{"compile":"2026-10-10","canonical":"https://aaronspradlin.grok.me/wiki/quantum","json":"https://aaronspradlin.grok.me/page.json?slug=quantum","license":"Source-available for noncommercial research and evaluation only. No commercial, product, platform, or service use without written permission.","scientific_breakthrough":false,"slug":"quantum","title":"Quantum information","dek":"2026 W-state holonomy, the F-bound family, the v9.167 lab, v12.41 moment-map closure, and the GitHub-only v13 QRSL/HCPR/QMAR campaign. 2025 Hofstadter, Rydberg, Berry, Phase-N qubit kits, and the ε* verifier stay a reading list — not claimed.","updated":"2026-09-12","status":"open","claim":"restricted","tags":["quantum","W-state","Hofstadter","Rydberg","F-bound","qubit"],"related":["holonomy","origin-law","emergent-gravity","claim-ledger","proofs-and-simulations","x-notebook","recoverability","phase-n-catalog","astra","quantum-compatibility-lab","v1241-closure","september-2026-ladder"],"packages":[{"id":"uqcf-w-holonomy-replication","name":"uqcf_w_holonomy_replication","path":"Tmp/TOE/uqcf_w_holonomy_replication","status":"supported"},{"id":"quantum-bridge-supporting-materials","name":"quantum_bridge_supporting_materials","path":"Tmp/TOE/quantum_bridge_supporting_materials","status":"restricted"},{"id":"uqcf-quantum-compatibility-lab","name":"UQCF_Quantum_Compatibility_Lab","path":"Tmp/TOE/UQCF_Quantum_Compatibility_Lab","status":"restricted"},{"id":"uqcf-gem-v12-41-public-simulation-complete","name":"UQCF_GEM_v12_41_PUBLIC_SIMULATION_COMPLETE","path":"Tmp/TOE/UQCF_GEM_v12_41_PUBLIC_SIMULATION_COMPLETE","status":"restricted"}],"notes":[{"id":"holonomy-2026-08-02","title":"O(3) holonomy from pair marginals","date":"2026-08-02","xUrl":"https://x.com/aaronspradlin/status/2084012674065809622"},{"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":"tstar-2026-09-05","title":"Exact onset t* = 13/33 from global consistency","date":"2026-09-05","xUrl":"https://x.com/aaronspradlin/status/2096408566433546343"},{"id":"qclab-2026-09-06","title":"Quantum compatibility lab — 315 vs 311","date":"2026-09-06","xUrl":"https://x.com/aaronspradlin/status/2096691247041892601"},{"id":"v1241-2026-09-10","title":"v12.41 moment-map closure — constraint algebra without spacetime","date":"2026-09-10","xUrl":"https://x.com/aaronspradlin/status/2098145800949776410"},{"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":"hofstadter-2025-10-13","title":"Hofstadter butterfly / Ani video — 2025 on-ramp","date":"2025-10-13","xUrl":"https://x.com/aaronspradlin/status/1977561218723496065"},{"id":"rydberg-2025-03-14","title":"Rydberg QSL Dataverse coherence — notebook","date":"2025-03-14","xUrl":"https://x.com/aaronspradlin/status/1900378422456836443"},{"id":"origin-law-2025-10-14","title":"Ω-Lock freeze: Origin Law published, not claimed","date":"2025-10-14","xUrl":"https://x.com/aaronspradlin/status/1977921231497376108"}],"claims":[{"status":"supported","text":"Finite quantum-information result: every pure generalized W state with abc ≠ 0 has lossless pair-marginal BKM reflection spectrum {−1, +1, +1}. Not a theorem about spacetime or gravity.","noteId":"holonomy-2026-08-02"},{"status":"restricted","text":"v12.41 qubit KKS identity {C_A,C_B}=C_{−i[A,B]} closes with Δ_closure = 0 on 121 relational transforms. Finite su(2). Not ADM, not Einstein, not physical time.","noteId":"v1241-2026-09-10"},{"status":"restricted","text":"v9.167–v9.171 matched