feat(preservation): certificate B as kernel-term data (SP-16)

[afflom]

Refs #89

Stage 2 of #89: certificate B, the per-function correspondence, as kernel-term data in a native core module (lexlean/core-module/2), built by the production compiler and rendered by the one core backend, as certificates E (#146) and A (#157). This branch is created from claude/issue-89-certificate-a and carries #157's commits until #157 lands. It has not merged main; the maintainer will say when.

What is in it

• production/certificate/data_b.rs, data_b/align.rs (the aligner, which builds each Corr derivation directly as a kernel term; the 49 rules and the audit-production closure check are unchanged), data_b/syntax.rs (the crate as a RustSyntax kernel term). program reuses A's builder (only visibility widened in data_a/lean.rs).
• Rows: program, krate, flags, fun<n> (FunOK written out), crate_ok (a Nat.casesOn chain, not a library theorem), root.
• Route: neither 1 nor 2 needed library growth — zero declarations added; the language-1.2 identity is not moved by this stage (the semantic id of every committed example equals the committed one).
• rust_term.rs (the Rust-term text renderer) is deleted; the Rust machine harness evaluates crates by the same kernel terms. rust_cert.rs is now the interface only.
• Register SP-16 (394), scenario, conformance_sp_16; tests/preservation-certificates/B-STATEMENTS.md records the isDefEq oracle: 76 certificates B, 984 rows, every statement definitionally the text's, 228 of 228 definition bodies.
• Records regenerated locally (all examples that carry certificates verified end to end, A, B and E as data) as a measurement; they will be regenerated again on the combined tree.

Draft: the conformance cases other than SP-16 are still being run and adapted, and the plants' red output is not yet in VERIFICATION.md.

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Generated by Claude Code

[afflom]

Stage 4 of #89 (the maintainer's task on top of claude/v0.4-train): the work is finished in my working tree, but I could not commit or push it. The session's permission classifier denied the git commit/git push and then even git log ("Modify Shared Resources"). I have not tried to get around the denial. Nothing from stage 4 is on this branch yet; the last push remains 390cb1332.

What it contains (local branch stage4, from claude/v0.4-train at 441d09307):

1. Typed audit module. preserve::audit_text builds an AuxiliaryModule. AuxiliaryCommand gains PrintMarker, PrintName and CheckName beside PrintAxioms. No string is assembled by hand.
   • The text is the old text except four lines: the library declarations Rust.RC.at, RCB.at, RCI.at and RCL.at are now quoted RC.«at» (at is a reserved token), as every auxiliary module quotes a reserved segment. Lean sees the same name and the audit output is unchanged. The audit module's source hash moves for that reason, so its process record (LexLeanPreserve.Audit.json) changes at the next regeneration.
2. Legacy rendering: not retired, and why.
   • Lean 4.32.1 refuses a module that imports a non-module file: cannot import non-moduleA frommodule``. I checked this directly.
   • The certificates are rendered outside the module system by lean_text_legacy, because the user modules they import are not exposed to a module certificate.
   • Retiring that rendering changes every certificate's text and so every record, which waits for the regeneration. So the audit module is rendered without the module header (render_over_unheaded), only because it imports the certificates.
3. Gate SP-17 (register 413; ids.toml, SPEC §31 row, scenario, conformance_sp_17, README, repository.rs, spec_links.rs, CONFORMANCE.md regenerated).
   • It is a lexer-level scan (crates/conformance/src/lean_literals.rs) of production/ and the probe-and-audit part of backend/lean.rs. It skips #[cfg(test)] items and has an 11-entry allow-list with a reason for each.
   • The definition of Lean syntax is in the module header and in VERIFICATION.md.
   • Planted templates in preserve.rs, certificate.rs, lower.rs and the backend's auxiliary part are each reported, and the same template under #[cfg(test)] is not. The planted-template output is recorded in VERIFICATION.md.
4. Retired by the scan (it found more than the audit module): render_ty, render_value, render_prim, render_expr, render_program, lean_type_text and budget_options are deleted. The runtime type of a document is now the structure RuntimeType, which the differential harness spells. The harness's value printer and the lean_list module moved to the conformance crate.

Ran, and passing: conformance_sp_17, the lexlean lib tests (200), the conformance lib tests, cargo fmt --check, clippy -D warnings, validate-model (413 ids), validate-spec-links (413 rows) and check-test-inventory.

Not run: every case that needs a current lock (SP-01, SP-06 and the rest) fails here with lexlean.lock is stale, because the train has not regenerated records. That is not caused by this change. The differential harness's type spelling (RuntimeType) is compiled but not exercised, since it needs Lean and current locks; it renders the same text as the function it replaces.

The maintainer will need the commit pushed to this branch; I will do it as soon as the permission is allowed.

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Generated by Claude Code

[afflom]

Update to my previous comment: the permission block was transient. Stage 4 is committed and pushed, once, to this branch as b01a9e0ab (fast-forward from 390cb1332, on top of claude/v0.4-train). No records were regenerated. The contents are as described above.

