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R0013-07170 · q-20261011-advance-20261015-r05-sequence-0070
N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[7, 0, 7, 1] and candidate nexts=[19, -18]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.
G001 — N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[7, 0, 7, 1] and candidate nexts=[19, -18]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.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.
Before
N starts at0;ordered finite indices and repeated values retained
After
given recurrences differ from guessing an infinite rule from observations
Conditions: none
Sequences are ordered and may repeat.A finite observed prefix alone does not determine a unique infinite rule;when a recurrence is explicitly supplied,use that rule rather than inventing one.
Rule: finite_ordered_sequence_scope · Uses: G001
Before
original prefix=[7, 0, 7, 1];candidate next=19
After
[7, 0, 7, 1, 19]
Conditions: none
The first candidate appends only its own fifth term,leaving the original prefix unchanged.
Rule: first_given_sequence_extension · Uses: G001, S001
Before
original prefix=[7, 0, 7, 1];candidate next=-18
After
[7, 0, 7, 1, -18]
Conditions: none
The second candidate appends afresh to the original prefix,not to the first candidate.
Rule: second_given_sequence_extension · Uses: G001, S002
Before
same prefix=Yes;nexts=(19,-18)
After
same fifth term=No
Conditions: none
The same prefix may have different proposed next terms,so the first four do not select a unique one.If the candidates coincide,do not call them distinct extensions.
Rule: finite_extensions_not_unique_rule · Uses: G001, S003
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.([7, 0, 7, 1, 19], [7, 0, 7, 1, -18], Yes, No)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 7305c965ce5ee305c5dd6c27c92cdef3737c5168d7b756b996fec024c2cab351candidate record SHA-256: ec2eaacd33febb74db0ca555031a01ddb0f9c1dc3767dc2b3ababf54570c37a3semantic review receipt SHA-256: e89fc6d4a50a4a7fc942c6c8939a92f835e30105a9a5850e37dd198f31c1ed59question-first witness SHA-256: 0e1039f4cf022bf35af4e5531651c9a2b7ca7a5fdacac34fb1e4bcd9a81f6299Lean: NOT_RUN · human review: NOT_PERFORMED