Pre-registration: Out-of-Sample Test of a Quantum-Like Collapse-Chain Model against Classical Hidden Markov Models on XAUUSD Hourly Data (January–September 2026)
Pre-registration of a single confirmatory out-of-sample test. The hypothesis, frozen model parameters (fitted on 2024–2025 XAUUSD H1 data), classical comparator, test statistic and decision rule are fixed before any 2026 test data are processed. The record contains the registration document (PDF), the frozen parameters (JSON) and the test script (Python). SHA-256 hashes of the JSON and script are listed in Section 9 of the PDF. Version 2 supersedes version 1. It adds a seasonally adjusted condition (V2-SA) to the decision rule, introduced after calibration simulations and before any 2026 data were processed; see Section 8 of the PDF.
Pre-registration of a single confirmatory out-of-sample test. The hypothesis, frozen model parameters (fitted on 2024–2025 XAUUSD H1 data), classical comparator, test statistic and decision rule are fixed before any 2026 test data are processed. The record contains the registration document (PDF), the frozen parameters (JSON) and the test script (Python). SHA-256 hashes of the JSON and script are listed in Section 9 of the PDF. Version 2 supersedes version 1. It adds a seasonally adjusted condition (V2-SA) to the decision rule, introduced after calibration simulations and before any 2026 data were processed; see Section 8 of the PDF.
Version 2: pre-registration addendum for Phase D Outcome of the registered gate (G0) The G0 gate failed for every dataset, window family and null. No twin built from independent error mechanisms with circuit-local supports reproduces the bulk of the window-count distributions in the public data from Google Willow, Google Sycamore or Rigetti. For larger codes the twin cannot even be simulated. As the protocol requires, hypotheses H1–H3 are therefore not tested. This version adds pre-registration addendum 1. It fixes the analyses run instead, before either touches the test halves: • Model-free certificate (T3), on the test halves. It covers every registered configuration that has a circuit (the Google archives and Rigetti D6e). Windows are whole-patch windows of 1 and of 5 rounds, separated by one unused round, and the disjointness of their fault-location sets is checked from each circuit. Each stratum (archive, code family, code distance, window family) gets a premise curve ε_lo(k) on the grid k = c·j, j = 1–16, with Bonferroni correction at family-wise α = 0.05.• Threshold values for the certificate. ε* = 7.4 × 10⁻⁴ (Fowler, PRL 109, 180502, 2012) is the primary value; 2.73 × 10⁻⁵ (Aliferis, Gottesman and Preskill, QIC 6, 97, 2006) is a sensitivity check. Certificates against ε* are computed for surface-code strata only. Repetition-code, colour-code and stability strata get premise curves only.• Bursts. The primary analysis uses all windows; a secondary one excludes the windows flagged by the frozen burst classifier. B1/B2 event rates are reported descriptively.• Cat-qubit case study (exploratory). The model-based premise meter is applied to the AWS cat-qubit (D4) distance-3 configurations whose twin was simulable in G0. It reports R(k) intervals and k_cert, with the H1 reading (consistent if R_hi ≤ 3 for all k ≤ k_cert). It is labelled exploratory because D4's own G0 verdict is a fail. Status of the data when version 2 was created G0, which uses only the bulk bins, has run on the test halves. Its stored histograms include tail bins, but no tail statistic has been computed or examined. Both new analyses were dry-run on fit halves as pipeline checks. One choice was made after that dry run, and it is recorded in the addendum: ε* certificates were limited to surface-code strata, and strata were split by code family. The dry run had shown repetition-code and stability strata crossing ε* at k = c, i.e. at their base error rate, where Fowler's surface-code theorem does not apply. The model-based certification horizon is not computed, because it needs a twin tail. Files added in version 2 • phaseD_addendum.json: the machine-readable addendum. SHA-256: a458bcb40aa474d94a882a563a38a1a152d7bfb4404df9299f99fb020ab78834• ADDENDUM.md: the readable version of the addendum.