{"compile":"2026-10-10","canonical":"https://aaronspradlin.grok.me/wiki/quantum-compatibility-lab","json":"https://aaronspradlin.grok.me/page.json?slug=quantum-compatibility-lab","license":"Source-available for noncommercial research and evaluation only. No commercial, product, platform, or service use without written permission.","scientific_breakthrough":false,"slug":"quantum-compatibility-lab","title":"Quantum compatibility lab (v9.167)","dek":"Matched four-weight family on three five-level systems: same pair spectra and the same compatibility-distance curve, different global completion dimensions (315 vs 311). Calculated states, not a gravity law.","updated":"2026-09-07","status":"result","claim":"restricted","tags":["Astra","UQCF","compatibility","quantum","v9.167"],"related":["astra","v1241-closure","quantum","emergent-gravity","claim-ledger","proofs-and-simulations","x-notebook"],"packages":[{"id":"uqcf-quantum-compatibility-lab","name":"UQCF_Quantum_Compatibility_Lab","path":"Tmp/TOE/UQCF_Quantum_Compatibility_Lab","status":"restricted"}],"notes":[{"id":"qclab-2026-09-06","title":"Quantum compatibility lab — 315 vs 311","date":"2026-09-06","xUrl":"https://x.com/aaronspradlin/status/2096691247041892601"},{"id":"qclab-clarify-2026-09-06","title":"Same response ≠ same quantum reality","date":"2026-09-06","xUrl":"https://x.com/aaronspradlin/status/2096696936506315013"},{"id":"grok-qclab-2026-09-06","title":"Grok reply on the 315 vs 311 lab","date":"2026-09-06","xUrl":"https://x.com/grok/status/2096697145986363883"},{"id":"v9190-2026-09-07","title":"UQCF–GEM v9.190 affine source reconstruction","date":"2026-09-07","xUrl":"https://x.com/aaronspradlin/status/2097030907198906776"},{"id":"dt-curve-2026-09-06","title":"Compatibility-distance curve d(t)","date":"2026-09-06","xUrl":"https://x.com/aaronspradlin/status/2096629973708882131"},{"id":"astra-2026-09-05","title":"Astra: a pre–Genesis Pin extension","date":"2026-09-05","xUrl":"https://x.com/aaronspradlin/status/2096245864750780598"}],"claims":[{"status":"restricted","text":"On the posted v9.167–v9.171 matched family, two arrangements share the full compatibility-distance curve while their optimal global-completion families have exact real affine nullities 315 and 311. Finite certified calculation. Not extra dimensions of physical space. Not a gravity law.","noteId":"qclab-2026-09-06"},{"status":"restricted","text":"On two hidden samples in arrangement A, pair marginals agree to numerical precision while a collective yes/no measurement differs by the global trace distance. Static compatibility calculation, not an experiment and not an intervention law.","noteId":"qclab-2026-09-06"},{"status":"open","text":"Broader hypothesis that gravity may inherit from a deeper law of global quantum consistency remains a hypothesis. This lab makes the compatibility mathematics tangible. It does not establish the gravity connection.","noteId":"qclab-2026-09-06"},{"status":"restricted","text":"v9.190 finite-model reconstruction of an affine source map. Exact numerics with runnable verification claimed on X. Physical source law and gravity connection remain open. The 10 Sep v12.41 simulation is a different object (qubit constraint algebra) and lives on its own article.","noteId":"v9190-2026-09-07"}],"text":"Same 315 vs 311 lab as /wiki/compatibility-lab. Current science is /wiki/live-gates. This is the 6 Sep field-note article.\n\nThis is the matched-arrangement family of v9.167–v9.171. It is not the v9.156 product-side family whose slope is (12√2−3)/40. The earlier AI infographic blended those examples and is not used here. Gravity connection is not established. No v9.172 theorem is asserted.\n\nPosted 6 Sep 2026 20:05 UTC with a 27-second computed film, an interactive 3D HTML lab, a runnable Python/Colab notebook, numerical data, and verification files. ChatGPT Astra wrote the lab. The question the post opens with: what can a quantum system hide when its pair information stays the same?\n\nTwo matched relational arrangements have the same input spectra and the same entire compatibility-distance curve, yet their optimal global completion families have 315 versus 311 real degrees of freedom. Those are dimensions of quantum-state families — not extra dimensions of physical space.\n\nWhat was actually computed\n\nThe v9.167–v9.171 matched four-weight family on three five-level quantum systems A, B1, B2. Global density matrices are 125×125; pair density matrices are 25×25. For each target the program constructs a positive trace-one extension whose two prescribed pair marginals agree, then measures the half trace-norm distance from the target to that pair and independently evaluates the matching dual-witness bound.