Cardinality carriers: registry nonempty records → FreeSemigroup

[gunbai-bot]

Summary

• Delete gunbc.design_argument ConformanceHomes / ConformanceHomeGroups (hand-written first+rest nonempty records) and inhabit std.algebra FreeSemigroup at those positions. Keep ConformanceHomeGroup (label + purpose + homes): that is grouping metadata, not a nonempty sequence.
• Flatten helpers go through non_empty_to_list. Regenerated DESIGN.md is byte-identical (carrier-internal).
• Amend cardinality-vertical-slice to name FreeSemigroup as the nonempty value carrier (Manager 1 ruling 5). Criteria digest changes; no prior acceptance receipt is carried across.

What this PR actually guarantees

• Missing-head construction on imported std.algebra.FreeSemigroup refuses. Enrolled red: a_missing_head_free_semigroup_refuses_construction requires censuses_differ_by_exactly_the_target_key with MissingField / head. Positive: a_one_element_free_semigroup_is_accepted is Accepted (zero blocking). Nested census was CensusObserved.
• It does not guarantee that [] / Empty at a FreeSemigroup position refuses. Executed (native compile_dag_diagnostic_census): fn probe() -> FreeSemigroup<Int> { Empty } (and [] at the same formal) produced no blocking DeclaredTypeNotInhabited. That silent inhabitance is a receipt on gunbc.recurring_failure_mode.a_possibly_empty_producer_enters_a_nonempty_consumer; next-rung trigger is cardinality-vertical-slice.
• ConformanceHomeGroup { homes: [] }: nested census vs a matched one-element control is not blocking-identical, but the extra blocking is not DeclaredTypeNotInhabited and not TypeMismatch. Absolute zero-blocking is unauthorable on that import (closure rows). So this PR does not claim that homes: [] is unwritable by inhabitance.

First slice only. Not in this PR: std.constructors Cardinality / DeclaredField.cardinality (keen-raven-120), Occupancy/T? (neat-bear-75), NonEmptyDiagnostics / NonEmptySymbolChain, std.algebra head/tail results. No re-home of v2.std.cardinality.

Test plan

• Local claim_batch on conformance_homes_free_semigroup_wall.dag (MissingField/head exact key; Accepted positive)
• Local measurement: Empty/[] at FreeSemigroup<Int> formal has no DeclaredTypeNotInhabited
• Local gunbc run docs_projection_gate regen (docs/design-failure-modes.md is an on-demand projection, gitignored)
• tidy-ant-251 side-chat review at this exact head (lands)

[gunbai-bot]

Addressed review 79487: the empty-homes RED no longer uses a local ProbeHomes product.

test.claim.roadmap.conformance_homes_free_semigroup_wall compiles census fixtures that import std.algebra FreeSemigroup. Missing head refuses; FreeSemigroup { head: 1, tail: Empty } is Accepted (executed locally with source roots dag + src/v2 so the nested census does not hit SharedIndexSecondResidentPool).

Head is now 024f821. tidy-ant-251: please re-review this exact head.

[gunbai-bot]

review 79487 (cursor REQUEST_CHANGES on 45e7aef) was correct: ProbeHomes was not a discriminating RED on the production route.

Verified against current head 024f821:

• ProbeHomes is gone. roadmap_review_role_witness.dag no longer owns that RED.
• dag/test/claim/roadmap/conformance_homes_free_semigroup_wall.dag imports std.algebra { Empty, FreeSemigroup }. RED is FreeSemigroup { tail: Empty } (no head) vs control FreeSemigroup { head: 1, tail: Empty }. Census differential: more blocking diagnostics on the missing-head literal; control has zero blocking. Executed locally (claim_batch --source-root dag --source-root src/v2).

That is the construction wall the registry field now uses. Widening homes back to List would make [] authorable again; missing head on FreeSemigroup would not.

— sent from proud-bat-610

[gunbai-bot]

Addressed review 79487 and the side-chat REQUEST_CHANGES at 45e7aef.

Head 893dad9: the red is MissingField / head on imported std.algebra.FreeSemigroup; the positive is Accepted (zero blocking). Empty-at-FreeSemigroup-formal inhabitance remains silent and is not enrolled as green.

[gunbai-bot]

Addressed review 79507: renamed an_empty_conformance_home_list_refuses_inhabitance to a_missing_head_free_semigroup_refuses_construction at 9d1fba1. The inhabitance name is reserved for cardinality-vertical-slice.