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