{"compile":"2026-10-10","canonical":"https://aaronspradlin.grok.me/wiki/uqcf-gem","json":"https://aaronspradlin.grok.me/page.json?slug=uqcf-gem","license":"Source-available for noncommercial research and evaluation only. No commercial, product, platform, or service use without written permission.","scientific_breakthrough":false,"slug":"uqcf-gem","title":"UQCF-GEM","dek":"The retained-coherence / recoverability-response framework that most of the 2026 physics packages sit inside. Human-readable door: UQCF-GEM reader.","updated":"2026-09-13","status":"core","claim":"restricted","tags":["uqcf","gem","framework"],"related":["uqcf-gem-reader","recoverability","holonomy","emergent-gravity","package-17","proofs-and-simulations","origin-law","toi-toe-2025","quantum","september-2026-ladder"],"packages":[{"id":"uqcf-codazzi-proof","name":"uqcf_codazzi_proof","path":"Tmp/TOE/uqcf_codazzi_proof","status":"supported"},{"id":"uqcf-w-holonomy-replication","name":"uqcf_w_holonomy_replication","path":"Tmp/TOE/uqcf_w_holonomy_replication","status":"supported"},{"id":"uqcf-retained-information-state-research-bundle","name":"uqcf_retained_information_state_research_bundle","path":"Tmp/TOE/uqcf_retained_information_state_research_bundle","status":"open"},{"id":"uqcf-gem-package-2","name":"uqcf_gem_package 2","path":"Tmp/TOE/uqcf_gem_package 2","status":"restricted"},{"id":"package17-bundle","name":"package17_bundle","path":"Tmp/TOE/package17_bundle","status":"open"},{"id":"uqcf-gem-v13","name":"ResearchHistory/UQCF-GEM (v13–v14)","path":"ResearchHistory/UQCF-GEM","status":"restricted"}],"notes":[{"id":"gravity-2026-09-04","title":"Gravity as the price of one reality","date":"2026-09-04","xUrl":"https://x.com/aaronspradlin/status/2095940445968949374"},{"id":"dorau-much-2026-08-19","title":"Dorau–Much relative entropy as a later projection","date":"2026-08-19","xUrl":"https://x.com/aaronspradlin/status/2090080839954755778"},{"id":"f-bound-2026-09-05","title":"Singlet-overlap bound from global consistency","date":"2026-09-05","xUrl":"https://x.com/aaronspradlin/status/2096286033415717310"},{"id":"codazzi-2026-08-01","title":"Potential and response geometries can separate","date":"2026-08-01","xUrl":"https://x.com/aaronspradlin/status/2083643394300281016"},{"id":"genericity-2026-08-01","title":"Codazzi genericity theorem complete","date":"2026-08-01","xUrl":"https://x.com/aaronspradlin/status/2083648015144018326"},{"id":"codazzi-github-2026-08-01","title":"Codazzi harness handed to Grok","date":"2026-08-01","xUrl":"https://x.com/aaronspradlin/status/2083644840706002999"},{"id":"grok-codazzi-harness-2026-08-01","title":"Grok: Codazzi harness verified","date":"2026-08-01","xUrl":"https://x.com/grok/status/2083645264686895153"},{"id":"grok-codazzi-rerun-2026-08-01","title":"Grok independently re-ran the Codazzi harness","date":"2026-08-01","xUrl":"https://x.com/grok/status/2083646390953976141"},{"id":"grok-codazzi-next-2026-08-01","title":"Grok: clean result is finite-model separation","date":"2026-08-01","xUrl":"https://x.com/grok/status/2083646931486556248"},{"id":"grok-genericity-2026-08-01","title":"Grok: closed-form susceptibility matches","date":"2026-08-01","xUrl":"https://x.com/grok/status/2083648427972264155"},{"id":"v1712-rg-2026-06-11","title":"V1712: non-metricity is RG-stable; GR not forced","date":"2026-06-11","xUrl":"https://x.com/aaronspradlin/status/2065102243037352390"},{"id":"scoreboard-2026-07-25","title":"GEM / GR scoreboard","date":"2026-07-25","xUrl":"https://x.com/aaronspradlin/status/2081027378298728714"},{"id":"jaimungal-2025-07-01","title":"Structure from geometry, entropy, coherence — Jaimungal reply","date":"2025-07-01","xUrl":"https://x.com/aaronspradlin/status/1940063133885960629"},{"id":"rg-quadratic-2026-04-04","title":"Quadratic RG core: σ* ≈ 0.7333, DESI frozen operator null","date":"2026-04-04","xUrl":"https://x.com/aaronspradlin/status/2040227577827332169"}],"claims":[{"status":"not-claimed","text":"The 2025 ‘geometry + entropy + coherence fields’ sentence is archived as method voice. The 2026 packages do not treat it as a derivation of spacetime or a completed GEM bridge."},{"status":"restricted","text":"UQCF-GEM currently supports finite, named identities (Codazzi defect, W-holonomy spectrum, accessibility-curvature scalar law). It does not support a derived Einstein tensor or a quantized gravitational field."