BL-IS-013: Orthogonality by Co-firing

BIJECTIVE LABS

BIJECTIVE LABS . SEP 7, 2026

BL-IS-013: Orthogonality by Co-firing

Status: RELEASED

Classification: PUBLIC

Revision: 1

Date: 2026-09-07

1. What it measures

Whether two gates in a confirmation ladder are actually independent evidence, or the same evidence counted twice.

At K timestamps drawn at random from the lake, each candidate gate is evaluated as a mechanical binary, fired or not, with no reference to what happened afterward. The association between two such binary series is the phi coefficient on their 2x2 co-fire table, identical in form to the Matthews correlation coefficient applied to the firing pattern rather than to a prediction outcome. A pair above roughly 0.3 in absolute value is treated as redundant.

Nothing in the computation touches profit. The instrument runs before a single trade is priced, which is the point of it.

2. Why it exists

BL-D-007 rule 1 requires gates to be orthogonal by construction, derived from different observables. Rule 2 exists because construction is not proof: two gates can be built from different pipelines and still fire together almost every time, if both pipelines key off the same underlying flow.

That is what happened to the strategy that produced the doctrine. A confluence gate requiring two conditions cut trade frequency from 1,522 per day to 438. Frequency was the only thing that moved. Both conditions were derived from the same order-flow measurement, one reading its imbalance and the other its toxicity, and requiring both was close to requiring the first one twice.

Run before a redesign, this check prices that kind of redundancy in minutes. On a later four-gate candidate it was run first: three of the four gates were mutually redundant above threshold, and the specification was reduced to a three-gate ladder before a single return was computed.

3. Interface

phi_coefficient(n11, n10, n01, n00) -> float
  n11, n10, n01, n00   the four cells of the co-fire contingency table
  phi = (n11*n00 - n10*n01) / sqrt((n11+n10)(n11+n01)(n00+n10)(n00+n01))
  a zero-margin table (one empty row or column) returns 0.0 rather than
  raising, because an undefined statistic on a degenerate table is a
  low-information result, not an error condition
 
contingency(x, y) -> (n11, n10, n01, n00)
  x, y   binary firing vectors of equal length, sampled at the same times
 
redundant(pair) = abs(phi) > 0.3 and n11 >= 5
low_power(pair) = n11 < 5

Twenty-eight tests cover the phi statistic, the individual gate functions, and the sampling primitives, written before the instrument was run against the lake.

4. Where the threshold sits

0.3 is a judgment stated once, applied everywhere, and not tuned after the fact. It sits below the level at which two gates would be functionally the same test wearing different names, and above the level of coincidental co-firing between mechanically unrelated conditions sharing a clock.

The instrument also declines to adjudicate a pair with fewer than five joint firings. A phi coefficient computed on four points describes the sample rather than the relationship, and reporting one without that guard would let sparse data masquerade as a finding in either direction.

5. A worked result

Applied to a three-gate candidate after its fourth gate could not be constructed, co-fire between book-supply texture and HLP absorption returned phi = +0.261 on 1,177 joint firings [BL-SD-022 section 6], below the discard threshold. The gate against the primary itself fired too rarely in the random-time sample to adjudicate, fewer than five joint firings, and the instrument correctly declined to score it rather than report a number built on four points.

Neither result decided the eventual verdict. The doctrine this instrument serves also holds that a gate ladder confirms a working primary and cannot resuscitate a failing one, and in that measurement the primary failed its own null before the ladder was ever applied.

6. What it does not do

It does not decide whether a gate ladder helps. Orthogonality is necessary and not sufficient; two gates can be perfectly independent and still add nothing if neither carries information the primary lacks.

It does not run on outcomes. Gates are evaluated as mechanical binaries at random times, with no return, label, or profit figure anywhere in the computation. A version of this check that touched return would be answering a different, contaminated question under the same name.

It does not resuscitate a primary. Passing this test says a confirmation ladder is not double-counting one signal. It says nothing about whether the primary the ladder would attach to has any edge to confirm, and BL-D-007 forbids applying the ladder before the primary clears its own null, regardless of how clean the gates are.

It has not yet produced a registered machine-readable artifact of its own. Its results to date are recorded in the dossiers that used it rather than filed under an evidence identifier, and that gap is stated here rather than left for a reader to discover a missing citation.

7. Cross-references

BL-D-007 rules 1 and 2. BL-SD-009 for the failure that produced the doctrine. BL-SD-022 section 6 for the applied measurement. R-28 for the rule under which the instrument carries its own test file, written before the measurement ran.