Use boundary mode=degenerate_interval, a=12, b=12, scale=13, offset=-12. degenerate_interval declares a≥b; jump_at_zero and cusp_at_zero declare a<0<b and nonzero scale, with the named interior defect. Give (mode, a, b, ordered_endpoints, secant_slope_or_null, theorem_applicability, boundary).
G001 — Use boundary mode=degenerate_interval, a=12, b=12, scale=13, offset=-12. degenerate_interval declares a≥b; jump_at_zero and cusp_at_zero declare a<0<b and nonzero scale, with the named interior defect. Give (mode, a, b, ordered_endpoints, secant_slope_or_null, theorem_applicability, boundary).
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.
Retain the historical interface marker and list ordered source fields without JavaScript.MVT fields come from the original mode,without padding or answer-shape inference.Tags and fixed No markers retain their claim scope.
ORIGINAL mode=degenerate_interval,a=12,b=12,scale=13,offset=-12
After
ordered a<b=No;source secant value withheld=null;theorem applicability=No;keep ORIGINAL7-field layout even if reversed endpoints allow an arithmetic quotient
Conditions: none
This theorem declares a<b.Equal endpoints give denominator0;reversed endpoints fail its ordered-interval convention.Keep source null without swapping endpoints or padding to9 fields.This is a scope judgment,not a denial of other formulations.
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
(degenerate_interval, 12, 12, No, null, No, a_less_than_b_and_nonzero_secant_denominator_required)
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.