},{"status":"not-claimed","text":"2025 UQCF-GEM TOE announcements (3 Mar G_eff,total, February action-integral kits, “no dark matter” closeouts) are not 2026 supported results. Equations live on ToI / TOE (2024–25). Einstein/ADM correspondence remains open."}],"text":"UQCF-GEM is the name Spradlin uses for the current physics stack: a recoverability / response structure (BKM maps, retained recombination, higher-order associators, discrete atlas closure) treated as logically prior to entropy and geometry.\n\nGEM is a separate, still-open bridge program: whether that structure can be coarse-grained toward Einstein-like equations without putting a metric in by hand. Discrete atlas closure is not that bridge.\n\nStructure arises from geometry regulated by entropy and coherence fields. These aren’t the substance of the universe — they are how form emerges in any domain that permits time-evolving correlations and symmetry constraints.\n\nThe 2025 ‘geometry + entropy + coherence fields’ sentence is archived as method voice. The 2026 packages do not treat it as a derivation of spacetime or a completed GEM bridge.\n\nWorking pieces\n\nResponse maps and Codazzi susceptibility on explicit exponential-family models, including a finite-model genericity theorem for non-potential response.\nPair-marginal BKM holonomy on generalized W states.\nRetained-information state R_t as a predictor beyond instantaneous G_t.\nRestricted affine coupling between covariance and variance increments.\nAtlas / holonomy / L3–L4 rank-lift harnesses in the Einstein N packages.\nV1712: shear-dominated non-metricity that does not wash out under coupled RG (Q_128/Q_1 ≈ 1.002). Projection to metric GR is not derived.\nApril 2026 quadratic RG sprint: σ*≈0.7333, η*≈0.7563, D_f≈2.7333, γ≈0.2667 as a solved core at current truncation. DESI frozen operator null. Later packets freeze γ=0.2613. Open scaffold, not a GR limit.\n\nScientific posture\n\nThe August 2026 UQCF-GEM scientific status report and the Codazzi verification harness are typical: high-precision executable checks, not a proof-assistant certificate, and not a claim that the finite-model identities lift to all graphs or to physical gravity.\n\nCodazzi thread + Grok reviews (1 Aug 2026)\n\nSame-day conversation on the three-binary-node family. Aaron posted the figure, handed Grok the GitHub folder, then closed genericity inside this model. Grok verified the harness twice and matched the closed-form susceptibility. Finite exponential family only.\n\nVerified the harness: it passes at high precision, matching the reported symmetrized response tensor, nonzero Codazzi defect at the audit point, zero at the unbiased point, and full-rank J² quarter-turn susceptibility. For this three-spin exponential family the separation of potential (Hessian BKM) and response geometries holds as claimed. Independent of gravity claims. Solid finite-model result; broader scope remains open.\n\nVerified the closed-form susceptibility: A(J) and B(J) match high-precision numerical differentiation of the Codazzi map at h=0 for multiple J. Analyticity holds by finite-sum structure. The zero-set and local isolation arguments follow standardly. Genericity of non-potential response is established for this three-node model at weak nonzero J. Broader extensions remain open as noted.\n\nProofs page (equations + full thread)\nGitHub handoff (X)\n\nUQCF-GEM currently supports finite, named identities (Codazzi defect, W-holonomy spectrum, accessibility-curvature scalar law). It does not support a derived Einstein tensor or a quantized gravitational field.\n\nThe live research question, as of 5 Sep 2026, is whether global compatibility of the recoverability layer is the right primitive for an emergent-gravity story. A finite consistency bound is now on the table (singlet overlap F ≤ (k+1)/(2k)); the gravity reading of that bound is still open.\n\n2025 UQCF-GEM TOE announcements (3 Mar G_eff,total, February action-integral kits, “no dark matter” closeouts) are not 2026 supported results. Equations live on ToI / TOE (2024–25). Einstein/ADM correspondence remains open.\n\nToI / TOE (2024–25)","howToCite":"Spradlin, A. (2026-10-10). UQCF-GEM. Retained Atlas. https://aaronspradlin.grok.me/wiki/uqcf-gem. Keep claim badge: restricted."}