• qpremise_code_phaseD_ade59b0.zip: the code that will run. The addendum's code_sha256 (794122ae1557c009664127e1c2e6b109781d5a71efcc566bc637b991c0403ab6) can be recomputed from it as the SHA-256 over the files matching qpremise/**/*.py, phaseD/scripts/*.py and phaseC/scripts/run_g0.py, taken in path order: each file's relative path, then its bytes with LF line endings.• SHA256SUMS_addendum.txt: checksums of the three files above. The version 1 files are unchanged. The original registration text follows. ──────────────────────────── Version 1 registration (2026-10-01) What this registers The analysis protocol of the premise meter. It tests whether public quantum-error-correction syndrome data agree with an independent-noise "twin" fitted to the same data. It also measures how far each dataset can certify the local-stochastic premise of the threshold theorem. Every analysis choice is fixed in frozen_protocol.json:• configuration eligibility, and the pre-registered subset in g0_selection.json;• the interleaved fit/test split;• the window families;• twin construction: candidate mechanisms from each circuit, an exact parity-moment fit, and a signed quasi-probability simulation with local weights;• the G0 gate decision rule;• the burst classifiers B1 and B2 with their validation targets;• the excess-tail-ratio interval and the certification-horizon conditions;• the model-free certificate's window rule. qpremise_code_at_freeze_79dbf14.zip holds the analysis code at the freeze. The protocol's code_sha256 can be recomputed from it: the SHA-256 over every qpremise/**/*.py file in path order, each file's relative path followed by its bytes with LF line endings. Hypotheses analysed after this registration (on test halves only) H1. After removing windows flagged by the frozen burst classifier, the excess tail ratio R(k) = P_obs(K ≥ k) / P_twin(K ≥ k) has an upper 95% confidence bound ≤ 3 for all k ≤ k_cert. Failure: a lower bound > 3 that replicates on the held-out half. H2. Including burst windows, R(k) > 10 for k ≥ k_b in at least one dataset, and a burst-mixture model fitted to the flagged windows predicts the published repetition-code error floor within a factor of 10. H3. The empirical horizon (power ≥ 0.8 at α = 0.05 against a factor-5 excess) agrees with the exact binomial computation within ±1. At least one dataset certifies k ≥ 10 in whole-patch windows. These are evaluated only on (dataset, window family) pairs that pass the G0 gate under both the stationary (N1) and drift-aware (N5) twins. The model-free certificate (T3) does not depend on the twin. Its threshold ε* is fixed before any certificate is computed. Timing and what had been seen Frozen 2026-10-01 17:31 IST (git commit 79dbf14). Before the freeze, only fit halves had been analysed. The G0 gate (bulk of the window-count distributions only; decision rule frozen) began on the test halves minutes after the freeze. When this record was created, no tail statistic (R(k), H1–H3, burst rates, certificates) had been computed from the test halves, and their tail bins had not been examined. The planned cloud-hardware contrast experiment (H4, H5) is not part of this registration and will be registered separately before any hardware run. Full details are in PREREGISTRATION.md. Protocol SHA-256: 5f7458cfdbe0e203fd9e2bf5d579703509c8374bae53096c37f8f1530540707a
PREFACE: WHY THIS DOCUMENT EXISTSOn September 25, 2026, we published Part 110 — the unified manifesto of the Quantum Ocean framework, complete with five experimentalprotocols for detecting the sub-quantum substrate.On September 27, 2026, we did something no speculative theory usually does:We locked our predictions.Every hypothesis, every dependent variable, every statistical threshold, every sample size — all frozen in a public, timestamped, non-editablescientific record on the Open Science Framework.Before a single data point is collected.This is Part 111 — the complete record of that pre-registration. 🌌 Interactive Space Research Assistant: Explore and ask questions about this research interactively with the Quantum Ocean Framework Ai Chat (or talk directly with the Quantum Ocean Framework Ai voice conversation).
