feat(std): T-Numeric-Construction Slice 3 — Int = AbelianGroup<GroupCompletion<Nat>>

[briansrls]

Summary

T-Numeric-Construction Slice 3 (R3 lane #6, dispatch on inbox #1288 #4362239705). Pivots the default Int alias to the canonical Q6 single-authority form per the audit at docs/audit/t-numeric-construction-group-completion-6q.md. Builds on the now-merged GroupCompletion<M> substrate carrier (#1448) plus Slices 1/2 (#1378, #1399).

Construction-chain progression

Magnitude → Nat = Semiring<Magnitude> → Int = AbelianGroup<GroupCompletion<Nat>> → ...

What changed

dsl/std/integer.dag:45

-type Int = Int64
+type Int = AbelianGroup<GroupCompletion<Nat>>

Plus imports for AbelianGroup/GroupCompletion (from std.algebra) and Nat (from Slice 2's std.nat). Header MODELING NOTE updated to document the construction-chain pivot and the Q6 single-authority resolution.

Type-correctness under standard parametric reading

• T = GroupCompletion<Nat> — opaque atom denoting "the abelian-group carrier derived from Nat via the Grothendieck construction." Substrate-introduced in feat(std): GroupCompletion<M> opaque-atom substrate-introduction #1448.
• AbelianGroup<T> over that carrier types inverse: fn(GroupCompletion<Nat>) -> GroupCompletion<Nat> — honest by construction (every element of the group-completion carrier has an additive inverse). The earlier rejected AbelianGroup<Nat> form was M9-false because Nat's elements have no additive inverses; the carrier-construction layer fixes that.

What did NOT change (per dispatch guardrails)

• Fixed-width rows intact (Int8..Int128 = OrderedRing<Word*>, UInt8..UInt128 = Semiring<Word*>).
• UInt = UInt64 alias unchanged (per design doc §6 cascade scope).
• No quotient-of-pairs or sign-magnitude representation facts.
• No tokenizer / LitInt / literal-grammar / refinement-syntax work.
• Word* storage carriers stay storage refinements at dsl/std/bit.dag — not alternate Int/Nat/Magnitude/GroupCompletion authorities.
• No consumer migration of legacy chain.

Downstream impact verification

The dispatch's STOP+PING condition was: "if changing the alias triggers broad consumer migration beyond ratchets/generated outputs." Verified locally on the full integration suite — only 2 tests were affected by the alias pivot, both within "ratchets/generated outputs" scope:

1. m1_substrate_test::bootstrap_int_add_walk_reaches_ordered_ring_add_nobody_arrow — legacy Int → OrderedRing ratchet. Repointed to walk Int64 directly (the OrderedRing<Word64> chain it structurally tests now lives at the fixed-width row, not the default alias). Renamed to bootstrap_int64_add_walk_reaches_ordered_ring_add_nobody_arrow. The default-alias ratchet now lives in int_default_alias_resolves_to_abelian_group_over_group_completion_of_nat (new, see below).
2. parse_stage4_prep::handwritten_parse_snapshot_matches_manifest — integer.dag byte/hash drift from the alias edit; refreshed via refresh_handwritten_parse_snapshot_manifest.

Final: 740 passed / 0 failed / 26 ignored in the integration suite; 225 passed in lib; clippy clean; fmt clean.

New ratchet

src/v3/compiler/tests/integration/m2_substrate_inhabitance_test.rs::int_default_alias_resolves_to_abelian_group_over_group_completion_of_nat:

• Pins Int.span.file == "dsl/std/integer.dag".
• Walks the alias chain (cycle-bounded, max 8 hops).
• Asserts the outer instantiation is AbelianGroup (NOT OrderedRing/Int64, NOT the rejected compact GroupCompletion<Nat> form, NOT a Word* storage carrier).
• Asserts the carrier argument is itself an Instantiation { template: GroupCompletion, arguments: [Nat] } — proving the two-step construction.

Files

• dsl/std/integer.dag — alias pivot + header update.
• src/v3/compiler/tests/integration/m2_substrate_inhabitance_test.rs — new structural ratchet for the canonical Slice 3 form.
• src/v3/compiler/tests/integration/common/substrate_receipts.rs + m1_substrate_test.rs — repurposed legacy receipt to walk Int64 directly + renamed test.
• src/v3/compiler/tests/integration/parse_corpus_manifest.txt — refreshed.
• src/v3/compiler/src/bootstrap_{std_,}generated{,_without_parse_surface}.rs — regenerated.

Test plan

• cargo run -p v3-compiler --features bootstrap-regen-fresh --bin regen_bootstrap (clean).
• cargo test -p v3-compiler --lib -- --skip execute_command_timebound (225/0).
• cargo test -p v3-compiler --test integration (740/0/26 ignored).
• cargo clippy --all-targets -- -D warnings clean.
• cargo fmt --all --check clean.