integer.dag §2 remodel: derive all interval bounds from the width axis; decode chain -> roster fold

[gunbai-bot]

integer.dag §2 remodel — every interval bound derived, zero hand-spelled constants

The exemplar PR for the "reduce repeated patterns to folds/modeling" lane (operator request 2026-07-06). Survey of the ailment across the corpus (signature scan: dense constructor-list literals, numbered fn families, else-if chains, duplicate fn bodies modulo digits) ranked src/v2/std/integer.dag the top real offender (score 35: 9 dense digit-lists + 2 numbered fn families). The remainder class (authorization pending this PR): extdeps/languages/{rust,ecmascript,wasm,python}.dag (5–11 near-identical stamped fn bodies each), realization_width.dag, cpp_abi.dag, dag/std/integer.dag.

What dissolved

1. All 20 hand-spelled interval-bound constants deleted (2^7−1 … 2^128−1 as digit Cons-lists — int128's 38-digit magnitude spelled twice, ~8.7KB, 287 digit tokens). Every bound now derives from the width axis the Compose rows already declare: integer_machine_interval_spec(signedness, width_bits) = pow2 by repeated decimal doubling + sub_one by borrow fold. §5 upgrade: a transcription-wrong bound is now unwritable — nothing verified those digit strings before; now they cannot exist.
2. The 10-way decode if-else chain (from_node, each arm reconstructing a spec) → one fold over integer_standard_integer_type_roster (chain order preserved).
3. The 10-arm spec dispatch → derivation from the two irreducible axis groundings (signedness/width_bits tables — the name↔axis facts).
4. No re-invented digit tables: the arithmetic grounds in the existing decimal_digit_value bijection + two roster-fold inverses (decimal_digit_of_units, nonzero_decimal_digit_of_positive_units). All fns total; no impossible match arms (nonzero-ness carried structurally by NonZeroDoubleLead); no Outcome noise.

Honest size accounting

integer.dag: 782 → 946 lines (26.0 → 29.4KB). Hand-authored authority shrank massively (20 unverifiable constants → 0); raw lines grew because the file gains a genuinely new capability the substrate lacked: arbitrary-precision decimal arithmetic (double / sub-one / pow2 / canonicalize), ~200 lines, reusable (integer-literal rendering, emit lanes). integer.dag's repetition was constants needing an engine; the remainder files' repetition is fn-family stamping needing only dedup — those will show raw negative diffs.

Verification (all by execution, exact function named per receipt)

claim_batch --source-root src/v2 --entry src/v2/test/claim/integer/interval_derivation_test.dag --function <f>, release build @ afcbc5a, all PASS:

• interval_derivation_matches_all_legacy_spelled_bounds — the migration oracle: all 20 pre-remodel spelled bounds frozen VERBATIM as data rows in the witness; derived == legacy for all 10 specs (both bounds), 107ms.
• derivation_discriminates_planted_off_by_one — red control: a planted Int8 max=128 row is rejected (the oracle can go red).
• pow2_digit_shapes_hold — pow2(0)=1, pow2(7)=128, pow2(127) has 39 digits.
• interval_min_not_above_max_for_all_standard_types — roster property.
• from_node_round_trips_all_standard_types — decode(spec_node(t)) == Accepted(t), all 10.

Consumers re-run green on final tree: mvp_int_cross_target_coercion_test.dag::witness_cross_target_rust_i32_to_python_int_accepts (PASS, 7.7s — exercises Int32 bounds live through rust.dag emit + coercion_widening via the new derivation), staging_test.dag (5 PASS), byte_cardinality_grounding_test.dag (2 PASS). cargo test --workspace receipt in comment below.

Named follow-ups (not this PR, scope discipline)

• decimal.dag split: the decimal-numeral vocabulary (~330 lines) is §3-honestly its own std concept, but its compares need int_compare, which lives in integer.dag (importers: typescript.dag, swift.dag) — re-homing int_compare (algebra.dag beside Ordering/OrderedRing?) is a §3 placement decision to make first.
• rust.dag 12-arm interval dispatch collapse: blocked on the RustIntKind vs Signedness constructor-name collision (Signed/Unsigned both) — the Constructor-owner ruling (§1c): binding-edge resolution, collision wall, scan deleted — the engine PR #6235 wall forbids importing integer's constructors there; dissolves with the RustIntKind de-fork (31-duplicate census lane).
• The comparison band (integer_interval_bound_compare + pointer-width tables) was deliberately NOT refactored: pointer-width symbolic comparisons encode semantic choices (e.g. Signed×Unsigned ⇒ Less regardless of endpoint) that a rank-projection rewrite could silently change; behavior preservation wins.

🤖 Generated with Claude Code

[gunbai-bot]

CI red @ f1752a4 investigated — systemic compile-wall, no fix to push

Run 28805933233: rust_tests PASS (32m); sole red is the ci job's floor step "gunbc ci (.dag witnesses + gates)" killed at exactly the 135m step budget (16:19:01 → 18:34:14).

Step log breakdown:

• plan resolve: ~78m (batch walk started t+4670.5s)
• batch 1 of 5 (dag_compile_clean_gate): ~57m in-flight at kill
• zero witness/gate FAIL or Refused lines — the only error line is the GHA step timeout.

This is the same wall as every open PR and main today (compare #6314 receipt run 28798100556: 72m resolve + 51m batch-1). This PR's diff is not implicated; the f1752a4 head is just a main-integration merge picking up #6321.

Fix vehicles, both open: #6326 (interim floor budget 135→195, receipt-backed) and #6315 (structural: affected-set-scoped compile-clean gate). Note for the budget re-derivation: resolve on this tree is now ~78m (up from 72m), so the wall grows with the corpus — the structural fix remains the real dissolution.

No push; PR remains 2×-approved and mergeable.

[gunbai-bot]

CI red @ c82a8d3 (auto-refresh merge of main): ci job killed at 10m17s — the by-design #6323 job-level kill (operator re-ruling 2026-07-06), not a defect; rust_tests in flight. Correction to my previous comment: #6326 (interim budget raise) was closed as superseded by #6323; the remaining fix vehicle for the wall is #6315 (affected-set-scoped compile-clean) plus the census-cliff parse work. Under the era-4 regime this PR's merge basis is approvals on HEAD + rust_tests green + mergeable — ci will stay dark by design until the wall dissolves. No push.