Add exact scalar-shadow row update lemma

[1337isnot1337]

Result

Adds StreamShadowRowUpdate.S_append_event, a kernel-checked recurrence for one row of Lemma G's scalar-shadow matrix after appending any one event. It covers all five constructors: relabel (unchanged), add (target row plus the scaled source row), scale (scaled target row), copy (source row), and clear (zero row). scalRun_append proves the event-order composition used in the recurrence.

Exact scope

The theorem holds for every finite event prefix, event, row and column, with [DecidableEq ι] and [Semiring K]. It does not assume a field, commutative coefficients, finite registers, label admissibility, exact recipes, or a selected-word hypothesis.

This is an interface lemma only. It proves no unit-row certificate hS for an emitted helper and changes no selected exponent κ.

Verification

From research/stream-shadow-row-update/:

python3 verify.py

A clean replay with Lean 4.21.0, Mathlib v4.21.0 and a fresh cache completed lake exe cache get, lake build, and lake env lean PrintAxioms.lean. The axiom probe reports that scalRun_append depends on no axioms and S_append_event depends only on propext and Quot.sound, both allowed by the repository policy. The package metadata and commit-byte checks also pass. No numerical evidence is used.

Remaining gap

To obtain a concrete hS, bind one complete, source-pinned emitted helper's serialized events and ordering to Lean Event values, then fold this recurrence and prove the final row is the basis row. The serializer-to-Lean binding and the helper's recipe/footprint obligations are not established here; the global multiplication bound remains open.

Provenance

The scalar-shadow semantics are from Lemma G in PR #484. The relevant source and selected-result inputs are pinned in SOURCES.json. Prepared by 1337isnot1337 with OpenAI Codex assistance; no independent human review is claimed.