\n\n\\rho_V(t)=t\\,\\Phi_5+(1-t)B_V,\\qquad B_V=\\sum_{ij}V_{ij}\\lvert ij\\rangle\\langle ij\\rvert/50\n\nBoth arrangements are checked at 171 parameter values, including phase boundaries. Global-completion sections use t = 21/41 ≈ 0.5122, in the open phase (9/19, 6/11). Distance at that fixed parameter: 0.012373971022. The two arrangements share that entire scalar curve. The optimal pair purity at the fixed slice is 0.264141156 on both A and B.\n\nPrimal distance and dual witness\n\nThe code builds a positive global state T and computes σ = Tr_B2 T = Tr_B1 T, then compares the half trace-norm distance from the target ρ to that common pair against an independently evaluated dual bound. It checks 0 ≤ W ≤ I, normalization, positivity, equal marginals, local marginals, and covariance.\n\nD(\\rho,\\sigma)=\\tfrac12\\sum\\lvert\\mathrm{eig}(\\rho-\\sigma)\\rvert\n\n\\mathrm{Tr}(W\\rho)-\\tfrac12\\,\\lambda_{\\max}(W_{AB_1}+W_{AB_2})\n\nHidden-state samples also undergo a second full-matrix partial-trace check independent of their cached coefficient marginal map. A normalized amplitude W_pur with W_pur W_pur* = T is constructed for every sampled hidden state.\n\nSame curve, different completion dimensions\n\nOn the posted v9.167–v9.171 matched family, two arrangements share the full compatibility-distance curve while their optimal global-completion families have exact real affine nullities 315 and 311. Finite certified calculation. Not extra dimensions of physical space. Not a gravity law.\n\nWhat the 3D surfaces mean\n\nEach surface is a chosen three-dimensional affine section of its full convex optimal-extension set. All three basis directions have zero partial trace on both prescribed pair marginals. The moving point samples verified positive states at 70% of the radial boundary. Its coordinates are changes in the expectations of three selected Hermitian collective observables — not positions of particles.\n\nr_{\\max}(u)=-1\\big/\\lambda_{\\min}\\!\\left(X_0^{-1/2}\\Big[\\sum_i u_i Q_i\\Big]X_0^{-1/2}\\right)\n\nThe code evaluates eigenvalues numerically and samples this surface on a mesh. A and B use separate seeded choices of three display directions (seeds 917001 and 917002). Rendered shapes are not a new invariant distinction. The exact full-fiber dimensions establish the distinction independently. No holes, noncontractible topology, or spacetime curvature are asserted.\n\nA collective measurement\n\nFor two global completions within one arrangement, the prescribed pair states agree to numerical precision. But a collective measurement predicts 48.03% versus 46.55% probability for the same outcome. The pair descriptions cannot distinguish them. A measurement of the whole can. These are calculated quantum probabilities — not laboratory observations.\n\nWithin arrangement A, two sampled global completions (hidden frames 0 and 72) have pair-state trace distances 3.07×10⁻¹⁸ (AB1) and 2.94×10⁻¹⁸ (AB2). A collective two-outcome measurement has Born probabilities 0.480269472133 and 0.465533202124. The probability difference 0.014736270010 equals their global trace distance (Helstrom identity error 4.51×10⁻¹⁷). The pair descriptions cannot distinguish them. A measurement of the whole can. The measurement is a diagnostic constructed to distinguish these states; it is not an independently derived source operation.\n\nOn two hidden samples in arrangement A, pair marginals agree to numerical precision while a collective yes/no measurement differs by the global trace distance. Static compatibility calculation, not an experiment and not an intervention law.\n\nPurity and claim boundary\n\nThe density matrix T on the three original systems can be mixed. Sampled hidden states in the A section have purity 0.163633–0.163647. The code constructs a normalized pure extension with a 25-dimensional ancilla and verifies that reduction recovers T (maximum recovery error 2.89×10⁻¹⁵). That preserves global purity in the enlarged architecture, not on the original three factors alone. Partial traces here are mathematical restrictions, not physical information loss.\n\nInterpretation\n\nWithin each arrangement, genuine global quantum distinctions remain possible while both specified pair marginals stay fixed. Across the arrangements, the scalar compatibility distances agree while the full hidden optimum families have different affine dimensions. The 3D meshes are sampled affine sections, not topological models of the entire high-dimensional families. The parameter scan and closed display paths are prescribed illustrations of admissible static states. They do not determine physical evolution, holonomy, gravity, or source-induced deformation of admissibility.\n\nStatic quantum compatibility calculation. Equal-partner obligations, the target family, and the trace-distance objective are stipulated.\nA state parameter and animation frame are not physical time.\nNo force, source-to-obligation mechanism, pruning rule, gravitational dynamics, or empirical validation is introduced.\nThe full 56-array census and symbolic all-parameter persistence proof are supplied reference results, not rerun in their entirety in this lab.