Independent PhD Audit · Report 2 of 2

Independently audited — all four signals across the full S&P 500 market cycle

Determination · Validated with Qualifications

~86%

bear-market precision · flagship BRS · reproduced exact

✓ Genuine signal, confirmed. Across 1,000 shuffled-label trials, all four signals scored far above random chance — zero matched the real model.

A deliberately stricter, independent PhD replication and robustness audit of RegimeSignal's four S&P 500 prediction signals — the full market cycle — designed not to duplicate the validation. Auditor: Dr Jamal Hossain, PhD · July 8, 2026.

PhD Independent Auditor

Dr Jamal Hossain, PhD

Lecturer in Applied Health Statistics · University of Southampton

PhD · MSc, Statistics (with distinction) · BSc (Hons), Statistics · FHEA · Member, Statistical Sciences Research Institute (S3RI)

PhD in Social Statistics & Demography (University of Southampton, 2023), completed as a Commonwealth Scholar. Peer-reviewed publications in journals including JAMA Network Open and PLoS ONE, with research spanning statistical modelling, multilevel & longitudinal analysis, classification metrics, reproducibility, and machine-learning methods. ORCID: 0000-0002-2728-1055.

Independence: No role in the model's construction and no financial relationship with Cronus Market Intelligence beyond the audit fee. The engagement was limited to statistical audit, replication, implementation-integrity, and robustness checks — not an assessment of market or investment merit.

Four signals across the full cycle

BRS — Bear market (−20%)

−20% · audit-clean

MBS T1 — Pullback (−5%)

−5% · audit-clean

MBS T2 — Correction (−10%)

−10% · audit-clean

RRS — Recovery (+10%)

+10% · exploratory*

SignalPrecisionAUCRepro
BRS — Bear market (−20%)85.7%0.91Exact
MBS T1 — Pullback (−5%)83.3%0.88Bit-exact
MBS T2 — Correction (−10%)84.4%0.92Bit-exact
RRS — Recovery (+10%)81.8%*0.76Exact

What the audit confirmed

  • Every signal sits far above the permutation-null baseline — genuine signal, not artifact.
  • Benchmarked against three independent alternative learners on identical data — all within a tight AUC band; one scored marginally higher. Results are not algorithm-picked.
  • Three of four signals (BRS, MBS T1, MBS T2) reproduced audit-clean and well-supported on the out-of-sample record.
  • All 35 locked files checksum-verified and matched; four signals reproduced with no divergence.
  • MBS T1 and MBS T2 reproduced bit-exact (~1×10⁻⁸; every one of 154 fire/no-fire decisions).
  • No feature-level label leakage — the predicted month is excluded and features are lagged one month.
  • The Market Break signals degrade gracefully under a 12-month cutoff shift.

⚠ Qualifications — disclosed in full

RRS — real signal, conservative claim. RRS cleared the same chance test, so the signal is genuine. The one caveat is narrow: its 82% was measured on the window used to tune it, so we publish it as a historical upper bound and treat ~69% as the honest prospective estimate. Precision-first · recall ~39% by design.

Small event counts across all signals (67 / 46 / 33 / 23) — bands are wide. No purge/embargo for the 4-month label horizon; BRS reproduced on a locked Layer-1 composite.

* RRS 82% = 9 of 11 fires correct at the locked high-conviction threshold, reproduced exactly. Because the threshold was chosen on the reported window, it is in-sample-optimistic; prospective estimate ~69% (Wilson 95% CI ≈ [0.52, 0.95]). Presented as exploratory pending out-of-sample data postdating the lock.

Full report available to qualified reviewers under NDA on written request to info@cronusmarketintelligence.com.

Independent review of the documented walk-forward methodology and reproducibility of the headline confusion matrices from locked artifacts as of June 3, 2026. Not an opinion on future results; does not validate production deployment; not investment advice. Past statistical results are not indicative of future results.