Quantum Wave Core
What QWC is
QWC stands for Quantum Wave Core: an independently developed, quantum-inspired and wave-based analytical framework for time series, developed and audited first on financial markets.
The word quantum describes the mathematics, not the market. QWC borrows its language from wave mechanics and statistical physics: amplitudes and phases, Schrödinger-type evolution and heat kernels, superstatistics. It uses that language to describe how price increments are distributed, how a series moves through business time, and how series couple in ways correlation cannot see. It makes no claim that markets are quantum systems, and each such claim is tested like any other.
The core is a compact system of named laws and axioms. The laws are organised in four pillars: Law (the measured shape of price increments), Dynamics (the business-time clock, jumps, the shape of the innovation), Coupling (joint structure between series) and Verification (comparison with an honest competitor, not with chance). Five axioms are the foundations the laws are checked against. Every law carries a verdict, and several are refuted.
What is public here is the audit, not the mechanics: measurements, verdicts, experiment outcomes and the places where QWC disagrees with the literature. Formulas, parameters and implementation stay private.
The public audit
QWC evidence atlas
QWC is an independently developed analytical framework for time series, audited so far mainly on financial markets. It is organised as 26 named empirical laws and 5 axioms across four pillars, and it is audited under pre-registered protocols: each experiment is frozen with a SHA-256 hash before it runs and thresholds are never revised afterwards. This page is the public record of that audit, including everything that failed. Mechanics, formulas and parameters are intentionally not disclosed.
Structure
Four pillars
Pillar F · 6 records
Law
The measured marginal distribution of price increments: a shape that is measured, not assumed.
Pillar Q · 6 records
Dynamics
How a series moves: the business-time clock, jumps, and the shape of the innovation.
Pillar C · 12 records
Coupling
Joint structure between series that correlation cannot see.
Pillar A · 3 records
Verification
Comparison with an honest competitor, not with chance.
Interactive atlas
The 26 laws
Filter by family or verdict, or search. All data is embedded in this page; nothing is loaded from a server.
Hurst exponent of the increments
OpenL-DIFF
Diffusion exponent
Not refuted on recheckMeasurement. Hurst exponent of the increments
Result. 0.48 (crypto about 0.5; across domains 0.0 to 0.83)
Tail index of extreme returns
OpenL-EVT
Power-law tail
Not refuted on recheckMeasurement. Tail index of extreme returns
Result. alpha about 2.5 (range 2.3 to 2.9), Pareto fit R² 0.994
Width of the multifractal spectrum
OpenL-MFRAC
Multifractal width
Not refuted on recheckMeasurement. Width of the multifractal spectrum
Result. 0.19; 0.05 once measured in business time
Share of tail mass invisible to a Gaussian
OpenDARK
Dark fraction
Not refuted on recheckMeasurement. Share of tail mass invisible to a Gaussian
Result. 0.38 (corridor 0.28 to 0.44)
Serial dependence of squared increments
OpenL-DISP
Volatility clustering
Not refuted on recheckMeasurement. Serial dependence of squared increments
Result. Ljung-Box 10,257 (p = 0) against a Brownian control of 26 (p = 0.16)
Asymmetry of increments
OpenL-SKEW
Skewness
Not refuted on recheckMeasurement. Asymmetry of increments
Result. Significant in 31 of 32 series; median -0.08
Difference between left and right tails
OpenL-TAIL
Tail asymmetry
Not refuted on recheckMeasurement. Difference between left and right tails
Result. Asymmetric in 7 of 32 series; passes by a thin margin
Rate of entropy production of the series
OpenL-ENTROPY
Entropy production
Not refuted on recheckMeasurement. Rate of entropy production of the series
Result. Matches the entropy rate on self-similar controls to about 0.01
Bits of predictability left in direction
OpenL-INFO
Residual information