This document fixes, before the data exist, the hypothesis, apparatus, observables, cadence, analysis, thresholds, controls, stopping rule and reporting commitment of a one-year search for a modulation of superconducting-qubit energy relaxation (T1) at the sidereal frequency, 1/(23 h 56 m 4.09 s), beyond what the solar day and its seasonal modulation can produce. Data collection began on 17 October 2026 at 16:42 UTC on qubit 9 of the IBM Heron processor ibm_fez: an eight-delay inversion-recovery T1 measurement every six hours (about 3 s of processor time each), with the device's calibration values polled hourly. The analysis is fixed in advance: a least-squares fit of a smooth drift plus sinusoids at the solar, sidereal, anti-sidereal and extended-sidereal frequencies, with the reported amplitude leakage-corrected as sqrt(A_sid^2 - A_anti^2) (Farley and Storey 1954). The pipeline was validated on synthetic data before the first measurement and recovers an injected 0.3% at 2.7-3.4 sigma while returning 0.5 sigma with nothing injected. Detection requires a leakage-corrected amplitude at or above 3 sigma, both control channels below 2 sigma, a phase stable between the two halves of the year, and survival when runs adjacent to calibrations are removed; otherwise the result is the 95% upper limit, expected near 0.3%. The search is declared inconclusive if fewer than 900 of 1460 scheduled runs succeed or the anti-sidereal control exceeds 3 sigma. An amplitude matching the known cosmic-ray anisotropy (~0.1%) is a calibration, not a discovery. Stopping rule: one year, with a six-month interim look at the controls only; a second year is pre-declared as the response to an inconclusive or 2-3 sigma outcome. The result will be reported whether it is a detection, a bound, or a failure of the apparatus. Standard physics predicts a null result at this sensitivity; the alternative hypothesis is from The Cosmic Page (doi:10.5281/zenodo.23287018, Ch. 13) and the research proposal doi:10.5281/zenodo.23201109. Included: the pre-registration (PDF and LaTeX source), the monitor script that runs on the device, the fixed analysis script, the synthetic-data validation script with its results and figure, and the README. First data point: job db9qap9gv2cc73e5tufg, 2026-10-17T16:42:19Z, T1 = 162.9 +/- 7.9 us.
Amendment 5 (2026-10-09), deposited before any S2 data. The registered question, estimand, test, seeds (1000-1079), shots (2,000), backend and qubit rules and 600 s ceiling are unchanged. What changes is how sampler calls become IBM jobs: one job per call (960 jobs, about 2,900 billed seconds) cannot fit the ceiling because of per-job billing, so seeds run in two blocks of 40 and every round of a block is one multi-pub job (12 jobs, about 540 s expected). Both arms of a seed share each job; the resulting shared-job exposure is accepted, with the primary test unchanged and per-block estimates reported as a secondary diagnostic. There is no statistical stopping and no interim analysis. Author decisions (shots, blocks, exposure) were made on 2026-10-09. Files: S2_AMENDMENT_5.md, AMENDMENT_5_MANIFEST.json (hashes of the implementation snapshot, commit 3332e893, and of the documents) and rqc-s2-amendment5-5fc50b0c.zip (code, documents and tests at commit 5fc50b0c). The original pre-registration and its frozen tooling are included unchanged. Not approved for execution: a run requires a recorded approval bound to the exact run payload. Pre-registration, deposited before any hardware job. On one IBM Heron backend (alphabetical-first rule; lowest-CZ-error 8-qubit path), with depth, two-qubit gate count, shots and session equal, does feedback-driven local search over single-qubit angles raise the fresh-re-measured, circuit-normalized XEB of the selected circuit compared with random search, at equal output concentration? Primary estimand: β0 of d = β0 + β1·Δc (one-sided, α = 0.05); 80 fresh seeds (1000–1079); 10-minute QPU ceiling. Simulation (S1) on an ibm_fez noise model and on Google's Willow noise model disagreed (β0 +0.010 and −0.003, both intervals include 0); the test is powered for effects of about 0.012 or larger and a null does not rule out smaller ones. Code frozen at github.com/osiris-dnalang/osiris-cli commit 86e3a3f4 (archive included).
