Independent verification (no κ): PR3605's span(429,30) entrance residual passes a separate-kernel native check

[Mainzu]

This answers open question 1 of thakrarsagar's PR3687 for RossRichardson's PR3605 at head 3efbb5de. The question is whether the native phases of the paired span(429,30) entrance of helpers 644/660 hold when checked without the bw_* lineage code. PR3605's 8→7 width saving rests on this residual, and so do the consumers that reuse its STAGED words (#3624, #3626, #3630, #3633, #3638).

Result: it holds, for both providers and both orientations.

• Residual identity. The emitted width-7 recipe for [429,30] → FULL satisfies L·F_7·R = T_FULL·T_E^-1 on all 512 Gaussian columns, including global phase. Operators are in product order, with the rightmost acting first.

  • The check uses Sagar Thakrar's separately written kernel, research/frontier1094-recipes-exact-seed76/clifford.py. No bw_* module takes part in the identity check.
  • All ten distinct climb recipes of 644/660 also pass.

• Binding. The unchanged producer's emitted program is bound to the source word.

  • Each helper has one pre/post residual wrapper pair at [429,30] and one new_to_old exit adapter at FULL, with no private buffer.
  • The climbs are [2,1,2,1,1] (644) and [2,2,1,1,1] (660), each summing to 7.
  • All 17 direct scalar clocks per helper match the source.

• Single-change control. The parent PR3133 words go through the same producer. There, 644/660 have width 8, and their first climb is 3 instead of 2. Every climb ends at the same frame.

  • Across all 408 helpers, only 644 and 660 change their entrance/terminal pair.
  • The serialized residual recipes go from 56 to 57.

• Retimed and delayed consumer words. The RETIMED644-660 words of Improve conditional T530 κ through two commuting release retimings #3642 (reused byte for byte by Compose retimed T488 suppliers: conditional kappa 0.00173041889976 #3653) and the DELAYED words of Consume retimed staged releases with smaller T360 stock #3682 keep this entrance, for both providers and both orientations.

  • 644/660 still enter at [429,30] with recipe key 137, and the width-7 recipe passes the separate kernel on all 512 columns.
  • The residual-adapter files and all 408 entrance/terminal pairs equal the STAGED ones. For 644/660 the emission clocks move, and the release that reads each helper now runs at Q instead of [429,30]. Binding the STAGED word to a consumer program is rejected.
  • Donors 640/656 merge two climbs into one rank-3 climb, which also passes the separate kernel.
  • Each regenerated LOCAL-CHECKS.json, in LF form, equals the receipt that Improve conditional T530 κ through two commuting release retimings #3642 or Consume retimed staged releases with smaller T360 stock #3682 recorded from its own native run.

• Controls. Seven per provider are rejected:

  • three at the all-column operator check: a global-phase change, the parent's right wrapper, and the wrong plane [429,18];
  • four at the width check.

  test_verify.py adds wrapper, climb, exit-adapter, scalar, orientation, word, recipe and pin corruptions.

• Local-only cross-check. The producer's bw_adapters.py, run under Python 3.13.1 with numpy 2.2.2 (not the declared 2.5.4), writes adapter files whose LF-normalized bytes equal this package's reconstruction for both providers. This is not part of the registered replay.

What this adds over PR3605's own chain. PR3605's bw_audit_local.py already binds every emitted wrapper, climb and scalar frame, and bw_adapters.py checks every entrance recipe. Both rely on the bw_gauss lineage kernel. This package supplies the missing independence: a separate kernel for the identity, and its own source-to-emission binding.

Not covered:

• the other 56 recipes, the 72 warp records and the scalar macros under an independent kernel;
• whether the consumers' moved releases commute (their authors' argument), the donors' other climbs, and 644/660 words on other PR heads;
• owner journals and the releases;
• the inherited all-size hypotheses.

No κ, supplier admission or selected-frontier change.

Checks (Windows 11, Python 3.12.10, standard library only):

• verify.py: PASS_STAGED_644_660_NATIVE_BINDING, about 80 s.
• test_verify.py: 8 tests, OK.
• research_package.py --check-only: PASS_PACKAGE_METADATA_AND_PINS.
• py -3.12 -Werror -B scripts/research_package.py --package research/staged-644-660-native-binding-audit: PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=completed.

PR3605's two STAGED words and the four consumer words are vendored in inputs/. They are bound to provenance pins at their PR heads, and the verifier byte-checks them. The repository's head: pin must name the live path, so it cannot pin a relocated copy directly.

Credit:

• Ross Richardson: PR3605 construction.
• dcharb78: PR3133 parent words, with their lineage.
• roger-sato (Improve conditional T530 κ through two commuting release retimings #3642, reused by rohanarun's Compose retimed T488 suppliers: conditional kappa 0.00173041889976 #3653) and zxv (Consume retimed staged releases with smaller T360 stock #3682): consumer words.
• Sagar Thakrar: posed the question in PR3687, and wrote the kernel.
• DreamingOfClouds/PR458 and t74-native-fast: producer lineage.
• Wentao Li: group-D native-widths audit, whose method and code are adapted here, building on the group A–C audits.

Prepared by Mainzu with substantial assistance from Claude Code (Claude Opus 5.5). No independent human or formal-kernel review is claimed.

🤖 Generated with Claude Code