Measured boundaryMeasurement. Bits of predictability left in direction
Result. About 0.0014 of 0.030 bits for financial series; a martingale GARCH gives 0.037
A conserved quantity of the state
OpenL-IOM
State invariant
Measured boundaryMeasurement. A conserved quantity of the state
Result. Direction AUC 0.499: measured, not predictive
A scale or structural invariant
OpenL-SM
Scale invariant
Measured boundaryMeasurement. A scale or structural invariant
Result. Magnitude AUC 0.496: measured, not predictive
Distribution family of the activity clock
OpenCLOCK
Business-time clock law
Not refuted on recheckMeasurement. Distribution family of the activity clock
Result. A normal-inverse-Gaussian clock wins on 17 of 32 series by AIC
Whether a stated state can be falsified
OpenSTATE
State falsification
Not refuted on recheckMeasurement. Whether a stated state can be falsified
Result. Live-data record
Expected increment given the past is zero
OpenL-MART
Martingale axiom (A1)
Not refuted on recheckMeasurement. Expected increment given the past is zero
Result. t = 1.16, p = 0.24: direction is not predictable
Characteristic-exponent slope of the evolution of increments
OpenL-SCHR
Propagator law
Not refuted on recheckMeasurement. Characteristic-exponent slope of the evolution of increments
Result. Slope 1.49 against exactly 2.00 for Brownian motion; heat-kernel description rejected. Author's measurement, not independently reproduced; provenance being rebuilt
Moment-scaling exponents
OpenL-THERM
Thermostat frame
Not refuted on recheckMeasurement. Moment-scaling exponents
Result. 0.51, 0.97 and 1.58 for orders 1, 2 and 4: concave, as required
Response against fluctuation
OpenL-FDT
Fluctuation-dissipation
Not refuted on recheckMeasurement. Response against fluctuation
Result. 0.99 against 0.65 for Brownian motion
No-arbitrage inequalities
OpenL-ARB
Arbitrage bounds
Not refuted on recheckMeasurement. No-arbitrage inequalities
Result. 0 violations in 200,000 checks (a database also scores 0, so this is correctness, not discovery)
Spreads and baskets inherit the tail
OpenL-CLOSE
Closure (A5)
Not refuted on recheckMeasurement. Spreads and baskets inherit the tail
Result. Tail df 2.44 single, 2.62 basket, 7.3 without dependence; gap 2.22 on recheck
Adaptive conformal coverage
OpenL-CONFORMAL
Distribution-free coverage
CorrectedMeasurement. Adaptive conformal coverage
Result. Holds on 9 of 9 series with adaptive correction; plain split-conformal fails on 2 of 9 (0.57 and 0.68 against a 0.75 target)
Detection of changes in tail shape
OpenL-SHIFT
Shape-shift detector
Wins in a nicheMeasurement. Detection of changes in tail shape
Result. Beats BOCPD on tail-shape changes (+0.159 AUC, p = 5.6e-9); loses heavily to CUSUM on mean and variance shifts (-0.17 and -0.27)
Predictive claim of precision 0.74 to 0.96
OpenACP
Amplitude-cap predictor (A4)
RefutedMeasurement. Predictive claim of precision 0.74 to 0.96
Result. AUC 0.496 on a direct test, precision 0.577 against 0.519 trivial: not reproducible. Only the algebraic ceiling survives
Option smile against market quotes
OpenL-PRICE
Tail-aware option price
Wins in a nicheMeasurement. Option smile against market quotes
Result. Clean win in the wings with 3 quotes over four rivals (746 smiles, 59 expiries); loses to SVI with 5 or more quotes
First-passage probability under GARCH
OpenL-DPF
Retention-probability term structure
UntestedMeasurement. First-passage probability under GARCH
Result. Not yet tested
Out-of-sample interval coverage
OpenL-ARC
Reference intervals
ParityMeasurement. Out-of-sample interval coverage
Result. Coverage 0.698 to 0.784 against a 0.75 target, median 0.752
Option sensitivities
OpenL-GREEK
Sensitivities
ParityMeasurement. Option sensitivities
Result. Equals Black-Scholes in the Gaussian limit: correctness, not an advantage
Not refuted on recheck means the record survived a frozen test on 21 crypto series and 29 ETFs; it does not mean the law is proven. Most measurers are expected to pass, because any real series beats a Gaussian surrogate; the table says so where it applies.
