[pinterbanget]

Summary

This adds research/pr4436-direct-flow-check/. It is an independent check of zxv's #4436 §2: the partially matched integer lockstep flow for overlapping ranks. Unmatched issued jobs become paid boundary exits, and absent parents are supplied by sources.

Claim type: an independent re-implementation checked against #4436's recorded flows, plus exact recurrence values. No new κ.

Results

• Recorded flows. All 9 of Bound compiler width by exp(O(N log N)) and route overlapping ranks #4436's finite flows are reproduced exactly by separate code: separated control, strict overlap and source-open equality, each at n = 20, 40, 80. That covers sources, exits, boundary exits, column mass, units and matched jobs.
• Raw p7, every rank 121 ≤ N ≤ 1000. Sources lie in (N/m, N], exits are below N, and the exact potential identity Σ S s − Σ X e = 608 × (column mass) holds.
• Exact L(1000). It equals 995.6296444195137…, inside Bound compiler width by exp(O(N log N)) and route overlapping ranks #4436's printed interval. The effective saving is 0.000634, which confirms that rank 1,000 misses the target.
• Local float trend, not in the verifier: the effective saving is 0.000634, 0.000750, 0.000800 and 0.000835 at N = 10³, 3·10³, 10⁴ and 3·10⁴. That climbs more slowly than the separated p3 compiler, which reached 0.001193 at 10⁴. This is finite evidence only, and Bound compiler width by exp(O(N log N)) and route overlapping ranks #4436's exponent gate remains open.

Evidence

python3.12 -B scripts/research_package.py --package research/pr4436-direct-flow-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/pr4436-direct-flow-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4436-direct-flow-check outcome=completed   (<1 s, stdlib only)

VECTORS.json copies #4436's recorded flows and its L(1000) interval with the source SHA256. Head: bbef80cd12c66afa31cb347c7393fafc873a0c88. Base: canonical main 2a13eb18.

Not covered

• Bound compiler width by exp(O(N log N)) and route overlapping ranks #4436's size bounds and batching.
• Native premises.
• The asymptotic direct saving.

Task and overlap

• Card: independent-moment, refined.
• Claim: Handoffs and requests for independent checks #1166 (comment)

Credit

@zxv (#4436) and Jacob Alan Sussman (Theorem 1G).

Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance; no independent human review. Apache-2.0. This PR does not merge anything or change the frontier.

🤖 Generated with Claude Code

[pinterbanget]

Local trend update (not in the verifier). The exact recurrence L(N) on raw p7 gives effective savings of 0.000800 at N = 10^4, 0.000827 at 2·10^4 (new), and 0.000835 at 3·10^4. That is a slow, decelerating climb, consistent with the single-step ceiling analysis in #4465 and #4467.