Card 78 — Hoeffding Φ² oracle grounded S1 DONE

The mission of this campaign is to add four new "measurements" (features) to every price bar the pipeline produces. Think of a bar as a snapshot of trading activity; each feature is a number that describes some aspect of it — this batch adds numbers that are deliberately different from everything already measured (they passed two independence audits), so a machine-learning model gets genuinely new information.

This iteration started feature #1 of 4: card 78, "Hoeffding's Φ² (phi-squared)". In plain terms it asks: over the last 200 bars, is there any relationship — of any shape — between how much the price moved and how long the bar took to form? Classic correlation only spots straight-line relationships; Hoeffding's Φ² spots any pattern (curved, U-shaped, threshold-like). It answers on a 0-to-1 scale: 0 = "move size and bar duration are unrelated", 1 = "one completely determines the other".

What was actually built today is the answer key, not yet the engine part. Before any feature is allowed into the production Rust engine, we first write a slow-but-trusted reference version in Python and freeze its answers on 10,000 real Bitcoin bars and 10,000 real Ethereum bars ("the oracle"). Later stages must reproduce these answers to within 0.000000001 — that's how we prove the fast production code computes exactly the same mathematics as the reference.

Two safeguards worth explaining: (1) the reference computed every answer twice, via two completely different mathematical routes — a grid-counting method and an exact whole-number formula — and required both routes to agree on all 19,602 windows before writing anything (they did, to better than one part in a trillion). (2) The price inputs were passed through the same rounding step the production engine uses, so the reference and the engine literally see identical numbers — a past incident (I3) taught us that even a rounding difference in the 9th decimal can flip a rank and corrupt this kind of statistic.

One surprise: the shared test dataset used by earlier features stores only closing prices, but this feature also needs each bar's duration. When we went back to the production database to fetch durations for the same bars, we found the database had been legitimately repaired since May (gap-healing), so those exact old bars no longer exist. Rather than corrupt the old dataset, card 78 got its own fresh, self-contained dataset (price + duration), fingerprinted (SHA-256) so any future tampering or drift is detected instantly.