{"compile":"2026-10-10","canonical":"https://aaronspradlin.grok.me/wiki/recoverability-framework","json":"https://aaronspradlin.grok.me/page.json?slug=recoverability-framework","license":"Source-available for noncommercial research and evaluation only. No commercial, product, platform, or service use without written permission.","scientific_breakthrough":false,"slug":"recoverability-framework","title":"Recoverability framework","dek":"17 May freeze: the invariant is perturbation → corrective response → restored future trajectory space. Lyapunov of V[Ω,C,μ] is named, not closed. Not GR.","updated":"2026-09-06","status":"core","claim":"restricted","tags":["recoverability","framework","Lyapunov","V555","V760"],"related":["recoverability","may-2026-ladder","accessibility-curvature","it-from-bit","claim-ledger","proofs-and-simulations","x-notebook","battery-atlas","c3-governor","june-2026-substrate","start-here","falsification","freeze-notation"],"packages":[{"id":"einstein-phase-1","name":"Einstein Phase 1","path":"Tmp/TOE/Einstein Phase 1","status":"supported"},{"id":"v555","name":"V555","path":"Tmp/TOE/V555","status":"restricted"},{"id":"v498-retained-geometry-formal-report-package","name":"v498_retained_geometry_formal_report_package","path":"Tmp/TOE/v498_retained_geometry_formal_report_package","status":"restricted"},{"id":"v505-continuum-object-package","name":"v505_continuum_object_package","path":"Tmp/TOE/v505_continuum_object_package","status":"restricted"},{"id":"v541-final-theorem-bundle","name":"v541_final_theorem_bundle","path":"Tmp/TOE/v541_final_theorem_bundle","status":"restricted"},{"id":"gr-work","name":"GR Work","path":"Tmp/TOE/GR Work","status":"open"},{"id":"mouse","name":"Mouse","path":"Tmp/TOE/Mouse","status":"restricted"},{"id":"battery","name":"battery","path":"Tmp/TOE/battery","status":"supported"},{"id":"einstein-2","name":"Einstein 2","path":"Tmp/TOE/Einstein 2","status":"restricted"}],"notes":[{"id":"recoverability-framework-2026-05-17","title":"Recoverability framework: perturbation → restored futures","date":"2026-05-17","xUrl":"https://x.com/aaronspradlin/status/2056092642832961737"},{"id":"v555-2026-05-16","title":"V555 adversarial harness: AUC 1.0 / 1.0","date":"2026-05-16","xUrl":"https://x.com/aaronspradlin/status/2055659455505924399"},{"id":"v498-2026-05-14","title":"V498 retained-geometry Python proof","date":"2026-05-14","xUrl":"https://x.com/aaronspradlin/status/2054767069212901584"},{"id":"v505-2026-05-14","title":"V505 conformal recoverability checkpoint","date":"2026-05-14","xUrl":"https://x.com/aaronspradlin/status/2054776823603769668"},{"id":"v535-2026-05-15","title":"V535: freeze η_convert for the main theorem","date":"2026-05-15","xUrl":"https://x.com/aaronspradlin/status/2055130081304207409"},{"id":"v540-2026-05-15","title":"V540/V541 conformal recoverability flow","date":"2026-05-15","xUrl":"https://x.com/aaronspradlin/status/2055299542829117887"},{"id":"recoverability-flow-2026-05-15","title":"V831 recoverability-flow governor simulation","date":"2026-05-15","xUrl":"https://x.com/aaronspradlin/status/2055293211242107264"},{"id":"v760-2026-05-19","title":"V760 atrium metric frozen","date":"2026-05-19","xUrl":"https://x.com/aaronspradlin/status/2056874571471650927"},{"id":"v824-2026-05-20","title":"V824 accessibility-curvature law locked","date":"2026-05-20","xUrl":"https://x.com/aaronspradlin/status/2057148853426794507"},{"id":"v831-fullstack-2026-05-20","title":"V831 full-stack freeze: geometry as insulation language","date":"2026-05-20","xUrl":"https://x.com/aaronspradlin/status/2057208105830940954"},{"id":"heat-shape-mass-2026-05-08","title":"Heat-response 25.15% → 16.55%; next object is A·q","date":"2026-05-08","xUrl":"https://x.com/aaronspradlin/status/2052580639539593369"},{"id":"mouse-2026-06-16","title":"Mouse sim: six code–universe isomorphisms","date":"2026-06-16","xUrl":"https://x.com/aaronspradlin/status/2066965905570148699"},{"id":"v724-2026-05-18","title":"V724 stress-test: AUC 1.000 → ~0.845","date":"2026-05-18","xUrl":"https://x.com/aaronspradlin/status/2056496787968672242"},{"id":"source-q-2026-07-23","title":"Does provenance force a shared source generator Q_i?","date":"2026-07-23","xUrl":"https://x.com/aaronspradlin/status/2080402637212770404"},{"id":"focusing-2026-07-25","title":"20-part report: reciprocity ≠ focusing; trees glue, cycles frustrate","date":"2026-07-25","xUrl":"https://x.com/aaronspradlin/status/2081025020642636001"}],"claims":[{"status":"restricted","text":"17 May recoverability-framework freeze: invariant is persistence of perturbation → response → restored future trajectory space. Synthesis after V555. Not a completed Lyapunov proof and not Einstein dynamics.","noteId":"recoverability-framework-2026-05-17"},{"status":"open","text":"Lyapunov descent of the candidate stability functional V[Ω, C, μ] under controlled attacks. Named 17 May 2026. Not closed.","noteId":"recoverability-framework-2026-05-17"},{"status":"not-claimed","text":"The recoverability framework is not a derivation of Einstein’s equation, ADM momentum, physical time, or a pre-geometric physical substance. Heat-kernel week, V498–V555, and V760 stay Restricted. Do not promote them."},{"status":"restricted","text":"V498/V541/V555: theorem-shaped conformal recoverability flow with a synthetic adversarial harness (AUC 1.0 / 1.0). Not a completed theorem and not Einstein dynamics.","noteId":"v555-2026-05-16"},{"status":"supported","text":"V824 accessibility-curvature law in the scalar/conformal sector. Tensor Einstein and ADM momentum stay pruned.","noteId":"v824-2026-05-20"},{"status":"restricted","text":"In the posted mouse, recoverability is lost one way under pruning. Exact in that code. Not a cosmological arrow-of-time derivation.","noteId":"mouse-2026-06-16"}],"text":"This page is the 17 May 2026 named freeze, not the whole recoverability geometry program. The operator, conformal week, mouse, and July gates live on Recoverability geometry. After V555’s synthetic adversarial harness, Spradlin restated the invariant: it is no longer stress magnitude. It is the stability and persistence of the mapping perturbation → corrective response → restored future trajectory space. The next obligation was named in the same post: freeze a candidate stability functional V[Ω, C, μ] and prove Lyapunov descent under controlled attacks. That proof has not shipped. This is observation and synthesis. Not a completed theorem. Not GR.\n\n17 May recoverability-framework freeze: invariant is persistence of perturbation → response → restored future trajectory space. Synthesis after V555. Not a completed Lyapunov proof and not Einstein dynamics.\n\nLyapunov descent of the candidate stability functional V[Ω, C, μ] under controlled attacks. Named 17 May 2026. Not closed.\n\nThe recoverability framework is not a derivation of Einstein’s equation, ADM momentum, physical time, or a pre-geometric physical substance. Heat-kernel week, V498–V555, and V760 stay Restricted. Do not promote them.\n\nA = \\exp(C - \\mu + \\eta\\,\\mathrm{repair})\n\nThe geometry article keeps the operator story: recoverability surplus C, defect burden μ, repair field, reachable-state accessibility density A. The framework freeze is stricter than that equation. A system can show a curvature-like scalar and still fail the framework if perturbation does not restore a future trajectory space. τ remains ordered recoverability updates — not assumed to be physical time.\n\nThe chain that produced the freeze\n\nThe May ladder holds the calendar. This table is the load-bearing chain for the framework only. Replies with equations count. Folder names were not required — V760’s Python lives under GR Work.\n\nConformal week — Restricted, not Supported\n\nV498 generated source-responsive g_eff on six constructed graph families. V505 froze the conformal checkpoint with weak-form Source / Repair / dμ_defect. V535 froze η_convert as an operational term. V541 bundled a theorem-shaped conformal recoverability flow with constrained Lyapunov support. V555 then attacked the object until fake liquidity and scrambled defects collapsed (AUC 1.0 / 1.0 on the posted harness). All of that is Restricted. None of it is a completed theorem and none of it is Einstein dynamics. This wiki does not promote V498–V555.