Source and priority ledger — global meridian-index detector

Inspected 8 September 2026. Only primary mathematical sources are used. No author contact, endorsement, or external review is implied. Primary full texts are not redistributed in this archive.

Contents

Formal external inputs

Source	Exact inspected location	Role and limitation
Stavros Garoufalidis, The 3D index of an ideal triangulation and angle structures	arXiv:1208.1663v2, Definition 3.1, Section 4.5; also Definitions 2.1–2.3 and Theorem 2.4	Source for the DGG tetrahedron-index formula and recurrence. Index structures and strict angle convergence are established prior art. Its general index theorem is not imported as an all-root, all-input native filling theorem.
Stavros Garoufalidis, Craig Hodgson, Neil Hoffman, Hyam Rubinstein, The 3D-index and normal surfaces	arXiv:1604.02688v1, Section 2, equations (4)–(7)	Symmetric $J_\Delta$ , translation, exact degree and nonzero leading coefficient. Equation (7) in this version is the degree formula; the quadratic identity is (8). GY’s later paper cites a differently numbered published degree equation. The $q$ -degree is doubled to obtain $q^{1/2}$ -degree.
Stavros Garoufalidis and Tao Yu, The 3d-index of the 3d-skein module via the quantum trace map	author PDF dated 6 August 2025, Section 5.1, (47)–(49); Section 5.2, (59)–(63); Definition 5.2, (67); full proof of Theorem 5.3	The closest methodological input: ambient quantum-trace lattice averaging, all-input degree estimates, and mixed-sided descent. Its stated even-target/homology restrictions are not dropped by citation. The note separately proves descent for the full root lattice and actual edge-plus-meridian character. This author version is not represented as arXiv v2; the arXiv record still lists v1.

Prior-art and scope checks

Daniele Celoria, Craig D. Hodgson and J. Hyam Rubinstein, The 3D index and Dehn filling, arXiv:2509.09886v2, revised 19 December 2025: the introduction, Theorem 6.2 and adjacent scope discussion were checked after first inspecting v1. Theorem 6.2 uses at least two original torus boundary components, a standard cusp and 1-efficiency of the specified triangulations before and after filling. It supplies important prior rigorous surgery work, not a comparison or nonzero-value theorem for the present functional. Its computational tables and triangulation searches are not used.

The construction of the tetrahedron index is due to Dimofte–Gaiotto–Gukov; their priority is acknowledged through the above primary mathematical treatments. This note makes no first-construction claim for a 3D index, an adjoint index solution, or a surgery index. No comprehensive novelty search or author-confirmed priority assessment was performed.

Retained FPRD dependencies

The native six-root presentation, additive named meridian and longitude, isotropy, and collar dictionary are retained from six-root-peripheral-attack/. The isomorphism between the intrinsic filled target and $\operatorname{coker}(m+A^2)$ , with vacuum image $1-l^2$ , is retained from the generic-boundary packet. The exact CK Laurent-target source-reading caveat remains unchanged. No new named-trace comparison or peripheral-sign argument is attempted.

The clean-excess packet is used only to delimit the failed point-local route. The new global proof does not use its local deformation theorem as a nonvanishing input. The positive-geometric theorem remains an independent earlier conditional result, including its separate vacuum test.

Working-copy hashes

The following retained PDFs were inspected locally. Hashes identify those working copies, not canonical publisher checksums.

GY-index, author version dated 6 August 2025, gy-index-author-2025.pdf: SHA-256 fe39f211f0d223bc452833f657730576802a0f5a3b0543844618c76c1e6c121d.
GY quantum-trace published source retained for the native-presentation dependency, gy-published-2026.pdf: SHA-256 0b7c6ffe350d0c625d27fdd6ee4795969e8f649918fe6611e170e52483d8af59.

The fresh arXiv HTML inspections are version-pinned in source-snapshots.json. No local-byte hash is claimed for a page that was inspected through the public rendering but not downloaded as a local file.

What is proved within the note

The all-root seed extension, full actual character average, exact all-input valuation transformation, affine Dickson argument, weak-angle compactness estimate, null-ray necessity for unordered convergence, and leading-unit detection are proved in the note. The quadratic/skew positivity device and the lattice-average strategy closely follow the established GY/GHHR method and are credited accordingly. The elementary Dickson and compactness steps need no specialized theorem beyond what is explained there.

The exact verifier audits formulas and conventions, not the literature’s all-orders theorems. It performs no topological enumeration and establishes no invariant-comparison or filled-vacuum result.