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mathematics
inverse-problems
observability
noncommutative-algebra
symbolic-computation
calibration-rigidity
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Claim ledger — v3.0.0
“New candidate” means developed here and not matched by the targeted comparison. It does not certify worldwide priority. The manuscript contains full mathematical hypotheses and proofs.
| Result | Mathematical scope | Status |
|---|---|---|
| Restricted-block row ideals | Exact direct-sum row module and supported generators | Retained candidate operational integration |
| Finite analytic ideal realization | Prescribed generators explicitly stored in coefficients | Retained construction; not free computation |
| Arc-blind examples | Same arc orders, different ideal membership | Observation realization of an established algebraic distinction |
| Elliptic m-fold point | Second-deficit axes-plus-diagonal curve | Known geometry; Smyth/Stevens credited |
| Third-deficit classification | m >= 6, independent parameters, reduced analytic germ near exterior point | New candidate theorem with proof |
| Six-channel threshold | Dense rational m=5 counterexample | Exact counterexample |
| Intrinsic linear rigidity | Aut_lin(Z_m) = C* x S_m | New candidate theorem with proof |
| Selected-component budget | ceil(2(m-1)/3) whole twin constraints | New candidate sharp theorem; not sample complexity |
| Full-state rank loss | Exact indicator formula; double-star locus | New candidate consequence with proof |
| Scalar certificate algorithm | O(m^4) exact rational scalar operations | Proven algorithm; bit complexity excluded |
| Core-capacity law | Generic rank for arbitrary core size and r >= 1 | New candidate model-specific law |
| Analytic feedback factorization | Complete joint analytic frame, finite analytic transcript | Explicit theorem under restrictive hypotheses; not a universal claim about adaptivity |
The all-size results are supported by written mathematical arguments. The 1,028 test cases and the two enumerations do not independently certify all analytic proofs. No theorem is counted as globally original merely because its notation or project name is new.