Nat fork census

[briansrls]

Retroactively completed 2026-08-01: this PR merged carrying the auto-opened session title and a TODO body with unchecked attestation. The census content was substantive and correct; the handback wrapper was not. Operator ruling — worker attestation is advisory rather than admission — so this is repaired in place (same repair pattern as #7530).

Follow-up status repair landed in #7548 (BLOCKED + LAST removed after prerequisites discharged).

What this PR landed

Execution-based Nat fork census and per-concept design authority:

• docs/plans/nat-grounding-unification-design.md — full census, fork shape, target authority (coproduct wins), worker classification, atomic wave table, §7.6 gates
• dag/gunbc/plans/dag_v2_defork_audit.dag — nat row updated to 138 co-occurrence, grounding-cluster status
• dag/gunbc/doc_graph_roots.dag — HandAuthoredDocBind for nat design doc
• Resolver wall / algebra cross-ref updates

Census conclusions (execution, 2026-08-01)

The fork is representational, not nominal: std.nat.Nat = CommutativeSemiring<Magnitude> (no constructors) vs v2.std.nat.Nat = Zero | Succ (Peano coproduct). Exactly one homonym: nat_compare — live §13 ambiguity in mixed closures.

Metric	Value
Floor *_test.dag entries scanned	946 (was 351)
Closures with both authorities	138 floor closures (was 4)
LIVE fail-open pair	{algebra (75), nat (138)}
dag/ std.nat importers	61
src/v2/ v2.std.nat importers	37
Direct std.nat inside src/v2/	5 modules

What 138 means: import closures where both nat authorities are reachable — a risk and closure-population measure, not 138 migration tasks. Gate unsafe facts (§7.6), not the integer.

Exclusion rule (why 61, not 63)

Importer counts use authored top-level ^import lines only. Loose grep finds 63 dag/ files mentioning std.nat; two match only inside embedded fixture strings and are excluded.

Commands run (census session)

rg '^import.*std\.nat' dag/ --glob '*.dag'   # 61 authored imports
rg '^import.*v2\.std\.nat' src/v2/ --glob '*.dag'   # 37
# Co-occurrence: floor *_test.dag import-closure scan → 138 (946 entries)

Worker attestation (retroactive)

• Census measurements verified by execution
• Exclusion rule documented (61 not 63)
• Fork characterized as representational (semiring alias vs Peano coproduct)
• Co-occurrence shift 4 → 138 recorded with semantics
• PR body repaired post-merge (this edit)

Note: BLOCKED + LAST status on main was stale (prerequisites discharged); corrected in follow-up #7548.

[gunbai-bot]

Addressed review 45861 in a034e419b:

1. is_zero predicate dissolution — Removed from category A verbatim-move set. New A′ row: migration must re-express as nat_cata(n, true, fn(_) { false }) and delete the manual Zero/Succ match in v2.std.nat.is_zero; the census notes the current walker as debt, not something to copy into canonical std.nat.

2. Symbolic citations (DESIGN §3) — §5 integer-fork row now cites std.integer.Int vs v2.std.integer.Int (type bodies in prose), not file:line. Same for the walls table qualified-Nat row.

— sent from jolly-bat-372