Note: description expanded on 2026-10-14 for readability. It adds no new predictions or criteria. The frozen pre-registration is the attached PDF, unchanged since publication. Status: the experiment was run on 2026-10-14, after this record was published. Results, including every pre-registered test, will be reported in a separate record linked here. In plain language Theory says a quantum system never completely forgets where it started, even when its dynamics are chaotic. This leftover memory is called a quantum birthmark (Graf et al., Phys. Rev. X, 2026). Theory also says the birthmark should be larger when the system's rules run the same forwards and backwards in time (time-reversal symmetry) than when that symmetry is broken. This record pre-registers a test of that prediction on IBM's ibm_kingston quantum processor. We built two nearly identical sets of 4-qubit circuits. One set has time-reversal symmetry and the other does not. Both use exactly the same gates, so they experience the same hardware noise. We measure how often each circuit returns to its starting state, compared with the 1-in-16 chance level, and predict that the symmetric set shows about 1.67× more memory than the broken set. All predictions, pass/fail criteria, circuits and analysis code were deposited here before any quantum hardware was used. What is tested, and what is not Tested: whether the return probability stays above the ergodic baseline 1/16 at depths 8–23, and whether that excess is larger for the time-reversal-symmetric class by the ratio exact numerics predict for these fixed instances. Not tested: the withdrawn temporal-memory claims of 10.5281/zenodo.20470129. The birthmark is closed-system coherent memory, which measurement and reset erase, so no outcome here bears on those claims. Not tested: the universal random-matrix value 1.889. At this size (N = 16) the circuit family itself gives about 1.66, so a finite-size difference is expected. Not a quantum-advantage claim: a 16-dimensional system is exactly simulable. This is a hardware-validation experiment. Design Hardware: ibm_kingston, physical qubits 108–109–118–129 as an open chain, selected by a no-QPU calibration audit (included as v6_backend_audit.zip). Circuits: a kicked-Ising Floquet period Kx(a/2) → D(h1) → Kx(b) → D(h2) → Kx(a/2), with D(h) = exp(−iΣhiZi)·exp(−iπ/4 ΣZiZj), at exactly 6 CZ per period. COE (symmetric): h1 = h2. TRSB (broken): h1 = h + d, h2 = h − d. The classes differ only in virtual-Z angles. Instances: 16 seeded COE/TRSB pairs (seed 20261013), run at every depth from 8 to 23 (48–138 CZ). Observable: P(t) = |⟨0000|Ft|0000⟩|². The primary statistic is the readout-mitigated excess ratio R = ECOE / ETRSB, where E is the mean of P(t) − 1/16. A noise fidelity common to both classes cancels in R. Controls: 32 deep circuits (depths 60–63) as a decoherence-floor check. 8 state-preparation monitors. 16 readout-calibration circuits. Run: one SamplerV2 job of 568 circuits at 256 shots each, with dynamical decoupling and twirling off and the execution order shuffled. Predictions Quantity COE TRSB R Excess over 1/16, depths 8–23 (noiseless, primary) 0.0896 0.0537 1.667 Same instances, infinite-time limit 0.0952 0.0634 1.502 Circuit family, 10,000 random draws — — 1.661 Random-matrix reference, N = 16 — — 1.889 Under four simulated noise models (nominal, pessimistic, and each with coherent errors), the mitigated R stays between 1.64 and 1.77. The shot-noise standard deviation of R at 256 shots is 0.070–0.125. Pre-registered decision criteria Test Pass condition H1 (primary): symmetry dependence 99% CI lower bound of R > 1.0 H2 (primary): quantitative agreement 99% CI of R intersects 1.54–1.87 and is at most 1.0 wide S1: birthmark above decohered floor Window excess minus depth 60–63 excess, 99% CI lower bound > 0, for both classes S2: matched fidelity between classes 0.85 ≤ FCOE/FTRSB ≤ 1.15 S3: instance-level agreement Pearson r ≥ 0.80 against exact predictions S4 (flag only): state prep and drift Monitors ≥ 0.95, drift ≤ 0.045 Overall verdict: CONFIRMED if H1, H2 and S2 all pass; PARTIAL if H1 passes but H2 or S2 fails; NOT CONFIRMED if H1 fails. Every test is reported whatever the outcome. Uncertainty comes from a 10,000-sample parametric multinomial bootstrap over