Research: certify all S4 two-premium two-register tariffs

[petalas]

Summary

Certify exact additivity for every diagonal S4 target pair on two arbitrary dirty registers when adjacent labels cost (2,1,2).

300 unordered pairs
  253 have matching inherited cut bounds
   47 need the new complete weighted meet
576 ordered pairs: minimum = d(a) + d(b)

The package is research/s4-two-premium-registers/. C++ left-multiplication and separately written Python right-multiplication engines regenerate the same 971,369 formal states and all 47 complete query receipts. Neither imports predecessor search code. Both implementations were prepared in this session; no independent human or proof-assistant review is claimed.

This follows Ross Richardson's #1989 weighted-price handoff, complementary to #2577's one-premium theorem and #2544's S3 tariff. The cut method retains credit to Adam Gall #1941 and Ross Richardson #1966; #1974 is a related exact-census precedent. Canonical claim and handoff.

Evidence

• Before, the combined cuts gave only 14 against direct bill 16 for two (14) targets, and 16 against bill 18 for two reversals. After, both complete formal engines certify minima 16 and 18 and settle every other pair.
• Registered replay passes under CPython 3.12.15/GCC 14.2.0. It includes 576 full dirty endpoints/inverses, 3,456 omitted-call controls, explicit cut ranks and seven behavioral test groups.
• State-capacity exhaustion, forced hash collisions, wrong order, dirty leaks, receipt/source corruption and optimized read-only Git-free replay are exercised.
• All 65 repository test_research_*.py tests pass. The full C++ census passes AddressSanitizer/UndefinedBehaviorSanitizer and strict warnings. Python development-mode compilation passes with warnings treated as errors.

python3.12 -I -B scripts/research_package.py --package research/s4-two-premium-registers

Base and final canonical main are 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Source pins, scope change, overlap freshness and structured next questions are in TASK.json and SOURCES.json. Final overlap covered 776 open PRs and 1,238 Discussion records with complete pagination; arbitrary diffs and comprehensive closed-PR coverage remain outside the helper.

Limits: fixed (2,1,2) prices and exactly two registers for the finite exclusion. Extra dirty roles, other tariff ratios, native/compiler/hosting admission, precision/tape and recursive moments remain open. No new kappa, selected-supplier adoption, full selected cold replay or multiplication theorem is claimed.

Merge danger

Door: reversible. Blast radius: research-only.

Adds one opt-in package. No selected frontier, frozen evidence, predecessor package or existing verifier changes. Hosted CI is separate from the local evidence above.