[pinterbanget]

Summary

This adds research/pr4412-pr4414-moment-check/. It independently certifies the strictification inequalities of #4412 (κ = 0.00247755) and #4414 (κ = 0.00267987), both by 1337isnot1337. These are the two predecessors of #4416, whose check is #4420.

Claim type: an independent certified finite check. No new κ. Native audits, outer ledgers and inherited premises are not checked.

Result

	#4412 (saving 0.00247756, cutoff 4^n)	#4414 (saving 0.00267988, cutoff ⌊(19/4)^v⌋)
α = P_τ/T_τ	0.999999996840, < 1 − 10⁻⁹	0.999999982435, < 1 − 10⁻⁸
γ = P_1/(b^C T_τ)	0.9989653420, < 999/1000	0.9998629803, < 9999/10000
Closing bound	surplus 1.4392544772·10⁻⁵ (n = 15000)	exactly 16386003/16408576 (v = 150000)
Limit saving C*	0.002477561641, 1.6·10⁻⁹ above the tested saving	0.002679889969, 1.0·10⁻⁸ above

• Every link holds. The enclosures are below 10⁻³⁰ wide and overlap the recorded intervals.
• The invoices are bound to each PR's native inventory: 3,528 / 25,774 and 6,648 / 48,442 fields and calls.
• Control. Conditional κ = 0.00267987 with a complete p6 native controller #4414's integer base-4 cutoff fails the tail (γ > 1), as it states.

Each tested saving sits at its own invoice's ceiling, with γ < 1 still at C*. This is as at #4416 (#4420: 9.05·10⁻⁹). A larger tensor power cannot raise these κ values; only a different invoice can.

Evidence

• Standard library only; runs in about 2 minutes.
• Exact rational enclosures.
• Imports nothing from either PR. Both TENSOR.md and RESULT.json files are vendored byte-identically, SHA256-checked, with vendor/NOTICE.md.

python3.12 -B scripts/research_package.py --package research/pr4412-pr4414-moment-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/pr4412-pr4414-moment-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4412-pr4414-moment-check outcome=completed

Head: 6977b9f52c8632d066b0d649f2a6280c5a96185e.

Not covered

• The native audits producing the invoices. Every α margin is below 10⁻⁸, while one paid call moves α by more than 10⁻⁶. Rebuilding the invoices is the open next question.
• Everything downstream: the tensor and splitting proofs, compiler ranks, outer rows and inherited premises.

Task and overlap

• Card: independent-moment, refined, priority revision 7.
• Base: canonical main 12fa8c5c844be21bfefb38a19503fbd867a11244.
• Claimed in Handoffs and requests for independent checks #1166 before starting (comment 19103631). The Conditional κ = 0.0023 (+5.690e-4, +32.87% over #4181): productive helper jobs compiled into a uniform supplier #4359/Refine PR4359: conditional κ = 0.00230509 and smaller explicit template ranks #4405 checks (Independently check #4359's explicit-rank chain: H0/H1, superpotentials, the exit recurrence and 19,895 exact lockstep flows hold (no new κ) #4404, Independently check #4405's refined #4359 ranks and endpoint family: all reproduce; z0 and the exit constant are not levers, the uniform saving is (no new κ) #4410, Rebalance #4359's own ledger at unchanged kappa 0.0023: explicit ranks shrink to 2^268300549 (complex) and 2^14664 (BIT) with all 54 predicates strict (no new κ) #4413) do not cover these successors.

Credit

The constructions and invoices are 1337isnot1337's (with OpenAI Codex assistance), building on zxv's #4359, #4405 and Jacob Alan Sussman's Theorem 1G. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance. Apache-2.0.

🤖 Generated with Claude Code