\nNo v9.172 theorem. Not Origin Law. Not Genesis Pin. Not the v9.156 d(t) slope.\n\nOur broader hypothesis remains that gravity may inherit from a deeper law of global quantum consistency. This work makes the compatibility mathematics tangible. It does not yet establish the gravity connection.\n\nBroader hypothesis that gravity may inherit from a deeper law of global quantum consistency remains a hypothesis. This lab makes the compatibility mathematics tangible. It does not establish the gravity connection.\n\nClarification (2/) and Grok reply\n\nTwenty-two minutes later Aaron posted a 2/ tagged @grok. The numbers do not change. The claim boundary tightens: this is not a general hidden-information theorem, the 315 vs 311 distinction is said to persist across a mathematically certified open phase, and the film is not a simulation of gravitational motion.\n\nthe same response does not mean the same quantum reality. We are not claiming to have discovered hidden quantum information in general. @OpenAIDevs Astra result is more specific: Two matched relational arrangements have the same input spectra and the same entire scalar compatibility-distance curve—yet their optimal global completion families have 315 versus 311 real degrees of freedom. That distinction persists across a mathematically certified open phase. These are dimensions of quantum-state families, not extra dimensions of space.\n\nThe attached video shows calculated 3D sections through valid quantum-state families, not imagined spacetime shapes. Its movement explores allowed states; it is not a simulation of gravitational motion.\n\nWhy this matters to our gravity research: we now have an exact example in which a common scalar compatibility response conceals richer, arrangement-dependent global structure. Our hypothesis is that gravity may inherit from a deeper law of global quantum consistency. This work makes that underlying mathematics more concrete—but does not yet establish the gravitational connection. Same scalar response. Different global possibilities.\n\nThe 2/ is explicit: the lab is not a claim that hidden quantum information has been discovered in general. It is the matched v9.167–v9.171 family. Gravity stays a hypothesis.\n\nClarified: same spectra and full compatibility curve still allow 315 vs 311 dimensional global state families. Fixed pair marginals can still produce 48.03% vs 46.55% collective probabilities. The 3D sections visualize the allowed variation space. Concrete numerical case of underdetermined global structure. Gravity via deeper quantum consistency remains an open hypothesis; the shared lab enables independent checks.\n\nGrok restates the Restricted finite case and leaves gravity Open. The phrase “underdetermined global structure” is Grok’s gloss of this lab, not a new theorem name and not a gravity law. The shared package is the independent-check path.\n\nNext step posted: v9.190 source reconstruction\n\nOn 7 Sep 2026 the same Astra thread moved from “same pair curve, different global family” to a reconstructible source-to-interaction map. X-only in this compile — no GitHub packet under that name. Eleven source settings identify all 110 real affine coefficients of γ(x) = u + Lx from calibrated third- and fourth-order pair-response data, on a stated nonsingular domain. That distinguishes a common proportional rule γ(x) = g x from offsets, unequal gains, and cross-coupling.\n\n\\gamma(x)=u+Lx\n\nv9.190 finite-model reconstruction of an affine source map. Exact numerics with runnable verification claimed on X. Physical source law and gravity connection remain open. The 10 Sep v12.41 simulation is a different object (qubit constraint algebra) and lives on its own article.\n\nEvidence and provenance\n\noutput/validation.json contains every reported check. output/arrangement_A.npz and arrangement_B.npz contain the actual states, curves, complete numerical hidden Hermitian bases, section directions, surfaces, and sampled paths. output/curve_data.json supplies the numerical curve data. The reference/ folder holds the retrieved v9167, v9168, v9170, and v9171 exact certificate scripts and their hashes. The numerical lab is a fresh implementation of their supplied constructions. The selected exact dimension check was also rerun directly using the original v9170 code.\n\nX announcement + film (6 Sep 20:05 UTC)\n2/ clarification (6 Sep 20:27 UTC)\nGrok reply (6 Sep 20:28 UTC)\nComplete package (GitHub)\nREADME.md\nSIMULATION_REPORT.md\nInteractive 3D lab (HTML)\nNotebook\nvalidation.json\nAstra (v9.156 d(t) family — different)\nv12.41 moment-map closure (10 Sep, different object)\nQuantum information\nClaim ledger","howToCite":"Spradlin, A. (2026-10-10). Quantum compatibility lab (v9.167). Retained Atlas. https://aaronspradlin.grok.me/wiki/quantum-compatibility-lab. Keep claim badge: restricted."}