Foundations
Five axioms
| ID | Axiom | Status |
|---|---|---|
| A1 | Martingale increments Holds: t = 1.16, p = 0.24. A consequence the programme accepts in full: directional alpha is structurally excluded. | Not refuted on recheck |
| A2 | State invariant Measured, not predictive (AUC 0.499). | Measured boundary |
| A3 | Scale invariant Measured, not predictive (AUC 0.496). | Measured boundary |
| A4 | Amplitude ceiling The predictive claim is not reproducible; only the algebraic ceiling holds. | Refuted |
| A5 | Closure under composition Laws are inherited by spreads and baskets, shown through L-CLOSE. | Not refuted on recheck |
What was tested
Pre-registered experiments
Each protocol was frozen before the run and checked by hash afterwards. A pass means not refuted on the stated panel.
Usable share 47.5% against 15% for a range check (McNemar p = 0.0044).
5 of 20 pairs against 0 of 20; the paired test could not run because the pre-registered minimum was 6 discordant pairs.
15 hold-out pairs where 30 were required; descriptively unfavourable.
8.9% significant after multiple-testing correction against 50% required; placebo 0.2%.
The extension beyond the earlier 12 domains could not decide; a recheck of the cross-domain matrix failed its parity-with-oracle criterion (Wilcoxon p = 0.016).
The full smile is worse than the market; the wings win only with three quotes.
Effect is mechanical: 0.1425 on markets, 0.1440 on shuffled surrogates. The first design was withdrawn because its metric was degenerate.
KS distance to the best parametric model 0.072 against a 0.03 threshold.
No such object exists in the source material; the number is a normalisation constant. Voided before the run.
8 of 8 applicable measures are deterministic and satisfy their own identities. This tests the tool, not any claim of quantumness.
AUC 0.508 against 0.636 on no-signal surrogates: leakage adds 0.136.
Information gain over volatility is zero on 55 instruments (interval -0.0044 to +0.0042).
Withdrawn on 1 October 2026: the code was a stub and the verdict was copied.
The amplitude-cap predictor failed again (median AUC 0.507).
Invariant boundary confirmed on 18 of 21 series where 19 were required.
Median tail df 2.786 against an upper bound of 2.74; one law could not be separated from its Gaussian control.
C-clock, C-contagion and C-nontrading were re-labelled; the original numbers are preserved and annotated.
Theory against measurement
Where measurement disagrees with theory
Standard theory, published formulations and the programme's own earlier ideas, each held to the same numerical test.
What the literature says
Brownian motion has a Gaussian heat-kernel propagator, and quantum-economics formulations describe price evolution with Schrödinger-type equations that are heat-kernel-like in the relevant limit.
What was measured
The measured characteristic-exponent slope is 1.49 against exactly 2.00 for Brownian motion (n = 96,000). Student-t degrees of freedom rise from 2.3 to 3.5 over horizons of 1 to 256 bars, where a Brownian series stays Gaussian at every scale.
Verdict
Heat-kernel description rejected in favour of a non-local, time-changed evolution. Status: the author's measurement, not independently reproduced; the data provenance is being rebuilt.
What the literature says
A density in the quantum-economics literature is stated to integrate to one with a normalisation constant of 1.493.
What was measured
Numerical integration gives 0.215, 1.132 and 1.954 at shape values 0.25, 1 and 2. The correct constant is 6.96 at 0.25 and tends to 0.564 for large values; the error approaches a factor of the square root of pi. On real data the best parametric model also fits better (KS 0.072 against a 0.03 threshold).
Verdict
The stated normalisation is wrong and the fit test failed. The comparison with Brownian motion was also made on a different variable (volume, not price).
What the literature says
Quantum-economics formulations claim direction is predictable from volume excess (an accuracy of 85%). Weak-form efficiency says the opposite.
