# Question 35179: Integer in a Signed Context

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0069-35179 · q-20260919-signed-context-integer-0004



## Original question and givens

The zero point is the entrance, the positive direction is upward, and the unit is floors. What signed integer displacement from zero is represented by position -3?


- G001 — The zero point is the entrance, the positive direction is upward, and the unit is floors. What signed integer displacement from zero is represented by position -3?





## 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.


- [mko-integer](https://ocme.evemisslab.com/en/mko/mko-integer/)





## Step-by-step derivation

S001 · impliesBefore

source roles = [qf-signed-context-integer, [positive_direction, unit, value, zero]]

After

derived = [BASE-no-required-operation, no-invented-domain]

Conditions: none

Keep EACH bank’s keys/operation/domain distinct:LDL/PULSE/function legacy table underscores,TREE full tree_* with its declared domain,and permissive BASE signed without invented op/domain.All arithmetic respects the binary-primitive contract.

Step identifiers and dependenciesRule: R69_SOURCE_specific_keys_operation_domain_AND_binary_contract · Uses: G001





S002 · impliesBefore

source roles = [-3, zero/direction/unit are GIVEN in G001]

After

derived = [-1, 3, opposite_declared_positive_direction]

Conditions: none

The zero point,positive direction,unit and position value are GIVEN in G001.Zero is at the origin;positive is along the declared direction,negative opposite,and abs(value)is magnitude.The25 ACTUAL bilingual frames were checked;do not invent a measurement or unit conversion.

Step identifiers and dependenciesRule: Signed_GIVEN_frame_and_position_not_an_inferred_measurement · Uses: G001, S001





S003 · calculationBefore

Signed ORIGINAL sign times displacement magnitude := mul(-1, 3)

After

Signed ORIGINAL sign times displacement magnitude = -3

Conditions: none

Use ORIGINAL operands exactly;mul/sub/div have EXPLICITLY TWO operands so the old binary primitive cannot ignore a third.Keep RAW SAFE bounds separate from unbounded derived BigInts;do not approximate to force answers.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S002





S004 · impliesBefore

source roles = [-1, 3]

After

derived = [-3]

Conditions: none

Reconstruct the ORIGINAL signed displacement as sign*magnitude.Do not replace a negative displacement by a positive distance or reciprocal.The position is GIVEN,not guessed from a metadata flag.

Step identifiers and dependenciesRule: Signed_RECONSTRUCT_integer_value_from_sign_and_magnitude · Uses: G001, S003









## Reverse checks


- S004 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
- S003 · premise_and_result_audit — Recompute Signed ORIGINAL sign times displacement magnitude with exact rational arithmetic, not rounded decimals.
- S002 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
- S001 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.





## Result

-3

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: c60c01bb0aea27f5ce9dea1e3fbd1bf391506d1d8ef6daa99615bd6c4d8b4029
- candidate record SHA-256: adadfb2663dcf18c27e524bd1244e9aad504497fc3a1ea723ca06a7fc5d5abcb
- semantic review receipt SHA-256: ccf93c72638d6abf6a412514da5838d55ecb09b71d0e4fdec2b559dc9fdee14b
- question-first witness SHA-256: 11af9a338b5a610342b2cfb2ee295683131b3139ac402dd19b1ba1725976d518
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20260919-signed-context-integer-0004.json)