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Depth-bias response and ambiguity results

Protocol frozen at ae51adee. All 54 fits completed, including 36 perturbed trials and 18 separately counted truth-start controls. All 18 zero-bias result objects exactly reproduce the previous occlusion study. No fitted bias parameter, retries or saturation changes were introduced.

Injected depth bias Perturbed recovery Truth-start within gates Perturbed median rotation Perturbed median translation
0 m 12/12 6/6 0.1268 deg 0.0341 m
+0.25 m 0/12 0/6 0.3875 deg 0.2324 m
-0.25 m 12/12 6/6 0.2452 deg 0.0488 m

All trials

Scene Population Bias m Seed Rotation deg Translation m Pass Residual calls
original exact_z_visible +0.00 +1 0.2116 0.0488 True 187
original exact_z_visible +0.00 -1 0.1985 0.0471 True 144
original exact_z_visible +0.00 +0 0.1986 0.0471 True 220
original exact_z_visible +0.25 +1 0.4664 0.2625 False 292
original exact_z_visible +0.25 -1 0.5172 0.2660 False 187
original exact_z_visible +0.25 +0 0.4708 0.2624 False 189
original exact_z_visible -0.25 +1 0.3006 0.0658 True 252
original exact_z_visible -0.25 -1 0.3006 0.0658 True 164
original exact_z_visible -0.25 +0 0.3004 0.0657 True 184
original exact_z_all +0.00 +1 0.2116 0.0487 True 186
original exact_z_all +0.00 -1 0.2118 0.0487 True 173
original exact_z_all +0.00 +0 0.1980 0.0469 True 163
original exact_z_all +0.25 +1 0.5005 0.2634 False 168
original exact_z_all +0.25 -1 0.5629 0.2672 False 227
original exact_z_all +0.25 +0 0.4715 0.2624 False 245
original exact_z_all -0.25 +1 0.3573 0.0726 True 214
original exact_z_all -0.25 -1 0.3574 0.0727 True 168
original exact_z_all -0.25 +0 0.3573 0.0727 True 150
near_foreground exact_z_visible +0.00 +1 0.1219 0.0336 True 200
near_foreground exact_z_visible +0.00 -1 0.1218 0.0336 True 179
near_foreground exact_z_visible +0.00 +0 0.1088 0.0319 True 137
near_foreground exact_z_visible +0.25 +1 0.2940 0.2324 False 586
near_foreground exact_z_visible +0.25 -1 0.5751 0.2352 False 535
near_foreground exact_z_visible +0.25 +0 0.3326 0.2375 False 216
near_foreground exact_z_visible -0.25 +1 0.2451 0.0487 True 221
near_foreground exact_z_visible -0.25 -1 0.2456 0.0488 True 220
near_foreground exact_z_visible -0.25 +0 0.2450 0.0483 True 176
near_foreground exact_z_all +0.00 +1 0.1318 0.0347 True 163
near_foreground exact_z_all +0.00 -1 0.1318 0.0347 True 143
near_foreground exact_z_all +0.00 +0 0.1318 0.0347 True 145
near_foreground exact_z_all +0.25 +1 0.3086 0.2323 False 592
near_foreground exact_z_all +0.25 -1 0.4800 0.2287 False 167
near_foreground exact_z_all +0.25 +0 0.2985 0.2341 False 316
near_foreground exact_z_all -0.25 +1 0.2452 0.0488 True 278
near_foreground exact_z_all -0.25 -1 0.2452 0.0488 True 347
near_foreground exact_z_all -0.25 +0 0.2438 0.0485 True 205
staggered exact_z_visible +0.00 +1 0.0684 0.0234 True 213
staggered exact_z_visible +0.00 -1 0.0637 0.0228 True 220
staggered exact_z_visible +0.00 +0 0.0623 0.0227 True 183
staggered exact_z_visible +0.25 +1 0.2489 0.2237 False 432
staggered exact_z_visible +0.25 -1 0.1414 0.2235 False 233
staggered exact_z_visible +0.25 +0 0.1528 0.2272 False 574
staggered exact_z_visible -0.25 +1 0.1217 0.0243 True 130
staggered exact_z_visible -0.25 -1 0.1143 0.0263 True 150
staggered exact_z_visible -0.25 +0 0.1217 0.0243 True 94
staggered exact_z_all +0.00 +1 0.0724 0.0237 True 238
staggered exact_z_all +0.00 -1 0.0715 0.0235 True 216
staggered exact_z_all +0.00 +0 0.0714 0.0236 True 131
staggered exact_z_all +0.25 +1 0.2497 0.2237 False 334
staggered exact_z_all +0.25 -1 0.0793 0.2266 False 383
staggered exact_z_all +0.25 +0 0.1288 0.2233 False 264
staggered exact_z_all -0.25 +1 0.1229 0.0241 True 149
staggered exact_z_all -0.25 -1 0.1229 0.0241 True 165
staggered exact_z_all -0.25 +0 0.1229 0.0241 True 86

