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Finite research construction: signed P104 mixed-carrier banks and E8 root-line gate (no new kappa) - #2844
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…gate Schematic signed banks, exact 4096-bank optimization and a full 7140-pair E8 root-line obstruction. No native supplier or new kappa. Substantial GPT-6 assistance; predecessors credited.
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Follow-up finite construction (pushed to this branch): rank2_gate.py stores each signed x_i +/- x_j mixer on the rank-two span of two genuine E8 root labels, rather than an unavailable pair-sum root line. It executes every signed target, reverses mixer preparation, restores all eight original source values, and erases all 16 auxiliaries. Exact exhaustive search of 4,096 cube-edge banks gives six symmetry-related optimal eight-edge banks, each costing 320 signed ADDs and 1,520 frame-rank units. Comparator: the specific nonoptimized unmixed home-return schedule, 416 ADDs / 2,224 rank units. zero_restore.py also checks the formal composite-rank-one variant after full cleanup, with 320 ADDs / 1,408 rank units, but that variant still needs a new label alphabet. Full isolated standard-library replay passed on Windows CPython 3.13: python -I -B research/p104-signed-mixed-carrier-bank/RUN_SUBMITTED.py. Research only: actual native operator phase, source delivery, physical frame realizability, recursive child costs, hosting/precision and outer-moment admission are unproved; no new kappa. See PROOF.md section F and NATIVE_GATE.md. |
2 participants
Research scope
Adds a finite schematic P104 construction with reusable signed pair mixtures, plus a native-realization obstruction. This is NOT a legal P104 supplier, new conditional exponent, or full multiplication theorem. Builds on #968 and merged #1125, with #2820 as projection-width context.
Finite result
Within a specified F2-frame, home-return direct baseline, exhaustive search of 4096 cube-edge banks gives 288 signed ADDs and 1312 frame-rank units versus 416 ADDs and 2224 rank units for the stipulated nonoptimized unmixed schedule. Unique rank-winning 12-edge bank uses 24 redundant auxiliaries. Primary checker exhausts 2288 signed target instances and 105 fixed matchings.
Physical gate
The composite line u_i + u_j is never an existing E8 root-line label. New root_line_gate.py reconstructs 120 root-line pairing signatures and rejects direct root-line adapters for all 7140 unordered pairs. This forbids a simple relabeling, not all generalized-frame implementations.
Verification
Run: python3 -I -B research/p104-signed-mixed-carrier-bank/RUN_SUBMITTED.py
Expected: PASS_P104_SCHEMATIC_SUBMISSION no_kappa no_native_supplier
This exact pushed code passed isolated Python on a separate Windows machine.
Outstanding obligations
Native generalized-line lowering, full source and phase access, helper ownership/cleanup, strict recursive children, physical hosting, a competitive optimized unmixed comparator, and selected moment/outer checks. This branch leaves upstream/ and selected frontier untouched.
Credits
Ali Romman (#1125); frame-pair decoder work #968 and predecessors; @Chrisbryan17 (#2820). Prepared for @Chrisbryan17 with substantial GPT-6 assistance. Apache-2.0. See research/p104-signed-mixed-carrier-bank/PROOF.md, README.md and NATIVE_GATE.md for exact scope.