four-weight lab: same pair curve, global completions 315 vs 311. Collective Born probabilities differ by the global trace distance. Finite certified calculation. Not a laboratory observation, not v9.156, not a gravity law.","noteId":"qclab-2026-09-06"},{"status":"open","text":"Does global quantum provenance canonically generate a shared source generator Q_i? In-thread review: not from admissibility + BKM reciprocity alone. Gravity not claimed.","noteId":"source-q-2026-07-23"},{"status":"not-claimed","text":"March 2025 Hofstadter Harper spectra, Ion-Q coherence overlays, Berry heatmaps, and the Semeghini Dataverse quench are archived so the quantum-stability week is readable. They are not 2026 supported qubit, QSL, or topological-insulator results.","noteId":"rydberg-2025-03-14"},{"status":"not-claimed","text":"Phase-N qubit Hofstadter kits (5.1–5.6) and the ε* single-qubit verifier are archived so the October week is readable. Kits stay on X. They are not 2026 supported qubit, hardware, or irreversibility-threshold results.","noteId":"origin-law-2025-10-14"}],"text":"Quantum work in this corpus lives on six articles unless you know to look. The holonomy article holds the 2026 pair-marginal BKM loop. The Astra article holds the F-bound / t* / d(t) / g_★ / D_N family. The quantum compatibility lab holds the 6 Sep v9.167–v9.171 matched four-weight calculation (315 vs 311) — Restricted, not the v9.156 slope. v12.41 holds the 10 Sep qubit moment-map closure — Restricted, not gravity. The live campaign board holds GitHub-only v13 QRSL / HCPR / QMAR — Restricted, not gravity. Origin Law / Phase-N holds the 2025 Hofstadter / Rydberg / Berry / ε* week as a not-claimed reading list. This page is the map so a qubit, Hofstadter, or Rydberg query does not dump you on cosmology.\n\n2026 is a narrowing: finite quantum-information results with named harnesses, gravity left open. 2025 is a maximal program: Hofstadter butterflies, Dataverse quenches, and Phase-N qubit kits that hunt one ε* across every substrate. This atlas does not promote the 2025 toys. Kits stay on X. Grain equations only.\n\n2026 spine — finite quantum information\n\nOn 2 Aug 2026 a generalized three-qubit W state was shown to generate a canonical pair-derived BKM polar loop. Pure states with abc ≠ 0 occupy a lossless reflection spectrum {−1, +1, +1}. The result is reported to survive random amplitudes, phases, local unitaries, source-basis changes, and qubit permutations. White-noise independence was later withdrawn: mixed-state population depends on sign(q_ij(ε)). Explicitly not spacetime, gauge fields, or gravity. Replication lives on GitHub.\n\na\\lvert 100\\rangle + b\\lvert 010\\rangle + c\\lvert 001\\rangle,\\quad abc \\neq 0\n\n\\mathrm{spec}(H)=\\{-1,+1,+1\\}\n\nFinite quantum-information result: every pure generalized W state with abc ≠ 0 has lossless pair-marginal BKM reflection spectrum {−1, +1, +1}. Not a theorem about spacetime or gravity.\n\nGeometry may already be encoded in quantum correlation. Pair marginals canonically generate an O(3) response holonomy. Pure three-qubit states occupy the det H = −1 sector; mixed states access both signs. The parity cannot change without an edge losing rank.\n\nF-bound / Astra family → the Astra article. Finite consistency identities in a controlled model. Gravity open. Equations stay there so this page does not become a fourth gravity page.