Special Functions: autonomous projections, Block14
SF-LEAN-B14 proves the registered main H.1 operator theorem for positive scales, without assuming contraction or distinct scale nodes. A nonzero complex row has an arbitrary scalar functional of its projection on every zero-constant analytic input exactly when q=a, r=b and the row is gamma*(1,-1), gamma!=0. The projected field is zero. No invertible constant complex 2x2 change decouples the operator. Entire-function and actual local analytic-germ versions are both proved; no quadratic ansatz on the scalar functional is imposed.
There are 27 new theorem declarations, for 369 registered names. All 57 fresh verification steps pass across fourteen coupled modules: 330 theorem axiom audits, fourteen kernel replays, four expected rejections and one positive fixture. The finite core's 39-name evidence is inherited; pinned Mathlib imports are cached. Review provenance is self-review.
The report, claim map, review, source, I/O inventory and receipt bind the proof and exact replay. Formal I/O has 50 inputs, 58 packaged outputs, fourteen generated objects and 33 staging copies. The separate remaining-work assessment has 26 inputs and two outputs. Development diagnostics are separately identified and are not accepted proof evidence.
Replay tools/verify_coupled_operator.py under Special Functions with
Lean 4.34.0-rc2, Mathlib aeb72f1e9981b6d35b426b16dca7759be3e7ba06 and
a new external work directory. The verifier installs nothing and makes no
network request. Live continuation
and remaining work
retain the exact next targets and boundaries.
Next major target: Appendix J arbitrary-radius exact evaluation. Some F explanatory correspondence, H's odd-input-only/tensor variants, I's resolution mechanisms and broad A-E analytic development remain. Ordinary type convergence is conditional. No exhaustive whole-book correspondence or completion percentage is established. Earlier sources and evidence retain their bytes.