From finite completed events to an infrared Einstein shadow: exact theorems, no-go boundaries, and gravity evidence in one auditable chain This paper asks a narrow question before writing any continuum field equation: when one completed finite source event funds one reversible Hamiltonian direction, which part of the Hamiltonian is forced by source law, and which part still requires a theorem? The complete natural primitive map is classified as \ R_ (p) = e, 0< 1, A ₒ₈₋₄₍ₓ= (₁-), ₂₇=. \ Thus finite-event provenance fixes one nontrivial Hamiltonian direction, but faithfulness, exhaustivity, and naturality alone do not fix its magnitude. The unit point \ (CH=1\) is isolated as the action-isometry theorem still to be proved. Reversal loops and equal-modular-scalar counterexamples show why endpoint winding or one scalar entropy measure cannot silently replace the path-complete action. The local finite geometry is constructed without choosing a coordinate triad: \ Pₓ=I-Rₓ{2, ₗₘ=PᵧPₓ|₈₌䂲 =Uₗₘ|ₗₘ| }. \ For full-rank overlap, the polar factor \ (Uₗₘ\) is the gauge-natural local connection. Global orientation, cycle holonomy, and a unique metric camera are kept separate rather than inferred from this local result. Finite local generators produce a quantitative quasi-locality statement: \ \|[Aₓ (T), Bᵧ\| C\, \|Aₓ\|\, \|Bᵧ\| \!- (d (x, y) -v ₋ₑ|ₓ|). \] The infrared metric face is then stated with every unclosed transfer collected in one visible remainder: \ G[₆ +₀ ₆_ -8 GA{c⁴T^ src_ = E^ (9) _ }. \] The Einstein equation is recovered on the declared infrared domain when the printed action, orientation, locality, reconstruction, covariance, clock, deformation, boundary, CEAC, and coefficient-transfer defects vanish. Until then, \ (E^ (9) _\) is the theorem ledger, not hidden prose. Empirical and falsification anchors The non-gravitational \ (GF\) route lands at \ (+0. 009416\) from its named comparator, with a central offset of \ (0. 211626\) ppm. The Abell 2744 central comparison is recomputed at \ (0. 5690\%\). The low-acceleration row prints both the full-uncertainty and statistical-only readings. The H1 out-of-sample failure remains printed as a failure. External clean-room replication remains open. Reproducibility receipt Complete inherited Gravity v3-v8 verification chain: PASS. Version 9 checks: 176/176 PASS. Targeted mutation gates: 12/12 detected. PDF render audit: PASS, 170 pages. Stable public anchors Main Book v10. 01: 10. 5281/zenodo. 17527179 Completed-Event Hamiltonian theorem: 10. 5281/zenodo. 21428033 Gravity reference surface: quantumtraction. org/gravity/ QTT Lexicon: quantumtraction. org/lexicon/ Two Universes: quantumtraction. org/two-universes/
Attar Ali (Sat,) studied this question.