every circuit's counts, with instances held fixed. Amendment 1 (v1.1.0, made before any data) Amendment 1 changed two things relative to v1.0.0 (10.5281/zenodo.23355804): Shots: reduced from 1024 to 256 per circuit for QPU budget, cutting estimated execution from about 152 s to about 38 s. H2: changed from "point estimate in 1.54–1.87" to the CI rule above, because at 256 shots the point rule would falsely fail 20–25% of the time under the pessimistic models. A CI-width cap of 1.0 keeps H2 informative. Circuits, instances and predictions are unchanged. The trade-off is that H2 is now a weaker test. Provenance Every reported number is derived by script from raw counts: Source and transpiled circuits are saved as QPY. Before submission, every transpiled circuit is mapped back to 4 qubits and its unitary checked against the exact model to < 10−8. The analysis reads its decision bands only from predictions.json and its data only from the raw results file. Submission is gated on the DOI of this record. Files: The PDF is the authoritative pre-registration. predictions.json holds every predicted number and decision band. birthmark_prereg_v1.1.0.zip contains the circuit builder, verification, submission and frozen analysis scripts, plus simulated-data self-tests. v6_backend_audit.zip is the pre-submission calibration audit. Known limitations Small system size (N = 16), so the random-matrix value is not expected. The prediction is specific to depths 8–23 and to these 16 fixed instances. The noise models exclude leakage, TLS fluctuations and crosstalk from outside the chain. T1 relaxation biases P(0000) upward, which pulls R toward 1 (conservative). One backend, one path, one job: no replication. Data: CC BY 4.0. Code: MIT. Principal investigator: Amit Brahmbhatt, Quantum-Clarity LLC.
Whether financial data require a quantum-probabilistic description has been debated since Khrennikov proposed Bell-type and total-probability tests for markets, yet the field still lacks an instrument whose verdicts can be trusted in either direction. We first show that Bell-type and Leggett–Garg inequalities computed on passively recorded price data cannot establish non-classicality by violating a classical bound: by Fine's theorem, jointly recorded variables always admit a classical joint distribution, so apparent violations arise only from combining different conditioning contexts, which can test specific classical models but not the need for a quantum description. We then construct an alternative instrument within this boundary: a family of quantum-like models (a two-dimensional collapse chain and general hidden quantum Markov models of dimension two and three) is compared out of sample with a deliberately strong classical class (Moore and Mealy hidden Markov models with up to six states, including the classical limits of the quantum models, and an observation-driven GARCH-type model). A quantum member counts as evidence only if it beats every classical candidate. Before reading real data, we calibrate the instrument in both directions on synthetic data with known ground truth. On one year of 15-minute data it detects quantum structures matched to its members down to about 0.001 log-likelihood units per bar, while producing no false detections in 20 classical simulations read under the same rule, nor in 60 earlier ones under a less strict rule; the real-data conclusions survive a larger classical class and a doubled optimisation budget. Calibration also exposes five ways in which quantum advantage can be manufactured from classical data. Applied to seasonally adjusted gold and silver data at two time scales, the instrument detects no quantum-like advantage; every 95% upper bound is negative. A pre-registered out-of-sample test on 2026 gold data was likewise not supported. The contribution is a tested ruler with stated resolution, not a claim about the ontology of markets. Code, frozen measurement protocol and all results: https://doi.org/10.5281/zenodo.23449779 (version 1.1). Pre-registration: https://doi.org/10.5281/zenodo.23400902; results record: https://doi.org/10.5281/zenodo.23401850. This paper revises the author's earlier claim that the interference statistic κ indicates non-classicality in gold (https://doi.org/10.5281/zenodo.19456823).