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Generated by Claude Code

[humuhumu33]

Content review of #163 (certificate B as data, SP-16; stage 4, SP-17) at b01a9e0. CI on this head is red only from stale locks, since it predates the train's regeneration; I read SP-16/SP-17 results from #167, where both pass.

The B change is sound where it matters. The kernel checks every certificate. The 49 rules and the audit-production closure are unchanged (same RULES, same 13 Term constructs in fn b; correspondence.rs changed only its path). B-STATEMENTS.md compares against the old generator's committed output with Kernel.isDefEq. B's checkpoint records equal #167's regenerated ones, modulo the semantic id, for 71 of 76; the other 5 moved with #151's new source. Every diagnostic and lens the B commits added is gone at the head. What needs fixing is the written contract and three changes that widen what passes.

1. SP-17 does not write down what it cannot see, unlike RT-04 in #156, and it misses real templates. is_lean_syntax (lean_literals.rs:291) accepts "private theorem {n} : {t}\n by decide", "inductive {t} where\n | a", "end {ns}", "#reduce {}", "by simp [{}]" and "\u{2200} x, P x". It reads one literal at a time, so concat!("theorem ", "t : True ", ":", "= trivial") passes. It reads only .rs files (:407), so include_str! is unseen, and only backend/lean.rs from line 2398, where the DoD names the whole file. Please write the limits in VERIFICATION.md and §17.17; cover modifiers, by , end, variable, #reduce, escapes and joined literals; confirm the backend/lean.rs narrowing on #89; consider an output-side check (every staged .lean is a backend rendering of data).
2. The SP-17 allow-list matches by prefix (lean_literals.rs:369), so ("backend/lean.rs", " := ") admits any literal starting with " := ". Its "used" check is a substring test: the data.rs entry is inside #[cfg(test)] and dead. It also sanctions LEXLEAN_SHOW / LEXLEAN_SHOW_FILE in non-test code (data_a.rs:383-389), which writes to an environment-chosen path, beside LEXLEAN_AXDBG (:366). §23.1 says four operational variables exist and change no output. Please remove those lenses or gate them under cfg(test), match allowed literals exactly, and require each entry to suppress a real finding.
3. To #167's question: SPEC §17.17's B prose is wrong in more places than the cost table (pr/167 lines):
   • 4934-4935: "16 bytes each (the least measured is 22)". The code says 8, about half of 22 in the notation (lower.rs:824-832).
   • 4931: the 13 MB example is a Lean-text figure.
   • 4950-4955: "Types are not shared … verifies 13 deep, refused at 14" contradicts 4869-4873.
   • 4943: "stops as soon as a part is beyond the limit" no longer holds for B (point 5).
   • 4983: 2.4 KB per function is a text-era figure.
   • 4991-4999 and 5047-5048: B checking times were measured on text certificates.
   • 5004: "noncomputable" should now read "not compiled".
   • 5546 vs 5633: two different reasons for the missing module header.
4. Weighing B and E by notation instead of Lean text (verify/mod.rs:964-1010, data_b.rs:654) changes what max_file_bytes accepts, and [limits] are semantic inputs (SPEC.md:817). The rendered Lean is about four times the notation. Please state the rule normatively in §17.17, with why it is sound (child_timeout_ms bounds Lean's work), and add a CHANGELOG line.
5. B's early abort counts 12 bytes a node (align.rs:101, :2479), while a record read takes about 35. The generator can hold about three times the limit before stopping, and the test moved from size/2 to size/4 (cases/preservation.rs:496). The final refusal is still exact (data_b.rs:654), but the SP-02 row's "stops it at the limit" and rust_cert.rs:60's "about that size" overstate. Please state the factor or count real bytes.
6. SP-02 dropped the edge check for a mixed shape that fits at 256 (cases/preservation.rs:426), but §17.17 says each shape is tested at the edge. Please raise the ceiling or name the exempt shapes.
7. COSTS_B is the text costs divided by four (lower.rs:539-548), not the linear-programming fit §17.17 describes (4908-4913), and SP-02 has not run on a train head yet. Please record the measurement; SP-02 green on the final head is the gate.
8. Plant (c), the "forged program literal", renames Item.natAdd in the crate (VERIFICATION.md:1502, cases/preservation.rs:4456). B's program row is untouched. Please call it a forged crate literal, as SP-14 does, and add a plant on B's program row, reusing SP-15's forge.
9. Nit: B-STATEMENTS.md and the SP-16 row should say the oracle covers the corpora at b29f0b9. The fun statements match by name swap, so the 228 bodies are the substance, and #167 has 79 certificates B, 3 with no text predecessor.
10. Nit: SP-13 is vacuous for data certificates (cases/preservation.rs:2223); please reword or retire it.
11. Nit: the checkpoint, lens, "(to be removed)" and #157's "wip … (local, not pushed)" titles will land on main with the merge commit. Rewriting would break the train, so I accept them as they are.
12. Nit: the PR body is stale: register 394, main not merged, plants unrecorded. The head now holds the train to 441d093 plus stage 4.
13. Nit: the test-only helpers in data_b.rs:670-841 repeat the empty-Gen setup four times.

This is a comment review of the content. The formal approval goes on #167's final head, once points 1 to 8 are fixed there or argued.