Directional Anisotropy Gravity — Technical Supplement

This document is the proof-audit companion to Directional Anisotropy Gravity (DOI 10.5281/zenodo.20397188). Every central claim of the core paper is restated here in its exact form and is followed by a full proof, an explicit assumption ledger, and an entry in the master dependency tree. The intended reader is the one who wishes to verify the core paper independently — by checking, theorem by theorem, that nothing is asserted there which is not closed here from: — the eight stated postulates P.1–P.8 (six substrate postulates and two substrate-to-geometry bridges);— two structural closure rules: the minimum-EFT scalar closure for the substrate clock variable, and the open-system Born–Markov reduction with channel-projector dephasing;— one empirical boundary condition imported from observed dark-sector phenomenology: flat rotation curves at large radius, used to fix the deep-memory exponent of the AQUAL-class transport equation;— one controlled approximation: the leading-order Nakajima–Zwanzig ordering of the memory transport. All four are labelled at point of use. No new theory content is introduced; the supplement reproduces statements and supplies proofs. Quantitative residuals and longer-horizon open items are catalogued separately in the programme sourcebook (DOI 10.5281/zenodo.20071356). The supplement is organised as a sequence of proofs ordered by dependency. An early section fixes the assumption ledger and the master dependency table. The substrate, gravitational, dark-sector, Standard-Model, and electromagnetic theorems of the core paper are then proved in that order. A cross-reference map at the end links each theorem statement here back to its appearance in the core paper, and forward into the corresponding section of the v12.2 programme sourcebook. Each theorem appears in the same form as in the core paper, with the same statement; only the proof is added here. Where a result depends on a result proved further down in the supplement, the proof says so and the dependency is also recorded in the dependency table. Companion documents in the DAG public set:— Core paper (DOI 10.5281/zenodo.20397188): the theorem statements proved here.— Predictions, SPARC Verification, and Operational Tests (DOI 10.5281/zenodo.20397375): the operational distillation and SPARC test for observational researchers.— Programme sourcebook v12.2 (DOI 10.5281/zenodo.20071356): the full research programme, where open items and quantitative residuals live.