Question 35365: Uncovered Codomain Targets

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Original question and givens
Definition and scope
Step-by-step derivation
Reverse checks
Result
This question review and source binding

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R0069-35365 · q-20261004-advance-20261005-r02-surjective-0040

Original question and givens

The declared total function f:A→B has A={-4, -3, -2, -1, 0}, B={1, 3, 5, 7, 9, 11}, and table {(-4, 1), (-3, 3), (-2, 5), (-1, 7), (0, 9)}. List the uncovered targets B∖f[A] in increasing order, using ∅ for the empty set.

G001 — The declared total function f:A→B has A={-4, -3, -2, -1, 0}, B={1, 3, 5, 7, 9, 11}, and table {(-4, 1), (-3, 3), (-2, 5), (-1, 7), (0, 9)}. List the uncovered targets B∖f[A] in increasing order, using ∅ for the empty set.

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-surjective

Step-by-step derivation

S001 · implies

Before

source roles = [qf-surjective-missing-targets, [A, B, operation, pairs]]

After

derived = [missing_targets, 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 dependencies

Rule: R69_SOURCE_specific_keys_operation_domain_AND_binary_contract · Uses: G001

S002 · implies

Before

source roles = [function ORIGINAL A, 100, [-4, -3, -2, -1, 0]]

After

derived = [[-4, -3, -2, -1, 0]]

Conditions: none

Type EVERY RAW SAFE label,distinctness and THIS bank’s cardinality bound;empty is allowed.Sort ONLY the derived representation,not original JSON.Do not exchange TREE and LDL limits.

Step identifiers and dependencies

Rule: Finite_RAW_ALL_SAFE_distinct_labels_then_derived_sort · Uses: G001, S001

S003 · implies

Before

source roles = [function ORIGINAL B, 100, [1, 3, 5, 7, 9, 11]]

After

derived = [[1, 3, 5, 7, 9, 11]]

Conditions: none

Type EVERY RAW SAFE label,distinctness and THIS bank’s cardinality bound;empty is allowed.Sort ONLY the derived representation,not original JSON.Do not exchange TREE and LDL limits.

Step identifiers and dependencies

Rule: Finite_RAW_ALL_SAFE_distinct_labels_then_derived_sort · Uses: G001, S002

S004 · implies

Before

source roles = [function ORIGINAL table, 0, [-4, 1]]

After

derived = [[-4, 1]]

Conditions: none

BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.

Step identifiers and dependencies

Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S003

S005 · implies

Before

source roles = [function ORIGINAL table, 1, [-3, 3]]

After

derived = [[-3, 3]]

Conditions: none

BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.

Step identifiers and dependencies

Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S004

S006 · implies

Before

source roles = [function ORIGINAL table, 2, [-2, 5]]

After

derived = [[-2, 5]]

Conditions: none

BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.

Step identifiers and dependencies

Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S005

S007 · implies

Before

source roles = [function ORIGINAL table, 3, [-1, 7]]

After

derived = [[-1, 7]]

Conditions: none

BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.

Step identifiers and dependencies

Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S006

S008 · implies

Before

source roles = [function ORIGINAL table, 4, [0, 9]]

After

derived = [[0, 9]]

Conditions: none

BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.

Step identifiers and dependencies

Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S007

S009 · implies

Before

source roles = [[-4, -3, -2, -1, 0], [1, 3, 5, 7, 9, 11], [[-4, 1], [-3, 3], [-2, 5], [-1, 7], [0, 9]]]

After

derived = [Yes]

Conditions: none

FIRST qualify the WHOLE total function A→B:EXACTLY one output for EVERY A and all pairs in A×B.Identical repeated rows normalize in THIS legacy bank,unlike a different PULSE table rule.Qualify ORIGINAL B even for later codomain changes.

Step identifiers and dependencies

Rule: Function_WHOLE_qualified_total_AtoB_before_SURJECTIVE_claim · Uses: G001, S008

S010 · implies

Before

source roles = [ORIGINAL B, -4, 1, 1]

After

derived = [Yes]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S009

S011 · implies

Before

source roles = [ORIGINAL B, -3, 3, 1]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S010

S012 · implies

Before

source roles = [ORIGINAL B, -2, 5, 1]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S011

S013 · implies

Before

source roles = [ORIGINAL B, -1, 7, 1]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S012

S014 · implies

Before

source roles = [ORIGINAL B, 0, 9, 1]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S013

S015 · implies

Before

source roles = [ORIGINAL B, -4, 1, 3]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S014

