research: independently audit L22 union prune on tiny domain

[1337isnot1337]

Summary

Adds an independent exhaustive audit of PR #3818's partial union-support
completion bound at (n,L)=(4,8). The verifier scans the full unpruned domain,
checks every canonical restored completion at every prefix, and compares the
surviving universal words with the unpruned set.

Result

• All 4^8 = 65,536 raw label words were scanned; 105 canonical restored
  words remain.
• All 26 unpruned universal words survive the proposed bound.
• Across 840 prefix/completion checks, 227 target/prefix pairs fail the
  completion-capacity condition; none has a universal completion.
• The exact PR Strengthen the length-22 seven-label census with a union-support budget; exclude the (9,9) split (no new kappa) #3818 engine at head
  e09a08b5f85e648be373bece1b6ea1265d5ea8fa was also compiled at N=4,L=8.
  In union-only mode its split (4,4) hit set exactly matched the independent
  unpruned set: 22 universal words.
• The 01021323 control reconstructs the old false-prune: bit-0 excess 8,
  invalid balanced budget 5, valid actual-size budget 9.

The argument behind the bound is that each future same-parity pair can add at
most one new nonzero even mask. A universal completion needs all
2^(n-1)-1 such masks, so the current union plus the maximum number of future
pair incidences is an upper bound on attainable support.

Separate source observation for PR #3818

In the same exact-source check, union-only mode reports
all_restored_leaves=22 although the unpruned (4,8,4,4) domain has 27
restored words; five are removed by the union budget. The JSON writer fills
that field when the two older budgets are disabled, even though the union
budget remains enabled. The full --no-budgets control correctly reports 27.
This package does not edit PR #3818's source; please correct that field's
enablement condition before relying on it as an unpruned count.

Reproduction

python3 -B scripts/research_package.py --package research/f7-l22-union-prune-audit --check-only
python3 -B scripts/research_package.py --package research/f7-l22-union-prune-audit

The second command prints PASS_F7_L22_UNION_PRUNE_TINY_EXHAUSTIVE and
PASS_REGISTERED_RESEARCH_PACKAGE. Full details and source pins are in the
package README and SOURCES.json.

This establishes finite evidence only. It does not replay PR #3818's seven-
label (9,9) L22 exclusion or certify the other five L22 node floors. Credit
Ross Richardson, Aaron Wang, Nicholas Stone and Nick Petalas for the model and
predecessor work. This audit used substantial OpenAI Codex assistance; no
formal proof-kernel or independent human review is claimed.

Current overlap

Open PRs #3699, #3708 and #3733 cover seven-label or length-22 functional classification. This package stays on PR #3818's (n,L)=(4,8) domain and independently checks its tiny union-pruning result, including the recorded reporting-field defect. It claims no f(7) bound.

Publication validation

python3.12 scripts/research_package.py --package research/f7-l22-union-prune-audit passed on CPython 3.12.3, and python3.12 scripts/check_research_commit.py --package research/f7-l22-union-prune-audit --check-source-history passed. The registered replay left the worktree clean. This supersedes any earlier pending note above for the registered package replay; separate full selected cold-replay limits remain as stated.