{"compile":"2026-10-10","canonical":"https://aaronspradlin.grok.me/wiki/accessibility-curvature","json":"https://aaronspradlin.grok.me/page.json?slug=accessibility-curvature","license":"Source-available for noncommercial research and evaluation only. No commercial, product, platform, or service use without written permission.","scientific_breakthrough":false,"slug":"accessibility-curvature","title":"Accessibility curvature law","dek":"V824: spatial compression of reachable-state accessibility generates conformal, curvature-like scalar structure. Scalar/conformal sector only. Not tensor Einstein.","updated":"2026-05-20","status":"result","claim":"supported","tags":["V824","curvature","conformal","accessibility"],"related":["recoverability","claim-ledger","emergent-gravity","recoverability-framework"],"packages":[{"id":"einstein-phase-1","name":"Einstein Phase 1","path":"Tmp/TOE/Einstein Phase 1","status":"supported"}],"notes":[{"id":"v824-2026-05-20","title":"V824 accessibility-curvature law locked","date":"2026-05-20","xUrl":"https://x.com/aaronspradlin/status/2057148853426794507"}],"claims":[],"text":"Author: Aaron Spradlin. Program: Recoverability Geometry / Accessibility Branch. Version V824, 20 May 2026. The paper asks whether ordered-update recoverability systems naturally generate geometry-like structure. The strongest validated branch was accessibility geometry, not tensor transport.\n\nG_{\\mathrm{proxy}} = 2\\alpha\\,\\Delta\\log(A + \\varepsilon),\\quad A = \\exp(C - \\mu + \\eta\\,\\mathrm{repair})\n\nWith accessibility potential φ = −α log(A+ε) and G_proxy = −2Δφ, the effective conformal factor is Ω = exp(φ), g_eff = Ω² g₀. Held-out R² ≈ 0.879 (mean), correlation ≈ 0.938; compressed operator R² ≈ 0.917; direct perturbation δG R² = 1.000; adversarial nulls next-best ≈ 0.\n\nSupported vs failed branches\n\nSupported: scalar/conformal accessibility-curvature law, Hamiltonian-like scalar closure, conformal geometry via Ω / g_eff.\nNot supported: full tensor Einstein closure, ADM momentum constraints, conserved vector current, physical spacetime interpretation, local PDE evolution law for A. Tensor-branch attempts failed.\n\nRecoverability pressure creates reachable-state density. Spatial compression of log accessibility generates curvature-like scalar structure.","howToCite":"Spradlin, A. (2026-10-10). Accessibility curvature law. Retained Atlas. https://aaronspradlin.grok.me/wiki/accessibility-curvature. Keep claim badge: supported."}