What was measured
The martingale axiom holds (t = 1.16, p = 0.24). The lead-lag test on 493 instruments finds 8.9% significant after correction against 50% required, with 0.2% under the placebo.
Verdict
The directional claim is unsupported; the programme's own axiom forbids it. No accuracy or Sharpe figure from that claim is shown here as a result.
What the literature says
Elliott-derived rules are said to predict turning points with a precision of 0.74 to 0.96.
What was measured
A direct test gives AUC 0.496 and precision 0.577 against a trivial 0.519 (p = 0.53); a BTCUSDT hourly recheck gives AUC 0.505. Treated as a hazard of reversal, the effect is mechanical (0.1425 on markets, 0.1440 on shuffled returns).
Verdict
Refuted as a predictor. It survives only as a naming system for market states.
What the literature says
Gaussian increments, constant volatility and thin tails, as in Black-Scholes.
What was measured
Tail index about 2.5 (2.3 to 2.9), Pareto fit R² 0.994, volatility clustering with p = 0, Hurst exponent 0.48, dark fraction 0.38. A Kolmogorov-Smirnov test rejects Brownian motion at 0.12 to 0.14.
Verdict
Rejected, and the literature has known this for decades: this is agreement, not a discovery. Against GARCH-t and extreme-value methods the programme is at parity. Mandelbrot and Taylor's subordination is credited as prior art.
What the literature says
A Gaussian whose variance fluctuates produces heavy tails (Student-t).
What was measured
The programme's decomposition into an innovation and an activity clock is the same structure. A control shows that dividing by hourly activity and clipping jumps compresses estimated degrees of freedom to 4.2 to 4.9 for any true value between 2.5 and 15.
Verdict
Agreement with the literature, and an honest limit: the estimator cannot distinguish tail shapes, so the claim of a universal innovation shape is marked untested.
What the literature says
Price-volume uncertainty, Bohm potentials, operator portfolios and quantum-cognition models are proposed as market models.
What was measured
The price-volume 'uncertainty' relation is an analogy, not a theorem: the commutator is zero and the bound collapses to Cauchy-Schwarz. Quantum-cognition models need human-decision data that markets do not provide. The 8 applicable measures pass a consistency test, which says nothing about quantumness.
Verdict
Kept as analogies and as tools, with no claim that markets are quantum.
What the literature says
CUSUM, PSI, EWMA, HAR-RV and SVI are standard methods.
What was measured
CUSUM beats the shape-shift detector on mean and variance shifts (-0.17 and -0.27 AUC). PSI beats it on drift for external models (-0.384). EWMA and HAR-RV beat the dispersion law. SVI wins with five or more option quotes. Claims that fat tails or a better measure win against historical simulation did not survive.
Verdict
The programme wins in two narrow places, where the competitor has no data to fit or one setting must work across many objects, and nowhere else.
Honest comparison
Scoreboard against standard methods
| Question | Standard method | QWC | Winner by measurement |
|---|---|---|---|
| How to set a threshold for a new object | Recalibrate | Transfer unchanged | QWC (Gates B and E) |
| Change in tail shape | BOCPD | L-SHIFT | QWC (+0.159 AUC, p = 5.6e-9) |
| Change in level or scale | CUSUM | L-SHIFT | Standard (-0.17 and -0.27 AUC) |
| Variance forecast | EWMA, HAR-RV | L-DISP | Standard (EWMA best) |
| Drift of an external ML model | PSI | Shape statistic | Standard (-0.384) |
| Option smile with 3 quotes | Regularised SVI | L-PRICE | QWC in the wings |
| Option smile with 5 or more quotes | SVI | L-PRICE | Standard |
| Tail risk | GARCH-t, EVT, FHS | Measured F | Parity |
| Gaussian increments | Known not to hold | Not Gaussian | Both: not a discovery |
QWC wins exactly where the competitor has no data to fit or one setting must work across many objects, and nowhere else.
Registry snapshot, October 2026
Evidence ledger
Quoted from the author's internal pre-registered registry. Single-operator means no independent replication yet.