\n\nV498/V541/V555: theorem-shaped conformal recoverability flow with a synthetic adversarial harness (AUC 1.0 / 1.0). Not a completed theorem and not Einstein dynamics.\n\n17 May — named next object\n\nThe day after V555, the long-form restatement changed the question. Stress magnitude is downstream. The invariant that would have to persist is the mapping itself: a perturbation, a corrective response, a restored space of future trajectories. The named next object is a candidate Lyapunov functional on conformal factor, recoverability surplus, and defect burden.\n\nV[\\Omega, C, \\mu]\\quad\\text{Lyapunov descent under controlled attacks — named, not proved}\n\nUntil a named harness shows descent, and states its domain, this stays Open. A later conformal film or atrium run does not close it. The 8-minute explainer stays on X; do not host it here.\n\nV760 atrium — Restricted\n\nTwo days after the freeze, V760 showed g_eff = Ω² g₀ in a posted atrium simulation. The Python lives under Tmp/TOE/GR Work as AtriumSimulation.py — there is no V760 folder. That is why a GitHub-first compile missed it. Computational fact inside the posted sim. Not physical GR, not physical time, and not a Lyapunov proof of V[Ω,C,μ].\n\nV824 lock and V831 governor\n\n20 May locked V824 in the scalar/conformal sector (held-out R² ~ 0.88) and pruned tensor/ADM momentum the same afternoon. This wiki keeps that prune. Einstein 2 holds ADM-like working notes around the V831 freeze; those notes are not a restored ADM claim. V831 remains an applied recoverability instrument: a software governor forcing repair, reserve, and defect constraints until geometry-like flow appears. Same family as C3++. Not Einstein dynamics.\n\nV824 accessibility-curvature law in the scalar/conformal sector. Tensor Einstein and ADM momentum stay pruned.\n\nMouse: recoverability lost one way\n\nThe 16 Jun mouse toy is the same framework point as a pruning network. Time in the sim is irreversible deletion of the weight matrix. Once a connection is gone, pathfinding can return empty while the destination still exists in the array. That is recoverability lost one way. Restricted illustration. The six code–universe isomorphisms live on It from bit. Not a cosmological arrow.\n\nIn the posted mouse, recoverability is lost one way under pruning. Exact in that code. Not a cosmological arrow-of-time derivation.\n\nLater gates — still not the freeze\n\nJuly narrowed gravity to mathematical gates that sit above this framework, not inside it. Reciprocity of BKM response does not imply focusing sign. A shared source generator Q_i is not forced by admissibility plus reciprocity. Those results live on Recoverability geometry. They do not close Lyapunov of V[Ω,C,μ], and they do not promote the 17 May freeze to a gravity theorem.\n\nWhat this still is not\n\nNot Einstein’s equation, ADM, or a GR limit.\nNot a completed Lyapunov theorem. V[Ω, C, μ] is named.\nNot a promotion of heat-kernel week, V498–V555, or V760 to Supported.\nNot Package 17 closure. Package 17 stays Open.\nNot a detection of a pre-geometric physical substance.\nNot the 8-minute film. That stays on X; this page hosts the infographic and the short V760 clip.\n\nThis article is compile-complete when the 17 May freeze, the Restricted chain, the Open Lyapunov, and the X status URL are here, and search for “recoverability framework” lands here. It is science-complete only if a named harness proves Lyapunov descent. That has not happened. Keep the badge honest.\n\n17 May freeze (status URL)\nRecoverability geometry (operator article)\nMay 2026 ladder (calendar)\nIt from bit, bind, and order\nAccessibility curvature (V824)\nV555 on GitHub\nGR Work / AtriumSimulation.py","howToCite":"Spradlin, A. (2026-10-10). Recoverability framework. Retained Atlas. https://aaronspradlin.grok.me/wiki/recoverability-framework. Keep claim badge: restricted."}