v1.2.0-candidate — exact two-item independent-cap gap

v1.2.0-candidate — exact two-item independent-cap gap

Status: unrefereed candidate computer-assisted result offered for scrutiny.

This additive release preserves the exact two-item certification and guaranteed-termination results from v1.1.0 and closes the extension's sharply declared two-item question:

Gamma_(2,box) = gamma, where

1.111889593939396 < gamma < 1.111889593940297

and gamma is the relevant real root of

262 g^4 - 916 g^3 + 863 g^2 + 150 g - 375 = 0.

The matching upper proof uses a symbolic critical interval and an exact 212-cell rational outer certificate; a separate 2,829-cell certificate provides a coarser cross-check. Floating-point optimization was used only for discovery, not verification.

Replay evidence

• exact archive SHA-256: a1103de05bf1793119fd005d4685e161aca8aafcb6fea71e67f63f6fb0a82b13
• source commit: b31ef2c15dcf184638c1b3d9f0730c12a8ed54cf
• fresh-extraction full reproduction: passed
• exact manifest: 92 entries, passed
• test suite: 17 passed
• ordinary and python -O release gates: passed
• re-hashed semantic mutations: rejected as intended

Scope boundary

The exact equality is for two items with independent frequency caps and nonnegative real coefficients. It is not a proof of the unrestricted multi-item relaxation gap. Multi-item equality, alignment-aware relaxation and rounding, the column-sparsity frontier, a three-item oracle, and operational field validation remain open.

The evidence is producer-side only. There has been no independent reproduction, formal verification, specialist human review, peer review, field validation, or complete novelty/priority audit.

Persistent identifier

• Version DOI: 10.5281/zenodo.21855894
• Concept DOI: 10.5281/zenodo.21855566

Software is MIT licensed. Original non-software contents are dedicated under CC0-1.0 to the extent the publisher holds the relevant rights; see LICENSE_SCOPE.md.

v1.1.0 candidate — exact two-item resource-constrained JRP

Status

Unrefereed candidate computer-assisted result offered for scrutiny.

This release supplies exact fixed-ratio optimisation, a resource-aware tail theorem, guaranteed finite termination for the stated two-item model, a real-coefficient cap-reduction lemma, and an exact algebraic relaxation-gap family with lower bound approximately 1.11188959394.

The archive passed producer-side fresh-extraction replay with solver-independent verifiers, mutation and fail-closed controls, 16 tests, and deterministic PDF/figure rebuilds. This is not independent reproduction, formal verification, human peer review, field validation, novelty certification, or evidence of operational benefit.

The exact global gap, multi-item alignment/rounding, sparsity frontier, three-item oracle, robust uncertainty, calendar extensions, and field validation remain open. See docs/EXTENSION_REQUIREMENTS.md and the producer adversarial review.

Integrity

• Commit: b7df3fb1b8b1f87d335952f22ba1389e98402b6f
• Release ZIP SHA-256: 5d3dd5fa39787c5b1461da12db83810c36eede33a3b595a953422998dfb2ed6a
• Original non-software contents: CC0-1.0, to the extent the publisher holds the relevant rights
• Software: MIT