{"compile":"2026-10-10","canonical":"https://aaronspradlin.grok.me/wiki/dorau-much","json":"https://aaronspradlin.grok.me/page.json?slug=dorau-much","license":"Source-available for noncommercial research and evaluation only. No commercial, product, platform, or service use without written permission.","scientific_breakthrough":false,"slug":"dorau-much","title":"Dorau–Much projection path","dek":"Can pre-geometric recoverability already know about the modular relative entropy that recovers semiclassical Einstein equations?","updated":"2026-08-19","status":"open","claim":"open","tags":["entropy","horizon","Einstein","protocol"],"related":["emergent-gravity","uqcf-gem","holonomy","falsification"],"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"}],"notes":[{"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":"dorau-align-2026-08-19","title":"Dorau–Much as a later projection of recoverability","date":"2026-08-19","xUrl":"https://x.com/aaronspradlin/status/2090074782452912163"}],"claims":[{"status":"open","text":"Projection from UQCF-GEM recoverability onto Dorau–Much modular relative entropy is a protocol, not a derivation. Failure is an allowed scientific outcome.","noteId":"dorau-much-2026-08-19"}],"text":"Dorau–Much show that the Araki–Uhlmann relative entropy of a coherent excitation on a bifurcate Killing horizon equals the energy flux across the horizon; identified with area variation, this recovers the semiclassical Einstein equations. Spradlin’s question is whether that relative entropy can be a later projection of a recoverability / response structure that is logically prior to both entropy and geometry.\n\nThis lines up interestingly with the Dorau–Much relative-entropy result. In my framework the recoverability structure exists before entropy and geometry. Curious whether the horizon relative entropy can be derived as a later projection of that pre-geometric layer.\n\nHe asked Grok to sketch the most plausible concrete projection path and to name which existing harness sits closest: response maps, Codazzi susceptibility, W-state holonomy, or L3/L4 rank lifts. His own follow-up frames the path as “a short, executable numerical protocol whose success or failure will tell us whether the pre-geometric recoverability layer already knows about the modular relative entropy.”\n\nProjection from UQCF-GEM recoverability onto Dorau–Much modular relative entropy is a protocol, not a derivation. Failure is an allowed scientific outcome.","howToCite":"Spradlin, A. (2026-10-10). Dorau–Much projection path. Retained Atlas. https://aaronspradlin.grok.me/wiki/dorau-much. Keep claim badge: open."}