Statuses: Confirms known literatureSingle-operator resultPreregisteredPreprintIndependently reproducedInconclusiveNot supported / refutedWithdrawn by the authorHypothesis
Structure of financial time series
Measured on public market data. Several of these confirm what the literature already knows; they are listed because they set the baseline every later claim is held to.
| ID | Finding | Status |
|---|---|---|
| S1 | The Gaussian random-walk description of returns is rejected On 32 crypto-asset series: heavy tails (Hill tail index about 2.3 to 2.9), strong volatility clustering and non-Gaussian increments. What survives is near-martingale increments and a Hurst exponent close to one half. This is common knowledge in the field and is recorded as a baseline, not as a discovery. | Confirms known literature |
| S2 | Returns decompose into heavy-tailed innovations, a persistent stochastic clock and jumps Marginals close to Student-t with about 2.3 degrees of freedom, strongly persistent log-volatility, and jumps contributing roughly 9 percent of variance on well under one percent of bars. A related claim that the innovation shape is universal is explicitly marked untested, because the estimator cannot distinguish tail shapes on synthetic data. | Single-operator result |
| S3 | Strong tail dependence between crypto assets, stronger in falls than in rises Lower-tail dependence about 0.47 where a Gaussian copula implies zero; 0.47 for joint falls against 0.32 for joint rises. Against plain historical-simulation risk models the dependence-aware model was not better. Reproducibility debt: the scripts for this block read a temporary panel that no longer exists, so eleven records currently cannot be rerun. | Single-operator result |
Transferable alarm thresholds
The programme's one claimed advantage: calibrate an alarm threshold on one series and apply it unchanged to another. How often does it stay usable, compared with simple range checks, CUSUM and Bayesian online change-point detection (BOCPD)?
| ID | Finding | Status |
|---|---|---|
| T1 | An unmodified threshold stays usable more often across 23 independent public sources 237 source-to-target pairs from spacecraft telemetry, cardiac signals, water treatment, cloud and web-service metrics. Share of pairs where the transferred threshold remained usable: 34.2 percent against 19.8 percent for a range check, 3.8 percent for CUSUM and 0.4 percent for BOCPD. Recall gain 0.19 against the best competitor (p below 10^-6). False-alarm drift: parity, honestly not significant. | Single-operator result |
| T2 | Same effect between tenants of one type 14 families, 126 pairs: 61 usable against 39 for the strongest competitor (McNemar p = 0.003). The recall difference is not significant (p = 0.57), and a bootstrap interval on false-alarm drift includes zero, so that axis is not counted. | Single-operator result |
| T3 | Third, blind replication on sealed families: same direction, not confirmed Pre-registration frozen with a SHA-256 hash and data hashes recorded before the run; thresholds not revised afterwards. 5 of 20 pairs usable against 0 of 20 for the range check; recall gain 0.15. The paired test could not be evaluated because only 5 discordant pairs occurred where 6 are required, so by the pre-registered rule the outcome reads as not confirmed at low power. Absolute level is modest: a quarter of blind pairs. | Inconclusive |
| T4 | Advantage proportional to the scale gap between sources: rejected Spearman correlation +0.03 (p = 0.93, n = 12). The advantage is therefore not explained by how different the sources are. On a canonical multi-server dataset the method loses clearly (recall 0.65 against 0.98). | Not supported / refuted |
| T5 | Competitiveness on public anomaly-detection leaderboards: not achieved NAB: rank 15 of 16, below the mean of a random detector. SKAB: rank 10 of 12. Threshold transfer is a narrow property, not a general detector. | Not supported / refuted |
| T6 | A system that predicts when its own transfer will fail One run: 58 percent coverage at 9 percent false abstentions on 132 hold-out pairs. A later pre-registered recheck was void (15 pairs where 30 are required) and descriptively unfavourable. The original figure remains the citation of a single run. | Inconclusive |
Duration modelling
Predicting how long a state lasts rather than which way the price goes.