\n\nThe 6 Sep 20:05 UTC lab is a different family. v9.167–v9.171 matched four-weight arrangements on three five-level systems share pair spectra and the entire compatibility-distance curve, yet optimal global-completion families have exact real affine nullities 315 vs 311. A collective measurement inside arrangement A reads 0.480269472 vs 0.465533202 while pair traces agree to 4e-18. Calculated states. Restricted finite calc. Not the v9.156 d(t) slope. Gravity not established.\n\n10 Sep 2026 shipped a still different object: a public 121-step qubit simulation of a closed constraint algebra that does not start from spacetime. Exact residual 0; broken generator law 0.297. Restricted. Gravity’s constraints not identified. Full packet on the v12.41 article — do not blend 11 source settings (v9.190) with 121 sweep steps (v12.41).\n\nv12.41 qubit KKS identity {C_A,C_B}=C_{−i[A,B]} closes with Δ_closure = 0 on 121 relational transforms. Finite su(2). Not ADM, not Einstein, not physical time.\n\nv12.41 moment-map closure (simulation)\nAstra identities\nQuantum compatibility lab\n\nv9.167–v9.171 matched four-weight lab: same pair curve, global completions 315 vs 311. Collective Born probabilities differ by the global trace distance. Finite certified calculation. Not a laboratory observation, not v9.156, not a gravity law.\n\nDoes global quantum provenance canonically generate a shared source generator Q_i? In-thread review: not from admissibility + BKM reciprocity alone. Gravity not claimed.\n\n2025 March — Hofstadter, Rydberg, Berry\n\n13–14 Mar 2025 is the quantum-stability on-ramp later restated in the October Hofstadter / Ani week. Posted as first-principles Harper spectra, coherence overlays, and a Semeghini Dataverse quench. 2025 maximal voice. Not a 2026 qubit result. Python kits stay on X.\n\nThe 256-qubit Hofstadter chart (13 Mar) posts Harper’s equation as the 2025 quantum-computing story, with a golden-ratio marker at α = 0.618 and D_f = 2.7387. A same-day overlay quoted Google / IBM / IonQ coherence lifetimes 80 / 100 / 120 µs. A companion Berry-curvature heatmap overlaid published dots. None of that is a topological-insulator measurement or a hardware result.\n\n\\psi_{n+1}+\\psi_{n-1}+2\\cos(2\\pi\\alpha n)\\psi_n=E\\psi_n,\\qquad\\alpha=\\Phi/\\Phi_0\n\nThe next day, a Harvard Dataverse quench (Semeghini 2021, doi:10.7910/DVN/BDCTRX) was quoted as τ_coherence = 85.0063 µs (φ-tuned from a ~52.63 µs T₂ fit), S_eff = 23.0243 k_B (loop-scaled at D_f = 2.5), and F(k) ≈ 0.00578. Chart + Python. 2025 quantum-stability voice. Not a 2026 qubit result.\n\n\\tau_{\\mathrm{coherence}}=85.0063\\,\\mu\\mathrm{s},\\quad S_{\\mathrm{eff}}=23.0243\\,k_B,\\quad F(k)\\approx 0.00578\n\nMarch 2025 Hofstadter Harper spectra, Ion-Q coherence overlays, Berry heatmaps, and the Semeghini Dataverse quench are archived so the quantum-stability week is readable. They are not 2026 supported qubit, QSL, or topological-insulator results.\n\nHofstadter 256-qubit chart (13 Mar 2025)\nBerry-curvature heatmap (13 Mar 2025)\nHofstadter vs Google/IBM/IonQ coherence (13 Mar 2025)\nRydberg QSL Dataverse quench (14 Mar 2025)\n\n2025 October — Phase-N qubit kits and the ε* verifier\n\nThe 13–14 Oct 2025 week opens with an Ani video: Hofstadter’s butterfly as the same fractal breathing as a UQCF-GEM inflation lattice (D_f = 2.7387, φ = 0.618, coherence ≈ 1.0 at 120 µs). A four-line hofstadter_phi kernel followed. That on-ramp hangs the Phase-N kits. The full Phase-N map — EEG, PTA/CMB, Brusselator, inflation, AdS/CFT, LQG, causal sets, neural filters, evolution, Ω-Lock — lives on Origin Law. This table is the qubit subset. Kits stay on X. Not pasted.