[tekuuu]

Construction and independent verification of a smaller H6 compensation factor.

The mixed sources (u,v) and (u,-v) have identical actual source frames. In target-label buckets where their C=I-K columns are equal or opposite, capture their sum/difference into one ordinary helper. Keep the rank-two exceptions and all pure-source helpers unchanged. The written proof gives DG=C and the complete arbitrary-dirt forward/same-order inverse-transpose splice under the inherited K/frame contracts.

Complete compensation counts change as follows:

• Helpers: 227,312,640 → 123,632,640, removing 103,680,000 [1,15,1] paths.
• Scatter entries: 480,337,920 → 260,536,320.
• Capture entries: 227,312,640 unchanged; both source reads remain paid.
• Prescribed component primitive allowance: 9,524,090,880 → 6,007,265,280. This is a semantic scalar upper invoice, not a measured runtime or tape-step speedup.

The primary checker recursively enumerates the integer lattice. A separate implementation uses pattern shells and direct E8 cosets, with coefficient/tariff/pad oracles extracted only after frozen-source authentication. They cover all root/root, root/pure and pure/pure entries and all 16 mixed pairing classes. Complete-fiber all-input-column fixtures check both orientations; 25 semantic/integrity controls reject wrong signs, full-rank compression, dirt/cleanup omissions, source-frame mismatches and weakened pins. All three registered checks and optimized read-only Git-free export replays pass.

python3.12 -B scripts/research_package.py --package research/h6-mixed-pair-capture

Base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90. Source Git blobs and SHA256 pins are in SOURCES.json. Conditional comparisons reuse Ross Richardson's asymmetric K histogram/bills at PR #4027 head 1bcc4f8261d2dc322c98fa9e44c4ced43cd1cd95; that pending implementation is not imported or independently admitted here. The full local rank mass conditionally changes from 3,865,333,216 to 2,102,773,216. The certificate includes unchanged-convention formal stock and padding deltas for stages 3, 5 and 7.

Scope: forward logical capture range grows from E+X to E+2X. Helpers return logically at FULL, with physical output F e. Copied-total erasure, literal physical restoration, full approximate-child precision, actual reserve/placement, source/tape access and joint BIT/complex admission remain unresolved. No full network tape, physical speedup, supplier admission or new κ is claimed. Only the new isolated package is added; frozen predecessors and the selected frontier are unchanged.

Credit: Dominik Scholz/PR #606 for H6 geometry and factor, DreamingOfClouds for the H6 proposal, PR #1830 and the inherited compensation/compiler contributors, and Ross Richardson/PR #4027 for the asymmetric K work and helper-burden handoff. Prepared by Tekalign (tekuuu) with substantial OpenAI Codex assistance; Apache-2.0. Exact checks and machine reviews are not human peer review or a formal verification of the multiplication theorem.