Interpretation

Positive bias is consistently absorbed into pose: the median camera-axis z translation error over perturbed trials rises from +0.0215 m (zero bias) to +0.2236 m (+0.25 m depth bias). All 18 positive-bias outputs fail the accuracy gates, including truth starts. Three reach max_nfev; the other 15 pass numerical convergence/support but remain inaccurate. Across all biases 51/54 converge; actual residual calls span 86–592, below 800. No failed fits were removed.

Negative bias instead gives positive depth residuals, whose influence the fixed visibility approximation suppresses. The twelve perturbed poses remain within gates, but their median rotation/translation errors increase versus zero bias. This is sign-dependent tolerance, not recovery of the missing depth correction. No bias value is estimated, and the one-sided residual cannot alone distinguish a camera-occluded point from a systematically underestimated depth.

Local identifiability diagnostic

The fraction of the bias Jacobian column unexplained by the six pose columns is 0.9539–0.9842 across all returned poses; none meets the preregistered <0.05 local near-confounding flag. The frontoparallel-plane unit control does expose exact axial-translation/bias degeneracy. On these sphere/plane layouts, raw supported residuals therefore have a locally distinguishable bias direction under this finite-difference model, even though the six-parameter optimizer displaces the pose.

These statements are compatible: the current optimizer cannot change a bias parameter and minimizes a one-sided, robustly weighted objective, not the raw Jacobian norm used by the diagnostic. Scene edges, bilinear sampling and active support can strongly affect local derivatives. This diagnostic does not establish global uniqueness, noise-conditioned bias precision or observability after robust weighting. Thirteen diagnostic residual passes per case are separate from fitting calls/time. Do not infer from a large unexplained fraction that bias correction is already safe to deploy.

Next decision

Proceed to a separately frozen experimental joint pose-plus-depth-bias fit, not production integration. Keep visibility treatment fixed, initialize correction at zero without exposing injected bias to the estimator, and include zero/positive/ negative bias, both signs and truth starts. Report estimated bias error and pose error separately; check both raw and actual robust-objective sensitivity. Include a plane-only degeneracy control and reject any claim of uniqueness there. Compare against this unchanged six-parameter baseline; do not use holdout labels to tune bias bounds or regularization. Zero-bias degradation, hidden behind-surface fits, and truth-start drift must remain explicit failure criteria.

The Japanese review at 780a61ea is a historical snapshot: its proposed stages A/B have now been executed here; stage C (joint bias fitting) remains unimplemented. The printed PDF is not silently rewritten as though these results were known earlier.

Evidence and schema contain all outputs, xyz errors, support/call counts, singular spectra and local projection coefficients. Nine focused tests, repository Ruff, strict docs build, source-hash checks, exact zero-bias reproduction and complete-denominator validation pass. No new real data, core/default change or SOTA claim.