{"compile":"2026-10-10","canonical":"https://aaronspradlin.grok.me/wiki/v1541-connection","json":"https://aaronspradlin.grok.me/page.json?slug=v1541-connection","license":"Source-available for noncommercial research and evaluation only. No commercial, product, platform, or service use without written permission.","scientific_breakthrough":false,"slug":"v1541-connection","title":"v15.41 connection / curvature","dek":"GitHub-only research freeze. Connection identifiable. Curvature exactly zero. No curvature–source correspondence. Not Einstein. Not a STATUS gate. scientific_breakthrough: false.","updated":"2026-09-19","status":"result","claim":"restricted","tags":["v15.41","GitHub-only","curvature"],"related":["v1543-geometry","v1542-transport","research-ladder","live-gates","rgcl","projective-obstruction","falsification","protein-closeout"],"packages":[{"id":"uqcf-gem-v13","name":"ResearchHistory/UQCF-GEM (v13–v14)","path":"ResearchHistory/UQCF-GEM","status":"restricted"}],"notes":[{"id":"v1541-2026-09-19","title":"v15.41 connection identifiable; no curvature–source correspondence","date":"2026-09-19","xUrl":""}],"claims":[{"id":"atlas:v15-41","status":"restricted","text":"v15.41: CONNECTION_IDENTIFIABLE_NO_CURVATURE_SOURCE_CORRESPONDENCE. Finite sizes L=5,7,9,11. Cartan rank = augmented rank (50, 98, 162, 242). Nullity 0. Curvature exactly zero on the complete source orbit. Correspondence false. 80 cells. Conditional on frozen v15.39 axioms and v15.40 operational metric. GitHub-only 19–20 Sep. scientific_breakthrough: false.","noteId":"v1541-2026-09-19"}],"text":"Lives on research/v15.41-formal-connection-curvature-source-correspondence. Main STATUS.md freeze remains v15.03 NO_CERTIFIED_GRAPH_SITE_FACTORIZATION. No X field note. Do not invent one. Pillar 3 OPEN.\n\nv15.41: CONNECTION_IDENTIFIABLE_NO_CURVATURE_SOURCE_CORRESPONDENCE. Finite sizes L=5,7,9,11. Cartan rank = augmented rank (50, 98, 162, 242). Nullity 0. Curvature exactly zero on the complete source orbit. Correspondence false. 80 cells. Conditional on frozen v15.39 axioms and v15.40 operational metric. GitHub-only 19–20 Sep. scientific_breakthrough: false.\n\nThe mechanically differentiated holonomy is exactly zero on the complete source orbit, so its centered contraction cannot equal α_L s_f for any required nonzero α_L. Connection is identifiable; curvature–source correspondence fails. Inherited control families do not pass the complete gate. Asymmetric scrambles fail correspondence.\n\nWhat this does not show\n\nA physical affine connection, spacetime curvature, or stress-energy law.\nA continuum result, Newtonian limit, or Einstein dynamics.\nA main-branch STATUS gate. Cite STATUS.md for current science.\n\nImmediate prior gates (same research line)\n\nv15.40 CANONICAL_INCIDENCE_GEOMETRY_SPECIFICITY_SURVIVES — global-balance response recovers B2 face-neighbor at L=5,7,9,11; four controls fail. Not a physical metric.\nv15.39 higher-incidence source axioms — supplied axioms this correspondence is conditional on.\nNext in this line: v15.42 transport certified, then v15.43 nonzero canonical response curvature with source correspondence NOT_EVALUATED.\n\nv15.41 demo folder\nv15.43 response geometry\nv15.42 transport\nResearch ladder through v15.45\nSTATUS.md (main, v15.03)\nLive gates","howToCite":"Spradlin, A. (2026-10-10). v15.41 connection / curvature. Retained Atlas. https://aaronspradlin.grok.me/wiki/v1541-connection. Keep claim badge: restricted."}