Open problem: a direction-sensitive cross-model discovery method

[fathomlab]

The open question: we can now read concepts across model families label-free, but the direction of "who reads whom" is currently unmeasurable - and we said so in the finding rather than claiming symmetry.

Why: the discovery machinery (TransferMap.fit, GW + orthogonal Procrustes) is direction-blind by construction. The map and its reverse are transposes; the induced assignment is identical. We caught this because three of six model pairs returned discovery accuracies exactly equal to four decimal places - precisely the pairs with matching ambient dimensionality (b37 FINDING, catch #1).

So our "legibility is symmetric" gate measured the instrument, not the minds. The empirical question is untouched: if mind A can decode mind B, can B decode A?

What is needed: a discovery method where source and target are not interchangeable - e.g. an asymmetric objective, a non-orthogonal map class, or a fitting procedure that conditions on source geometry. Then re-run the 12-pair matrix and report both directions.

Data is ready: the four extraction banks are committed (papers/disjoint-worlds/b31v2_pts*.npz), CPU-only, and
un_b37.py is the harness to modify.

This is a genuine open problem with a clean success criterion, and nobody has an answer.

[fathomlab]

Update 2026-08-06 — this open problem now has a number attached, from our own data.

We ran the full 45-pair legibility matrix on a ten-model cohort (b48), scoring both directions of every pair. The result:

42 of 45 pairs returned exactly equal scores in both directions.

Not similar — identical. The committed discovery machinery (TransferMap.fit + Hungarian) cannot see direction at all, which means our own design spent half its compute on a distinction its instrument cannot make. That is a design flaw and it is ours.

This is the same limitation the b37 finding impeached in its own author's gates (three exact ties in the symmetry test), now measured at scale rather than noticed in passing.

So the open problem is sharper than originally posted. It is not "would a direction-sensitive method be interesting?" It is: every asymmetry claim in the cross-model legibility literature that uses Procrustes-family alignment is unfalsifiable with that machinery. If A reads B better than B reads A, no method in this family can show it.

What would close this:

• A discovery method where score(A→B) ≠ score(B→A) is possible by construction, with a demonstration on a pair where ground-truth asymmetry is planted.
• Or a proof that label-free correspondence recovery is necessarily symmetric, which would be a stronger and more surprising result — and would mean the question of whether one mind reads another better than the reverse is simply not askable this way.

The b48 run is CPU-only from committed banks and reproduces in ~10 minutes: python papers/disjoint-worlds/run_b48.py. The per-pair both-direction scores are in b48_result.json for anyone who wants to check the 42/45 claim directly.

Note b48's own verdict was INVALID__null_leaks — we mis-specified a gate (judged a max-of-45 statistic against a single-draw bar) and the machinery refused the run. The direction-blindness observation above is reported as a lead, not a licensed finding, for that reason. It is still 42 out of 45 exact ties.