Unified Dynamics on Tetrahedral Packet Complexes: Exact Closure, Hodge–Dirac Transport, Branch Dynamics, and Retriangulation
Year: 2026
Type: preprint
Abstract: Unified Dynamics on Tetrahedral Packet Complexes develops a finite relational dynamics on tetrahedral packet complexes while explicitly separating exact combinatorial and operator-theoretic results from downstream physical interpretations. The local carrier is the tetrahedral graph K4 with automorphism group S4 and an opposite-edge parity fiber Θ ≅ F2^3, yielding a symmetry-resolved packet carrier of cardinality 24 × 8 = 192. On the filled tetrahedron and on glued tetrahedral complexes, the manuscript constructs a real skew Hodge–Dirac generator from oriented simplicial boundary maps and derives exact support conservation, single-cell spectral recurrence, invariant adjacent-degree exchange channels, hard transport and closure gates, endogenous Hamming branch projectors, receipt-conditioned affine Θ transport, and relative-frame extraction from oriented one-chain transport. The revised manuscript extends the receipt architecture with address-, frame-, and shell-resolved representations. On the current scoped receipt domain, the shell-resolved connection distinguishes all 44 active receipt labels and all 45 states including null. Constructive no-go results show that endpoint state, pair-address conservation, receipt-index totals, and carrier history do not by themselves determine lineage predecessor provenance. The manuscript also reports separately typed operational correspondence tests using public IBM quantum-error-correction datasets. These tests show that incomplete mid-circuit parity history does not generally determine a terminal residual and that a frozen last-transition predictor transfers across independent IBM backends. These correspondence results are not identified with the K4, Θ, or simplicial-chain carrier and are not treated as same-carrier validation of Unified Dynamics. Open-system extensions distinguish conservative redistribution from contraction and relate the transport Gram defect to complementary Kraus leakage under a unitary dilation. The paper also analyzes local 2↔3 Pachner retriangulation, glued support carriers, B/C dynamical isomorphism, topology-sensitive spectral splitting, and no-go results for finite global recurrence on the analyzed complexes. This release includes the revised peer-review manuscript together with a reproducibility supplement and provenance/hash records. The mathematical results are finite internal-structure statements. No identification with physical spacetime, Standard Model fields, elementary particles, or empirical coupling constants is claimed. Physical promotion remains 0 pending independently closed carrier, constitutive, unit, observable, continuum, and empirical-validation bridges.
Author: Mayes, Benjamin Walker
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208818365
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