Randomized trial develops a framework for gravity's allocation of completed events, highlighting implications for action payments.
One completed event, many records: which action was actually paid? This reference framework develops a finite source account of gravity in which laboratory geometry is a downstream readout of completed capacity events. The Version 8 theorem isolates the bookkeeping problem that precedes a physical Hamiltonian magnitude: several records may descend from one funded event, while identical visible labels may descend from different events. The provenance-complete funding quotient is \[ { PE = RE / NEᶠᵘⁿᵈ, PE_0=1 }. \] Thus one completed primitive event carries one funded source direction even when it produces several typed receipts. Representational subdivision cannot mint another action payment, and a second payment requires a second completed event token. The unique path-complete projective action on the reversible primitive sector is \[ { aTV[H] = ∫_0t_A { osc}\!( PₚᵣᵢₘH(T)Pₚᵣᵢₘ )\,dT }. \] This valuation is invariant under common energy shifts, basis changes, legal refinement, and concatenation. Unlike endpoint phase alone, it assigns positive action to a retraced internal history. The theorem leaves one exact source gate: \[ { Rspec(1)=1 Aₛᵢₗₑₙₜ=0 C_H=1 }. \] Here the silent-action residual is \[ Aₛᵢₗₑₙₜ = - ∫_0t_A { osc}\!( PₚᵣᵢₘH(T)Pₚᵣᵢₘ )\,dT. \] The quotient and projective valuation are closed on the declared primitive class. The source-history/eigenchannel intertwiner and the vanishing of \( Aₛᵢₗₑₙₜ\) remain the precise open theorem; consequently unconditional CEAC and \(C_H=1\) are not assumed. Reproducibility receipt Complete inherited Gravity v7 verification chain: PASS. Version 8 finite checks: 318/318 PASS. Targeted mutation gates: 15/15 detected. PDF render audit: PASS, 157 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/
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Attar Ali (2026) studied this question.
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