Research: Heisenberg central-pair call floor (no new kappa)

[1337isnot1337]

Result

This package gives an exact call-minimum result for one new nonabelian register model. In the formal algebra F2[UT3(F3)], with two scalar registers and paid shears over the four generator labels x, x^-1, y, y^-1, the endpoint diag([z],[z]) for z=[x,y] needs exactly eight calls.

Applying the commutator word x y x^-1 y^-1 once to each register gives the eight-call upper bound. A complete meet-in-the-middle search over all six binary rank-one idempotents and all four labels excludes every word of lengths 0 through 7. The exact sorted-state receipts cover 82,063 distinct length-four products; EXPECTED.json records hashes and every tested split. Free scalar GL2(F2) changes are absorbed because all rank-one idempotents are enumerated and the target is scalar.

Verification

python3 -B research/heisenberg-central-pair-seed0154/verify.py
PASS_HEISENBERG_CENTRAL_PAIR minimum=8 excluded_lengths=0..7 group_order=27 characteristic=2 registers=2 generators=4 idempotents=6 controls=6 matrix_crosschecks=144 state_counts=[(0, 1), (1, 24), (2, 413), (3, 5927), (4, 82063)]

python3 scripts/research_package.py --package research/heisenberg-central-pair-seed0154 --check-only
PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)

The exact replay also passes under python3 -I -O -B.

Scope and attribution

This is limited to the named finite group, two registers, four-label alphabet and endpoint. It rejects a commutator-sharing saving in this model; it does not bound other nonabelian groups or establish physical supplier adoption. No new kappa or integer-multiplication claim is made.

PR #1822 studies the related Q8 central pair. This changes the group to odd order 27 over coefficient field F2, and the central target has order three with a four-letter direct generator word. The full overlap refresh is recorded in README.md; the handoff is on Discussion #1167.

Assignment base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea; current PR base is the latest main. The selected record hash remains 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. Exact assignment and predecessor source pins are retained in TASK.json and SOURCES.json.

Prepared by Cinna Davis with substantial OpenAI Codex assistance. No predecessor code is copied. New work is Apache-2.0.

[Mister-Meeseeks]

Batch review at 549bb87fa1106ae4cad35706bcd9b5c7cc6fd1e3.

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

Reviewed scope: Complete two-role UT3(F3) formal-algebra meet-in-the-middle census excludes central-pair words through length seven and exhibits length eight. The rank-one alphabet, role count and full formal endpoint are fixed; extra workspace or different operations are outside the result.

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.