| # Mathematical inventory | |
| The standalone manuscript retains P1–P15 from v2 with the recorded regularity corrections. | |
| Their original index is `history/v2/THEOREM_INDEX.md`. The six new propositions are in | |
| Section 19.9 and `docs/INNOVATION_THEORY.md`: | |
| | ID | Result | Status | Essential limitation | | |
| |---|---|---|---| | |
| | C1 | Simultaneous covariance contraction after exact support removal | Proved | Same control/proposal comparison; exact current facts | | |
| | C2 | Sequential causal correction and covariance decomposition | Proved | Fixed budget; frozen scene; no same-draw fitting | | |
| | C3 | Motion/spatial visibility certificate | Proved in real arithmetic | Opaque indexed spheres; correct motion bounds; numeric kernel not formally verified | | |
| | C4 | Query count bounded by new unknowns and invalidations | Proved | Finite deterministic domain; no duplicate queries | | |
| | C5 | Deterministic direct-light output enclosure | Proved | Valid binary visibility facts and known nonnegative coefficients | | |
| | C6 | Arbitrary predictions cannot uniformly dominate raw sampling | Proved counterexample | A limitation, not an impossibility of useful learned priors | | |
| Total: 21 scoped results. These labels do not establish historical novelty. Core probability | |
| identities, control variates, visibility caching and certificate-based geometry have prior art. | |