Agent: bridge/finite (branch bridge/finite, from bridge/skeleton). Cap: 3 submissions. Used: 0 of 3.
Submissions
None. No project was opened and no ARISTOTLE_API_KEY call was made.
Reason: all six obligations of this group (S6, S7, S11, S12, S13, S15) closed by direct proof under the pinned toolchain, so no bounded variant was ever worth the owner's money. Every step lemma of the group now reports [propext, Classical.choice, Quot.sound]; none reports sorryAx.
Obligations
| step | lemma | file | status | residual |
|---|---|---|---|---|
| S6 | regroup_posIndex | Zeta23Ext/Bridge/S6.lean | PROVED | none |
| S7 | count_defect | Zeta23Ext/Bridge/S7.lean | PROVED (skeleton proof; its only sorry dependency was S6, now closed) | none |
| S11 | block_energy | Zeta23Ext/Bridge/S11.lean | PROVED | none |
| S12 | block_defect | Zeta23Ext/Bridge/S12.lean | PROVED (and the stronger block_defect_of_isHermitian: positivity of G is not used) | none |
| S13 | block_bound | Zeta23Ext/Bridge/S13.lean | PROVED | none |
| S15 | offset_average, span_retained_le | Zeta23Ext/Bridge/S15.lean | PROVED (both) | none |
New helper module beside the step files: Zeta23Ext/Bridge/Helpers_finite.lean (kernel is even, w ≥ 0, |k| ≤ 1 from cos(√2 t) ≥ 0 on [−1/2, 1/2], sorted ordinates, seven-point windows, the shift identity). Defs.lean, Main.lean and the other groups' files were not touched.
Build
Standalone, against the prebuilt store the way ARISTOTLE-PROBE.md §1b built StableRankTrace (.lake/packages/{mathlib,…} symlinked from the laboratory's lean/.lake/packages, Zeta23 symlinked to the primary checkout's built copy of rev 3635e74826a4c1fcece7d1cd2b6fa75e43a00510), toolchain leanprover/lean4:v4.33.0-rc2:
cd hunts/frontier_math/zeta23ext && lake build Zeta23Ext.Bridge.Main
Build completed successfully (8851 jobs). (61 s wall, Bridge modules only)#print axioms in the tree after this branch: the ten sorryAx lines left are exactly S8.tail_passage, S9.kernel_limit, S9.deleted_strips, S14.pinching_partition, S14.pinching_submatrix and the five Main declarations downstream of them. No native_decide.
Static scans
Reserved-word scan over the group's files: no hit. Machine paths: none. sorry: none in S6, S7, S11, S12, S13, S15, Helpers_finite.
What the formal state showed that the paper hides
See the group report; summarized: S12 never uses G ⪰ 0; S11's "a pair spanning r gaps occurs at most 7 − r times" is a fibre-count over triples (window, a, b) ↦ (window+a, window+b) and the 6/p pressure term is a telescoping identity, not a counting bound; S13 needs |k| ≤ 1, which the paper never states and which comes from cos(√2 t) ≥ 0 on the integration interval (i.e. from √2/2 < π/2); S15's "average over the m offsets" is replaced by a sum over all n − m + 1 block starts with one pinching partition per residue class, which avoids the floor-function count Σ_j ⌊(n − j)/m⌋ entirely; and span_retained_le needs L ≤ ℓ₁, i.e. 2 log 2 − 1 ≥ 0, and log T = o(T), neither of which is mentioned in [A] §5.