Add conditional query information for correlated partial gauges

[FlorianPfaff]

Scientific purpose

Advance the paper contribution beyond the already implemented observable-subspace factor (#332) and query-observability projection (#338): select and assimilate an additional learned window according to its conditional query information after the actual history, rather than its standalone covariance.

This is a method plus an executed controlled mechanism study, not another real-provider qualification protocol. No protected dataset, source residual, target outcome, BayesianPhysTwin result, or Causal4D outcome was opened.

Method

For the complete, externally justified joint observation-noise covariance, condition candidate noise on consumed history:

L = R_cH R_HH^-1
H_cond = H_c - L H_H
y_cond = y_c - L y_H
R_cond = R_cc - L R_Hc

The outcome-free selector evaluates expected metric-squared query-error reduction per cost. The session tracks consumed evidence, preserves partial gauge information without a ridge, supports compatible singular replay covariance, rejects informative deterministic constraints instead of silently dropping them, and returns the same local gauge-belief object for exact source replay.

The guide includes a proof of the query-value identity and a counterexample: a shared-noise reference has zero standalone state information, but after a signal-bearing window reduces scalar posterior variance from 1/2 to 1/12. Consequently no generic submodularity or multi-step greedy guarantee is asserted.

Gaussian conditioning, goal-oriented design, and correlated sensor selection are established prior work. The candidate contribution is their explicit composition with partial learned-window gauges, source-replay semantics, downstream queries, and executable failure controls; not invention of those general formulas.

Executed controlled study

10,000 independent synthetic episodes; one additional-window budget; all choices made before drawing outcomes; known local-linear Gaussian model; 2,000 paired episode-bootstrap replicates.

Arm	Selected window	Query RMSE (mm)	Normalized NEES	90% coverage
History only	none	1.6967	0.9934	89.96%
Marginal query selection + invalid independent update	near-repeat	1.7050	1.9597	64.06%
Marginal selection + correct conditional update	near-repeat	1.6965	0.9936	90.05%
Global gauge-variance selection + correct update	twist-only	1.6938	0.9943	89.96%
Conditional query selection + correct update	complementary	1.4434	0.9992	90.15%

The conditional-query arm reduces average query RMSE by about 14.93%. Its paired mean-squared-query-error improvement has a 95% percentile bootstrap interval of [0.7636, 0.8272] mm². 31.94% of individual episodes still worsen relative to history; this is an expected-value result, not per-update safety.

The conditional kernel agrees with a separately computed dense joint posterior to 1.93e-15 maximum absolute error. The correlation sweep retains the exact-replay zero-information endpoint.

Validation

Before push: 29 focused tests pass locally, including random correlated batch/sequential parity in every window order, singular repeated histories, exact object-identity preservation, no mutation after inconsistent replay, coordinate/unit invariance, deterministic constraints, and reproducible study decisions.

The hosted workflow additionally checks formatting, lint, typing, compatibility with the real existing observable-factor/query APIs, the existing observability regressions, and a full 10,000-episode reproduction. Repository-wide CI remains authoritative; no unexecuted integration or global test pass is claimed here.

Boundaries

• Experimental additive module; no stable exporter or production guard changes.
• Dense compressed-row implementation, not a large-stream performance result.
• Prior must not already have consumed these windows; every design must use a genuinely common chart.
• Cross-window covariance must be independently justified; missing covariance is not independence.
• No real-provider competence, physical-twin improvement, Causal4D benefit, calibration-transfer, or safety claim.
• Does not reopen any terminal MotionCrafter/CUT3R/Deform360 route or require new physical acquisition.

Paper-facing generated results and the exact source manifest belong in FlorianPfaff/BayesianPhysTwin-Paper.