docs: seed docs/proof-debt.md per trusted-base policy (#148)

## Summary
- Seeds `docs/proof-debt.md` enumerating the 3 known `Admitted`s in
`formal/Semantics.v` (lines 4924, 5983, 6572) and their planned
discharge.
- Follows the schema defined by
[standards#203](hyperpolymath/standards#203)
(trusted-base reduction policy).
- Closes part of Item-3 follow-up of the 2026-05-26 estate tech-debt
audit.

## Entries (§(d) DEBT)
| File:line | Lemma | Plan |
|---|---|---|
| `formal/Semantics.v:4924` | inside `step_preserves_type` | Discharge
per `project_ephapax_preservation_closure_plan` (6-9 day plan, deadline
2026-09-01) |
| `formal/Semantics.v:5983` | inside `step_output_context_eq` |
Corollary of the strengthened `step_preserves_type` |
| `formal/Semantics.v:6572` | inside `preservation` (top-level theorem)
| Lands automatically once the two feeder lemmas close |

## What this PR does NOT do
Discharge the proofs. That's separate, multi-PR work owned by the
closure plan. This PR just makes the debt *visible* in the agreed schema
so it's countable and so the future `scripts/check-trusted-base.sh` CI
gate has something to validate against.

## Companion
- standards#195 — estate proof-debt audit (the empirical motivation)
- standards#203 — trusted-base reduction policy (the schema)

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: hyperpolymath

docs/proof-debt.md

@@ -0,0 +1,104 @@
+<!--
+SPDX-License-Identifier: MPL-2.0
+SPDX-FileCopyrightText: 2026 Jonathan D.A. Jewell (hyperpolymath)
+-->
+
+# Proof Debt — ephapax
+
+**Schema**: [hyperpolymath/standards `TRUSTED-BASE-REDUCTION-POLICY.adoc`](https://github.com/hyperpolymath/standards/blob/main/docs/TRUSTED-BASE-REDUCTION-POLICY.adoc) (standards#203).
+
+This file enumerates every soundness-relevant escape hatch in the ephapax
+codebase and its disposition under the trusted-base policy. Markers without
+an entry below count as undocumented debt and will be flagged by
+`scripts/check-trusted-base.sh` once that lands.
+
+Markers in scope (from the 2026-05-26 estate proof-debt audit,
+standards#195):
+- Coq `Axiom`, `Admitted`, `admit.`
+- Idris2 `believe_me`, `assert_total`, top-level `partial`
+- `TODO PROOF` / `OWED:` / `FIXME PROOF` markers
+
+## (a) DISCHARGED in this repo
+
+*(None yet — entries move here when their proof lands.)*
+
+## (b) BUDGETED — tested with a refutation budget
+
+*(None — ephapax's proof targets are deductive, not property-tested. Items
+in this section would belong here if/when we add adversarial-test budgets
+for the Rust↔Idris2 ABI boundary code.)*
+
+## (c) NECESSARY AXIOM
+
+*(None — ephapax does not introduce any irreducible metatheoretic axioms
+in the working Coq logic. If future work adds e.g. `funExt`, list it here
+with a citation to its canonical formalisation.)*
+
+## (d) DEBT — actively to be closed
+
+### `formal/Semantics.v:4924` — `Admitted` inside `step_preserves_type`
+
+- **Lemma**: `step_preserves_type` (declared at `formal/Semantics.v:3615`).
+- **Statement (informal)**: small-step semantics preserve typing.
+- **Owner**: @hyperpolymath
+- **Plan**: discharge as part of [project_ephapax_preservation_closure_plan](https://github.com/hyperpolymath/standards/blob/main/docs/audits/2026-05-26-estate-proof-debt.md). Estimated 6–9 days. ~40 goals split into sub-buckets A/B/C/D; start with A.
+- **Deadline**: 2026-09-01 (per closure plan).
+
+### `formal/Semantics.v:5983` — `Admitted` inside `step_output_context_eq`
+
+- **Lemma**: `step_output_context_eq` (declared at `formal/Semantics.v:4944`).
+- **Statement (informal)**: output context is preserved across a step
+  (modulo region marking).
+- **Owner**: @hyperpolymath
+- **Plan**: discharged as a corollary of the strengthened
+  `step_preserves_type` proof; depends on the preservation closure plan.
+- **Deadline**: 2026-09-01.
+
+### `formal/Semantics.v:6572` — `Admitted` inside `preservation`
+
+- **Theorem**: `preservation` (declared at `formal/Semantics.v:5985`).
+- **Statement (informal)**: the main preservation theorem for the ephapax
+  region-aware operational semantics.
+- **Owner**: @hyperpolymath
+- **Plan**: this is the top-level theorem the other two Admitteds feed
+  into. Discharge order: `step_preserves_type` first → then
+  `step_output_context_eq` → then `preservation` lands automatically
+  modulo wiring.
+- **Deadline**: 2026-09-01.
+
+## Soundness-relevant escape hatches in non-Coq code
+
+The 2026-05-26 audit also surfaced:
+- 1 `believe_me` reference (a comment in
+  `src/formal/Ephapax/Formal/RegionLinear.idr:127` explicitly stating
+  "This is a REAL proof — not (), not believe_me, not assert_total" —
+  no actual `believe_me` use; the comment is documentation about NOT
+  using it).
+- 1 `partial` (Idris2 totality waiver) — TBD if real or comment artefact.
+- 14 `TODO PROOF` / `OWED:` markers — these were not located in this
+  repo by the per-repo scan; they likely cluster around the same
+  Admitteds above.
+
+When `scripts/check-trusted-base.sh` lands, any genuine occurrence of
+the above will require either a leading `TRUSTED:` / `AXIOM:` annotation
+or a `§(d) DEBT` entry here.
+
+## How to update this file
+
+After each PR that closes one of the entries above:
+
+1. Move the entry from §(d) → §(a) DISCHARGED.
+2. Update the closure plan referenced.
+3. Run `git cliff --output CHANGELOG.md` to regenerate the changelog
+   (see [standards#206](https://github.com/hyperpolymath/standards/pull/206) for
+   the canonical workflow).
+
+## Companion documents
+
+- [standards#195](https://github.com/hyperpolymath/standards/pull/195) — estate proof-debt audit
+- [standards#203](https://github.com/hyperpolymath/standards/pull/203) — trusted-base reduction policy (the schema this file follows)
+- `project_ephapax_preservation_closure_plan` (maintainer memory) — 6–9 day discharge plan
+
+---
+
+🤖 Initial seed by Claude Code, 2026-05-26.