| # Source ledger |
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| ## User-supplied lineage |
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| The original AHFM text supplies the phase-Hessian, connection/holonomy, and design-Hessian motivation. Its scalar-curvature issue is explicitly corrected; its acoustic or perceptual claims are not used as established physics. |
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| CHEONBAEK–Omega NEXIFORM, Section 12, supplies the loop-holonomy/common-fixed-vector interface. Selective Naturality Geometry v3, Theorem 10.6, supplies exact projection and rigidity-gap reasoning. Chronological Reserve Geometry v1, Results 12–13, supplies the distinction between exact and approximate spectral width. Only these mechanisms are imported, and the needed arguments are proved again in the manuscript. |
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| No previous user manuscript is redistributed. Their references in the bibliography identify provenance rather than create circular dependencies. |
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| ## Public primary literature checked |
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| - Vekhter, Chen, and Vouga, *Mint: Discretely Integrable Moments for Symmetric Frame Fields*, 2025, DOI 10.1111/cgf.70193. Publisher text and author project page checked. The relevant distinctions are local integrability, moment representations, and regular-frame smoothness. This release does not assert that Mint already supplies every global hypothesis. |
| - Kolda, *Symmetric Orthogonal Tensor Decomposition is Trivial*, arXiv:1503.01375. The whitening/contraction/eigenproblem idea is prior art; no first-in-history claim is made for it. |
| - Anandkumar et al., *Tensor Decompositions for Learning Latent Variable Models*, JMLR 15(80), 2014. Prior tensor-learning and whitening framework. |
| - Beben, *Topology of Frame Field Design for Hex Meshing*, arXiv:2011.05276. Important prior binary-octahedral rotational-topology work; not claimed as implemented here. |
| - Braune et al., *A Discrete Exterior Calculus of Bundle-valued Forms*, arXiv:2406.05383. Prior bundle-valued discrete calculus. No continuum convergence claim is transferred to this code. |
| - Brückler, Bommes, and Campen, *Volume Parametrization Quantization for Hexahedral Meshing*, 2022, DOI 10.1145/3528223.3530123. |
| - Brückler et al., *Volume Quantization with Flexible Singularities for Hexahedral Meshing*, 2026, DOI 10.1111/cgf.70349. These quantization works motivate why integral periods alone do not establish all required map/feature constraints. |
| - Lipman, *Bijective Mappings of Meshes with Boundary and the Degree in Mesh Processing*, DOI 10.1137/130939754. Prior global inversion context. The manuscript's convex-reference result is proved directly by monotonicity. |
| - SymPy 1.14.0 normal-form documentation and installed source. Smith transformations are independently checked by exact identities and unimodularity in every computation. |
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| The date of this review is 5 October 2026. This is a targeted prior-art check, not an exhaustive worldwide novelty audit. Citations do not imply author endorsement of AHTI. |
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| ## New deductions versus established ingredients |
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| The thirteen-point deterministic reconstruction witness, the regular moment-coordinate pullback metric, the full-noise repair identity coupled to a geometric tetrahedral metric, the boundary Schur-lattice formulation, and the geometry-validity/global-optimality certificate are derived and proved in this release. They are presented as deductions and an integrated formulation, not as certified world-first results. |
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