{ "researchProgram": [ "TRQC™", "Timeline-Relative Quantum Collapse™" ], "provider": "Jake Young", "study": "002", "version": "0.3.0", "generatedAtUTC": "2026-10-14T00:49:57.611572+00:00", "protocolSHA256": "04fc24b8812069e6a05b0dc3e00df6444461f21793f80419abb7a412a2161dc9", "graphCount": 23, "caseCount": 920, "comparisonProtocol": { "researchProgram": [ "TRQC™", "Timeline-Relative Quantum Collapse™" ], "provider": "Jake Young", "study": "002", "title": "Network sensitivity of C001 admission", "recordDate": "2026-10-13", "question": "Does the same smoothness-based admission principle retain a localized, approximately Gaussian position expression when relational connectivity changes?", "definitionStatus": "Design and metrics specified before the first computation in this study; not an externally preregistered protocol.", "fixed": { "vertices": 256, "generator": "H = 0.5 L, with L = D - W", "admission": "K = exp(-beta L)", "complement": "R = sqrt(I - K squared)", "positionMap": "x(j) = j - 128, held fixed across study graphs", "preparations": [ "concentrated pulse at vertex 128", "normalized Gaussian of width 8 and zero phase gradient" ], "selectivities": [ 8, 32, 64, 128 ], "evolutionParameters": [ 0, 20, 40, 60, 80 ] }, "families": [ { "id": "cycle2", "graphs": 1, "edges": "periodic nearest-neighbor links, weight 1", "role": "original reference" }, { "id": "path2", "graphs": 1, "edges": "open nearest-neighbor chain, weight 1", "role": "boundary control; endpoint weighted degree differs" }, { "id": "local4", "graphs": 1, "edges": "periodic links to +/-1 and +/-2, weight 0.5", "role": "local connectivity change; weighted degree remains 2" }, { "id": "rewire4", "graphs": 5, "acceptedSwaps": 4, "edges": "degree-preserving swaps of local4, all weights 0.5" }, { "id": "rewire16", "graphs": 5, "acceptedSwaps": 16, "edges": "degree-preserving swaps of local4, all weights 0.5" }, { "id": "rewire64", "graphs": 5, "acceptedSwaps": 64, "edges": "degree-preserving swaps of local4, all weights 0.5" }, { "id": "rewire1024", "graphs": 5, "acceptedSwaps": 1024, "edges": "strongly mixed degree-preserving local4 network, all weights 0.5" } ], "randomSeeds": [ 20261013, 20261014, 20261015, 20261016, 20261017 ], "displayRepresentative": "First predetermined seed, never selected from best or worst outcome.", "metrics": [ "raw expressed and unexpressed weights and conservation error", "conditional center and spread under the held-fixed position map", "total variation distance to the cycle2 candidate with identical preparation, beta, and evolution", "total variation distance to a Gaussian matched to the candidate's own center and spread", "conditional weight outside |x| <= 32", "conditional weight at |x| >= 110", "conditional probability concentration (sum p squared)", "candidate relational mismatch per unit expressed weight" ], "interpretation": "Report continuous metrics and seed ranges. No invented universal success threshold. Gaussian matching is a shape diagnostic, not a refitted physical prediction. Conserved weights and commutation follow from supplied mathematics.", "limitations": [ "The chosen position map is held fixed rather than derived or adapted to each graph.", "Changing topology changes the supplied Hamiltonian through L, as well as the admission operator; compare with the all-mode baseline on each graph to separate their roles.", "Normalizing weighted degree does not keep the full spectrum or effective dispersion fixed.", "Five graph seeds measure this limited construction's variability, not a population confidence interval or physical ensemble.", "The protocol does not test electron properties, geometry emergence, or the truth of TRQC." ] }, "summaryPreset": { "preparation": "pulse", "beta": 64, "time": 80 }, "summary": [ { "family": "cycle2", "graphs": 1, "candidateSpread": { "min": 9.424754715842287, "median": 9.424754715842287, "max": 9.424754715842287 }, "candidateGaussianShapeTV": { "min": 2.8051426207241815e-05, "median": 2.8051426207241815e-05, "max": 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"underlyingAmplitudeError": 4.166262659787999e-15, "expressedAmplitudeError": 6.623941136388575e-16 }, { "graph": "rewire64_20261013", "underlyingAmplitudeError": 4.331155357769344e-15, "expressedAmplitudeError": 4.0868391122441234e-17 }, { "graph": "rewire1024_20261013", "underlyingAmplitudeError": 2.904173721638398e-15, "expressedAmplitudeError": 3.125146532508076e-17 } ], "allNumericalChecksPassed": true, "scientificInterpretation": "Topology and held-fixed map sensitivity; numerical checks do not establish TRQC or intrinsic admission." }