Incomplete references leave bulk deconvolution targets non-identifiable, but identification has a computable precision price

Key results

1. 01

   ShownOn an identical reduced reference and bulk, carrying operator state learned on the full reference (frozen) versus re-learning it (refit) yields different compositions, attributable solely to re-learned state; neither path is consistently closer to orthogonal imaging truth.

   Frozen-refit total-variation distance exceeded 0.1 for 28.2% of 196,420 sample-deletion pairs; locking all learned components gave zero difference in 32 of 32 conditions. Against Huuki-Myers RNAScope/immunofluorescence composition, 13 of 24 prespecified contrasts excluded zero (10 frozen, 3 refit); astrocyte deletion favored frozen for Bisque in the Total×RiboZeroGold stratum (+0.044, 90% CI 0.035 to 0.050). · Fitting and deleting do not commute; Against orthogonal measurement, path advantage…; Estimators and operator states; Imaging-benchmark evaluation (Huuki-Myers DLPFC)

2. 02

   ShownSwitching operator history alone reverses the sign and significance of associations between estimated proportions and disease phenotypes in real cohorts, by amounts comparable to or larger than sampling error.

   In nine cohorts, 160 of 952 frozen/refit association pairs had opposite signs (31 with a significant path) and 126 changed significance; monocyte/macrophage vs COVID-19 was positive on frozen (FDR = 0.030) and negative on refit (FDR = 0.006); 220 of 952 between-path 95% intervals excluded zero; over 392 pairs, median |Δβ| was 0.52 times the frozen-path standard error (3.9 at the 90th percentile). · Operator history reverses cohort associations; Real-cohort associations; Between-path inference in real cohorts

3. 03

   ShownEven with the operator fixed, the observed bulk and incomplete reference do not point-identify the retained-type composition: at an explicit observation, exact completions realize every retained composition in the open simplex, and no observed-data rule picks the closer history uniformly.

   Exact witness (3 features, 2 retained types): two completions reproduce the bulk exactly yet give (3/5, 2/5) vs (3/10, 7/10). Theorem 1 extends this to the whole open simplex (condition number at most 1313/485); Theorem 2 gives minimax regret δ = 3/10 for deterministic selectors; 80 exact checks. Five diagnostics had AUC 0.445 to 0.574 for picking the lower-error path in 400 synthetic dictionary instances. · The full-reference target is not…; Synthetic deletion spectrum; Two-completion witness and theorems

4. 04

   ShownAdding uncalibrated views, finite profile libraries or exact RNA yields either leaves the identified set unchanged or narrows outputs while losing coverage; calibrated cross-modal anchors narrow width with coverage but yield no valid sign certificate.

   Uncalibrated views (one to six preparations) gave identical width 1.0000. Profile library: 98.93% contraction, 42.77% coverage of the full-reference effect (355/830), 19 wrong-sign certificates; conditional sharp bounds stayed [−1, 1]. Exact RNA yields covered 0 of 7 flow targets (CIBERSORT false certification 71.43%). Six anchored types cut width to 0.5067; none of 231 grid cells met both thresholds. · Proposition (shared completion structure); Contraction without coverage is false certainty; Three ceilings, and the measurement frontier; Multi-view and anchor analyses (Huuki-Myers)

5. 05

   SuggestedInverting the prespecified uncertainty model prices a decisive measurement: in blood, fixing the sign of T-cell fraction minus RNA contribution needs near-point joint precision, and direct mRNA-per-cell measurement across donors ranks ahead of deeper sequencing.

   Along the prespecified equal joint-scaling path, the sign requires total-RNA-to-mRNA proxy error within ±2.6% while 97.4% of the log-scale donor-heterogeneity and dynamic-range envelopes is removed; Shapley width shares: 60.1% donor/leaf heterogeneity, 33.6% proxy, 6.3% dynamic range; non-negative least squares (NNLS) needs a modeled 151, 381 and 25,168 donors at 0%, 2% and 5% systematic error, none at 10%. · Three ceilings, and the measurement frontier; A measurement contract, and what it costs to…; Precision inversion (absolute scale)