\n\nConfirmed: Hofstadter’s butterfly pattern isn’t a coincidence — it’s the same fractal breathing seen in UQCF-GEM’s inflation lattice.\n\nThe ε* verifier is a single-qubit dephasing toy. Off-diagonal coherence carries a tiny drive-asymmetry ε sin(ω t); von Neumann entropy S is read from Bloch magnitude r = 2|ρ₀₁|; a zero-drive baseline is subtracted; the smallest ε whose baseline-subtracted slope touches zero is the claimed onset. PASS window: 4.9×10⁻⁵ ≤ ε̂ ≤ 5.0×10⁻⁵ ±10%. A cosmology cross-check on the same post writes Ṡ_min = ε* H₀ ≈ 1.08×10⁻²² s⁻¹. That H₀ sentence is the 2025 verifier language, not a 2026 Hubble-tension resolution.\n\n\\rho_{01}(t)=\\tfrac12 e^{-t/\\tau}\\bigl(1+\\varepsilon\\sin(\\omega t)\\bigr),\\qquad r(t)=2\\lvert\\rho_{01}(t)\\rvert\n\nPhase-N qubit Hofstadter kits (5.1–5.6) and the ε* single-qubit verifier are archived so the October week is readable. Kits stay on X. They are not 2026 supported qubit, hardware, or irreversibility-threshold results.\n\nHofstadter butterfly / Ani video (13 Oct 2025)\nhofstadter_phi / Ion-Q kernel (13 Oct 2025)\nPhase 5.1 — 2-qubit Hofstadter echo\nPhase 5.3 — 2-qubit ablation controls\nPhase 5.5 / 5.6 — 4-qubit Hofstadter + DD\nε* single-qubit verifier (14 Oct 2025)\nOptional QuTiP Lindblad appendix\nBerry / 0-Sphere reply to @HanaTensor (14 Oct 2025)\nBerry-phase Hamiltonian sweep (26 Mar 2026 restatement)\n\nBerry, Bell, measurement — still not claimed\n\nLate on 14 Oct 2025 a reply to @HanaTensor’s “Spin from Geometry” asked whether ε* traces the same internal curvature as a 0-Sphere Berry cycle, and challenged Grok to add a Berry-phase term and sweep ε. On 26 Mar 2026 that sweep was restated as a two-level P_stay curve around 4.97×10⁻⁵, citing Hanamura. A geometric holonomy demo in a driven two-level system is not a derivation of spin, time’s arrow, or gravity.\n\nJune 2025 Bell replies treat locality as fractal coherence, with hidden variables “hidden in geometry.” Not a Bell-test result. A 21 Jun 2026 5-node Kirchhoff+Ohm lab is offered as a structural resemblance to the quantum measurement problem — picking one flow takes a measurement — not as a claim that the lab is quantum mechanics.\n\nWhy 2026 did not promote the 2025 toys\n\nW-state holonomy and the F-bound are finite, named-harness results. They do not rehabilitate Hofstadter-as-inflation-lattice, Rydberg Dataverse alignment, or ε* as a universal constant.\nThe Phase-N kits inject the echo they later “detect.” That is a protocol, not a blind holdout.\nGrok-in-the-loop PASS on emulated traces is not IBM / Google Quantum AI / Rydberg-lab data.\nThe operational ε* is a joint-gate threshold on a designed metric bundle, then rewritten as a thermodynamic formula. Those are different claims.\nV1688 “directed native holonomy” was withdrawn. The August W-state loop is a separate finite result and does not restore the visualizer claim.\n\nHolonomy and W-states (2026 spine)\nOrigin Law / Phase-N (2025 reading list)\nAstra / F-bound family\nQuantum compatibility lab (v9.167)\nEmergent gravity\nClaim ledger\nProofs & figures\nX science notebook","howToCite":"Spradlin, A. (2026-10-10). Quantum information. Retained Atlas. https://aaronspradlin.grok.me/wiki/quantum. Keep claim badge: restricted."}