[unpaidmoon]

Change and mathematical scope

Scoped audit, no new κ. The selected record stays 781451/250000000.

#5546 showed that the native variations (L300=u, L505=-4u) and (L301=u, L226=u) fix the three coframed rows at forward cut 9047 and move the pure helper coordinates. This package checks whether those variations are legal inputs of the #5402 entrance that the #5413 caller runs. It does not replay the native word and does not nominate a new prefix, basis, or anchor.

The entrance multiplies eight mode owners by 2, applies monomials Km, and runs the 834-instruction input basis on 122 helpers.

• Owner-rational reading: the map has rank 122. Public (L300=u, L240=-u/2, L505=-4u) arrives as the published L300 witness. Public (L301=u, L226=u) arrives unchanged. Both separators transfer verbatim.
• Empty-warp reading, with every mode input held at 0: the verbatim L300 pair moves coframed row L301 by -3u/8. The bare correction (L300=u, L505=-4u, L226=-3u/8) fixes all three rows and still moves native L300 by u. The L301 witness is already an empty-warp entrance state.

Either reading supplies a legal variation that preserves the cut rows and moves the pure coordinate. The obstruction transfers to this caller domain.

Task and overlap

Base: 7c49fe32c55de02c2c873655c804b16e4c3fef0a. Task complex-new-helper-inventory, scope refined to the live handoff on discussion #1166, comment 19176044. The canonical #5546 conversation remains the status thread.

Pinned inputs: research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz (compressed SHA-256 7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05, payload cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd), research/native-rank8-helper-provider/PROVIDER.json, and the #5546 row table research/shared-crossing-cut9047-20261025/expected/RESULT.json. The provider bytes match the capsule copy used by research/selected-caller-exact-grid.

Nearest work: #4610 (word), #5402 (entrance), #5413 (caller schedule), #5546 (cut). This adds the entrance image of those witnesses. It does not reopen scalar purification.

Scope is refined. The card asks whether a changed helper inventory survives the actual caller. The handoff asks only whether these witnesses are admissible there. The complete-supplier gate is not claimed.

Validation

Python 3.12, standard library only:

python3 -B scripts/research_package.py --package research/cut9047-caller-witness-domain

Expected marker: PASS_CUT9047_CALLER_WITNESS_DOMAIN. The command authenticates the three inputs, checks rank 122, the warp-blind preimage, the -3/8 leak, and the corrected separator. A zero scale, a dropped L226 correction, and a wrong L505 coefficient are rejected. The native word was not replayed. Km was not carried through events 0..9047. No Lean, Docker, or selected cold replay.

Credit

Cao Yifan: #4610 word. Dillon Amburgey: #5402 entrance. Chris R (Clear1nsight): #5546 cut and the #5413 caller schedule. The coded-native-caller and balanced-J lineage supplied the main/helper classification. Retain the source authors credited in those packages.

Prepared by unpaidmoon with substantial Cursor Grok assistance. New material is Apache-2.0. Pinned inputs are unchanged.

Open next questions

• After each mode monomial Km is carried through forward events 0..9047, does any Km-keyed term meet a coframed row on the empty warp word? The bare witnesses set every mode input to zero. A term that returns to the empty word would need its own separator. First step: replay each pinned Km word through the forward prefix and read rows L19, L300, and L301. Blocker: this package does not replay the native word.
• If a later caller replaces the Preserve all 632 native inputs in an eight-mode coupled helper provider #5402 basis, recompute the corrected witness before any prefix credit. No replacement entrance is proposed here.

Workflow feedback (optional)

The handoff's intended caller is the #5402 entrance inside the #5413 schedule. Checking that program against the published rows answered the admissibility question without another cut replay.