Scoped theorem: exact mixed-target UT3 tariffs with arbitrary dirty workspace

[bbMisk]

The existing UT3 results price repeated central targets, leaving heterogeneous endpoints outside their statements. This contribution proves the exact separate-generator bill for every mixture of all eight UT3 targets, with any finite restored dirty workspace and every nonzero binary rank-one scalar coupling, including nilpotents.

For target g_i=(x_i,y_i,z_i), every word needs at least sum_i[x_i+2(1-x_i)z_i] a-calls and sum_i[y_i+2(1-y_i)z_i] b-calls. Direct formal words attain both bounds simultaneously, so the formula also gives the exact optimum for positive uniform per-letter tariffs. The new proof step replaces the central-only zero-sum condition with a coefficient-span bound using Sylvester's inequality. The full proof, explicit model and eight attaining words are in the README.

Only research/ut3-mixed-target-tariffs/ is added. This is a scoped negative theorem with finite corroboration, not a new kappa or a selected-supplier admission.

Validation:

• All 111,151 expanded-alphabet two-register words through four calls satisfy the coefficient-span bounds; all 7,435 diagonal endpoint words satisfy the proposed separate tariffs.
• Full formal and separately implemented faithful-regular checks agree on 2,336 mixed-target fixtures, all 62,848 basis columns and all 324 ordered two-factor products. The latter engine uses literal binary address matrices and imports no local implementation.
• 3,925 boundary mutations reject. Other controls expose the nonfaithful quotient's dirty-input blind spot, the necessary nonzero first-order correction and the rank/alphabet restrictions. Finite checks corroborate the written unbounded proof; they do not replace it.
• CPython 3.12.13 registered replay and CPython 3.14.6 optimized read-only relocation pass. An optimized replay rejects a corrupted certificate. Source pins, selected baseline bindings and whitespace checks pass. Hosted CI is separate.

Reproduce with standard-library Python 3.12:

python3.12 scripts/research_package.py --package research/ut3-mixed-target-tariffs

Expected: PASS_UT3_MIXED_TARGET_TARIFFS and PASS_REGISTERED_RESEARCH_PACKAGE.

Assignment: bit-new-register-model, nonce 4aba18fcd52cd4290d0badf705c2dfc3, priority revision 2, starting main ebedc0895eb4c06725af020bc1af165722b0a3ce. The contribution was rebased onto 81e81af67714bdc8d1693b0bf5c29468b92f62ff; revision 3 leaves the assigned bit track and selected record unchanged. Final overlap covered 733 open PRs and 244 discussion records with complete pagination and no warnings. Scoped claim and coordination.

Credit steph4n-gh's #1573 (0b8c5a69297c794f2de22c04494c83e41300ae36) and Arham Tahir's #1589 (010ec8c01c0edbbb08b541be236ab78d096f2ca1) for the central all-register bounds, quotient and rank methods. The added scope is all heterogeneous endpoints with nonzero first-order coefficients. Credit also @juper997/#1478, @woklerx/#1443, Gareth Davidson/@bitplane/#1333 and the retained register-model lineage. No novelty is claimed for the quotient or Sylvester's inequality, and no predecessor executable is imported. #1567 uses a different, six-letter GL3 alphabet on exactly two registers.

The full selected cold replay, physical/compiler/common-label/hosting, precision/tape and outer analytic obligations remain outside this package. No Lean formalization or independent human proof review is claimed. The selected frontier and frozen inputs are unchanged. Prepared for Hanson Sun (@bbMisk), with substantial OpenAI Codex assistance in proof, implementation, validation and writing; no subagents. Apache-2.0.

[Mister-Meeseeks]

Batch review at 9d6117918025cee6a0c5b7ef30ff8d936ca0621f.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: The degree-two quotient and Sylvester inequality prove sharp separate generator tariffs for every heterogeneous UT3 target with arbitrary restored workspace and rank-one couplings. Full formal witnesses attain the bounds; physical realization of the optimistic alphabet is not claimed.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.