S016 · implies

Before

source roles = [ORIGINAL B, -3, 3, 3]

After

derived = [Yes]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S015

S017 · implies

Before

source roles = [ORIGINAL B, -2, 5, 3]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S016

S018 · implies

Before

source roles = [ORIGINAL B, -1, 7, 3]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S017

S019 · implies

Before

source roles = [ORIGINAL B, 0, 9, 3]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S018

S020 · implies

Before

source roles = [ORIGINAL B, -4, 1, 5]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S019

S021 · implies

Before

source roles = [ORIGINAL B, -3, 3, 5]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S020

S022 · implies

Before

source roles = [ORIGINAL B, -2, 5, 5]

After

derived = [Yes]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S021

S023 · implies

Before

source roles = [ORIGINAL B, -1, 7, 5]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S022

S024 · implies

Before

source roles = [ORIGINAL B, 0, 9, 5]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S023

S025 · implies

Before

source roles = [ORIGINAL B, -4, 1, 7]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S024

S026 · implies

Before

source roles = [ORIGINAL B, -3, 3, 7]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S025

S027 · implies

Before

source roles = [ORIGINAL B, -2, 5, 7]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S026

S028 · implies

Before

source roles = [ORIGINAL B, -1, 7, 7]

After

derived = [Yes]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S027

S029 · implies

Before

source roles = [ORIGINAL B, 0, 9, 7]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S028

S030 · implies

Before

source roles = [ORIGINAL B, -4, 1, 9]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S029

S031 · implies

Before

source roles = [ORIGINAL B, -3, 3, 9]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S030

S032 · implies

Before

source roles = [ORIGINAL B, -2, 5, 9]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S031

S033 · implies

Before

source roles = [ORIGINAL B, -1, 7, 9]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S032

S034 · implies

Before

source roles = [ORIGINAL B, 0, 9, 9]

After

derived = [Yes]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S033

S035 · implies

Before

source roles = [ORIGINAL B, -4, 1, 11]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S034

S036 · implies

Before

source roles = [ORIGINAL B, -3, 3, 11]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S035

S037 · implies

Before

source roles = [ORIGINAL B, -2, 5, 11]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S036

S038 · implies

Before

source roles = [ORIGINAL B, -1, 7, 11]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S037

S039 · implies

Before

source roles = [ORIGINAL B, 0, 9, 11]

After

derived = [No]

Conditions: none

Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone.

Step identifiers and dependencies

Rule: Surjective_EVERY_source_target_fiber_comparison · Uses: G001, S038

S040 · implies

Before

source roles = [[-4, -3, -2, -1, 0], [1, 3, 5, 7, 9, 11], [[1, [-4]], [3, [-3]], [5, [-2]], [7, [-1]], [9, [0]], [11, []]]]

After

derived = [[11], No]

Conditions: none

Surjectivity requires a preimage for EVERY declared target;multiple preimages are allowed.For a QUALIFIED empty function,the empty-codomain condition is vacuous.The missing set is B(or B2)minus range,not a replacement of the ORIGINAL codomain.

Step identifiers and dependencies

Rule: Surjective_ALL_codomain_targets_covered_including_EMPTY_vacuity · Uses: G001, S039

Reverse checks

S040 · 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.
S039 · 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.
S038 · 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.
S037 · 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.
S036 · 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.
S035 · 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.
S034 · 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.
S033 · 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.
S032 · 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.
S031 · 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.
S030 · 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.
S029 · 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.
S028 · 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.
S027 · 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.
S026 · 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.
S025 · 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.
S024 · 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.
S023 · 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.
S022 · 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.
S021 · 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.
S020 · 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.
S019 · 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.
S018 · 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.
S017 · 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.
S016 · 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.
S015 · 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.
S014 · 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.
S013 · 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.
S012 · 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.
S011 · 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.
S010 · 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.
S009 · 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.
S008 · 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.
S007 · 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.
S006 · 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.
S005 · 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.
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 — 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.
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

{11}

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: 44a09aa2291fb2594218e148c10984fba57b8bab041e9278c48e5928d20e9670
candidate record SHA-256: 23bb4b2dbada78c636a9d6462a32e935e5ff9826687475a4b432a3c721a9570b
semantic review receipt SHA-256: ccf93c72638d6abf6a412514da5838d55ecb09b71d0e4fdec2b559dc9fdee14b
question-first witness SHA-256: 11af9a338b5a610342b2cfb2ee295683131b3139ac402dd19b1ba1725976d518
Lean: NOT_RUN · human review: NOT_PERFORMED

Same-source full JSON