docs: Phase C deferred (2026-05-28) — option (c) analytical infeasibility - #199
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Records the 2026-05-28 finding that Phase C's structural admits at
`Semantics_L1.v:553/621` are not closable via any of the four design
paths surfaced in the prior session:
(a) Permutation-based perm-l1 — concrete output-list-structure
mismatch (R_body = [a; rr; b; c] vs R_body' = [b; rr; a; c]);
(b) multiset reformulation of remove_first_L1 — cascades through
every L1 rule's output threading;
(c) T_Region_*_L1 rule redesign — implemented in-flight on this
branch (TypingL1.v + Counterexample.v + count_occ_le_l1_m
successfully migrated to a Permutation premise), closes the
sub-sub-case where R has exactly one rr via count-vacuity,
BUT sub-sub-case where R has ≥2 rr requires body-input-
shrinkage which is NOT a theorem (T_Loc_L1 counterexample at
count=1; T_Let composition is unstable for the count-≥-2
precondition);
(d) defer — selected as the most mathematically safe + elegant.
The (c) experimental changes have been reverted; the 10/10 .v rebuild
is clean against the original rules with 2 documented admits at
553/621.
Phase D (L2 effect-typed TFun) is the natural setting: the lambda
body's R-flow becomes effect-typed, providing the structural
invariant that lets body-input-shrinkage discharge naturally. Both
Phase B Slice 1 and Phase C will land cleanly post-Phase D.
PROOF-NEEDS.md adds a near-term deferral row for Phase C alongside
the existing Phase B Slice 1 row.
STATE.a2ml records Phase D as next_action with cross-references to
both deferrals.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
hyperpolymath
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May 28, 2026 09:07
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Summary
Semantics_L1.v:553/621are not closeable via any of the four design paths surfaced in the prior session.proof/phase-c-l1-multiset-bridgebranch — TypingL1.v rules + Counterexample.v regression +count_occ_le_l1_mPermutation-bridged — but proven analytically to close only sub-sub-case (ii) (R has exactly 1 rr via count-vacuity) while leaving sub-sub-case (i) (R has ≥2 rr) requiring body-input-shrinkage which is NOT a theorem (T_Loc_L1 counterexample at count=1; T_Let composition unstable for count-≥-2 precondition).What changed
PROOF-NEEDS.md— adds a near-term deferral row for Phase C alongside the existing Phase B Slice 1 row..machine_readable/6a2/STATE.a2ml—next_actionmoves to Phase D (L2 effect-typed TFun) with cross-references to both Phase B + Phase C deferrals.Why option (d) defer was selected
Admitted.at 653 +preservation_l3cross-layer annotation continue to attribute the gap correctly to a pre-existing L1 obligation.Test plan
coqc 8.18.0rebuild — 10/10 .v files clean (no new admits/axioms)formal/PRESERVATION-DESIGN.md §5.1)🤖 Generated with Claude Code