| ID | Finding | Status |
|---|---|---|
| D1 | Time-to-reversal hazard model transfers between crypto and FX Discrete-time hazard formulation. Concordance index 0.605 on crypto (all 26 folds above 0.55) and 0.580 on FX daily data 2015 to 2026 (7 of 7 folds above 0.5). The same law on both markets. Direction of the move remains unpredictable: it was closed on four independent formulations. | Single-operator result |
Validation methodology
Instruments for telling signal from artefact.
| ID | Finding | Status |
|---|---|---|
| V1 | Naive cross-validation inflates results; purged validation removes the inflation On surrogate data with no signal, purged cross-validation gives AUC 0.508 against 0.636 for plain K-fold: leakage from overlapping labels adds 0.136. This is a validation instrument, not an advantage of any model. | Single-operator result |
| V2 | A conventional relative-value strategy passes the full written validation criterion Deflated Sharpe ratio 0.985 (threshold 0.95), probability of backtest overfitting about zero over 12,870 combinations, 45 of 45 combinatorial purged paths positive, robust to execution delay and funding stress and to a second exchange. Capacity is modest and simulated drawdowns are deep. This is a statement about validation rigour, not an investment claim, and it uses none of the proprietary indicators. | Single-operator result |
Negative results
Claims that were tested and did not survive. They are the most useful part of a research record.
| ID | Finding | Status |
|---|---|---|
| N1 | Proprietary indicators improving a validated strategy: refuted Used as a timing overlay on the strategy above they reduced risk-adjusted performance. A bug in the first implementation was found and fixed before reporting; after the fix the overlay was still worse. Attributed to cost drag from continuous reweighting. | Not supported / refuted |
| N2 | Directional timing from proprietary wave indicators: no pass in forty attempts Forty pre-specified timing experiments across direction, filtering, sizing and risk overlays: none passed. Direction was closed on four independent formulations, on two asset classes, before and after costs. Machine-learning uplift on a level indicator reached 9.9 bps against a 15 bps threshold and was closed. | Not supported / refuted |
| N3 | Standard technical indicators as the main signal: no edge after costs RSI, moving averages, momentum, MACD, ATR, breakout and Bollinger: no edge after at least 17 bps round-trip cost on any timeframe from 5 minutes to 4 hours, on any tested symbol. | Not supported / refuted |
| N4 | Shape changes warn of large moves: no information beyond volatility Best median AUC 0.525 against 0.760 for plain rolling volatility. A wave-phase hazard effect proved mechanical: 0.1425 on markets and 0.1440 on shuffled surrogates. Across 55 instruments the information gain over volatility was zero (confidence interval −0.0044 to +0.0042). | Not supported / refuted |
| N5 | Variance forecasting and model-drift detection: parity or worse Variance forecast loss 0.566 against 0.569 for HAR-RV and 0.517 for plain EWMA. Drift detection for external models was significantly worse than the population stability index (correlation 0.15 against 0.54). | Not supported / refuted |
| N6 | A published accuracy of 0.74 to 0.96 was not reproducible A direct test gave AUC 0.496. The figure had lived in project briefs for years before it was checked; it is now formally recorded as not reproduced. | Not supported / refuted |
| N7 | An automated hypothesis factory produced 4,054 hypotheses and none validated 4,004 rejected, 48 blocked, 0 validated. 99.3 percent of rejections carried no recorded reason, so the largest corpus of negative results taught nothing. The fix was a machine-readable register of refuted claims consulted before generating a hypothesis. | Not supported / refuted |
| N8 | Cross-domain black-box utility: terminal no-go A pre-registered hard gate on four labelled domains ended in a terminal no-go with zero replication candidates; the research line is closed and 54 negative records are preserved. | Not supported / refuted |
| N9 | A recheck of the core laws was withdrawn after one day The first pass was withdrawn on 1 October 2026 because the code was a stub and the verdict had been copied. The recheck was rerun with frozen pre-registrations: most records were not refuted on the panel, the accuracy claim failed again, one boundary claim failed, one family check failed. | Withdrawn by the author |