Regression, forecasting, inference, and forensic anomaly detection in one engine — deterministic, closed-form, and reproducible byte-for-byte. No training. No drift. No black box.
A forecast may tolerate uncertainty. A calculation, test result, compliance determination, or reported number may not.
GSP does not substitute confidence for correctness. It applies validated methods, tests whether the analysis is appropriate, exposes uncertainty, refuses unsupported conclusions, and returns the evidence required to reproduce the result.
Correctly computed. Honestly qualified. Proven on demand.
The tool everyone uses to catch fraud fails because of the fraud. GSP's doesn't.
The five frauds inflate the standard deviation until their own score falls back under the threshold — the everyday tool hides the very fraud it's hunting.
A median / MAD band can't be dragged by a few extreme values, so every planted $2,000 invoice lands far outside it and is flagged.
✓ Deterministic — the same 50 values reproduce this exact result through the GSP API.
Excel gives you the coefficient. GSP tells you which ones to believe.
| Predictor | Coef | t | p | Verdict |
|---|---|---|---|---|
| Intercept | 2.706 | 5.37 | 0.000 | — |
| marketing_spend | 2.118 | 60.2 | 0.000 | Significant |
| weather_index | 0.013 | 0.20 | 0.847 | Not significant |
Honesty layer: flags weather_index as an insignificant predictor while marketing_spend (t = 60) is real — fit strength strong. A high R² doesn't make every driver true; GSP names the false one.
✓ Solved by numerically-stable Householder QR — reproducible through the GSP API.
Cooked books leave a fingerprint in the digits. GSP reads it — and tells you when it can't.
Nonconformity · MAD 0.0597. Digit 1 appears 11.1% of the time against a 30.1% Benford expectation — grossly under-represented; digits 8 and 9 over-represented. Flagged for review — a screen, not a finding.
Benford applies only to the right population — thousands of transaction-level, same-unit amounts. The engine discloses when a dataset isn't screenable. That disclosure is the selling point, not the caveat.
✓ Screened against the published Benford / Nigrini thresholds — reproducible through the GSP API.
Every capability is deterministic and validated against a published reference — and domain-agnostic: the same call runs on a macro series, a P&L, or a raw ledger.
GSP is a governed HTTP API for statistics your app can trust. Send a series and a method — regression, forecast, hypothesis test, fraud screen — and get back the determination, how far to trust it, and a reproducible receipt. Your app renders the pixels; the engine owns the number.
Versioned and SHA-pinnable, so a pinned result reproduces forever. It's HTTP — drop it into any stack, any language. The processors never leave the engine, so you get institutional-grade statistics without building or maintaining a statistics layer of your own.
Pair it with a conversational interface and ship analytics for domains where a wrong number is unacceptable — finance, health, compliance.
DeliveryA full forensic battery consolidated into one review queue ranked by cross-method consensus — built on robust estimators the anomalies can't poison. Everyday mean-and-standard-deviation tools inflate their own fence and hide the very fraud they're hunting; these don't. It also discloses when a dataset isn't a valid population to screen, so you never get false confidence — and hands your auditor a defensible, reproducible flag with its reasoning attached.
Forensic battery✓ Validated against NIST, Rosner, and the published Benford / Nigrini thresholds.
A multi-model out-of-sample bake-off that selects the model which wins on the horizon you actually forecast — never on in-sample fit — then labels the result reliable, directional, or unreliable, or refuses outright when it honestly can't. You get the number and exactly how much to trust it.
Models & outputsFull multiple regression with the complete inference output, solved by numerically-stable Householder QR that holds up on ill-conditioned data which breaks naive solvers. It adds the honesty layer spreadsheets omit — insignificant predictors, multicollinearity, and the significant-but-weak trap, named in plain language — so you know which factors truly move the outcome, which don't, and when a "driver" is a false signal.
Outputs & methods✓ Validated against NIST reference datasets — Longley included.
Distributions computed from series and continued fractions, not table lookups, with the classical tests on top. This is the inference foundation that regression p-values, forecast intervals, and conformity tests all stand on — proven against the regression to the last digit: the two-sample t matches the equivalent regression coefficient exactly.
Distributions & tests✓ Validated against published statistical tables and exact analytic identities.
Relate any series to any other, with the discipline to say "this is context, not cause." Every relationship is labeled association-only — never fabricated causation — significance-gated against multiple-comparison inflation, and reported with its measured strength, so you never take a spurious correlation to your board.
MethodsPoint GSP at a claim it can compute — whether a person or an AI asserted it — and it checks that claim deterministically. It turns the engine's identity into a product: the governed, reproducible verifier for the flood of numbers now generated by LLMs. The deterministic fact-checker for the AI era.
Checkable claimsA spreadsheet gives you the number and hides the uncertainty.
GSPgives you the number, the confidence, and the receipt.
An LLM generates a confident number that won't reproduce.
GSPdetermines a number that reproduces byte-for-byte.
A black box can't tell you why.
GSPshows its work — and refuses when it can't.
Reliability labels, significance and coverage disclosure, applicability guards, and explicit refusals travel inside every result the engine returns. When the data can't support the question, GSP says so — and refuses an ill-posed input instead of fabricating a confident number.
The one statistics engine that won't let you fool yourself — or your stakeholders.
A statistic from the GSP isn't a claim you take on faith. It's a determination — computed by the engine, pinned to versioned logic, and reproducible byte-for-byte with no AI anywhere in the loop. Analytics stop being “trust the model” and start being “here's the proof.”
Hand a regulator, a board, or a court the receipt — and reproduce the number on demand, with no AI in the loop.
Bring a regression, a forecast, or a fraud flag your business runs on — a human's ledger or an AI's claim — and we'll put it on the Governed Statistical Processor and show you the same answer, reproduced and traceable, before anyone talks terms.
A standard z-score flags any value more than three standard deviations from the mean. But the five $2,000 invoices are themselves extreme — they pull the mean upward and inflate the standard deviation. With a wider spread, every value — the frauds included — now sits within 3σ. The fraud raises the very threshold meant to catch it. Statisticians call this masking: outliers hiding behind their own effect on the estimator.
GSP measures the center and spread with the median and MAD (median absolute deviation) — figures a handful of extreme values can't move. The band stays tight around the true ~$1,000 cluster, so each $2,000 invoice lands far outside it: a modified z-score of 26.84 against a 3.5 cutoff. Because the estimator resists contamination, the fraud can't inflate its own threshold. GSP then cross-checks with Grubbs' test, generalized ESD, and Tukey fences, ranking each flag by how many methods agree.