[unpaidmoon]

Change and mathematical scope

Scoped classification, not a new κ. The helper-462 / frame-506 route has 224 f² ordered shifts. The 64 f² earlier-target sites update the smaller address. They are add_high(..., reversed_fields=True): the proved forward shear conjugated by a swap of the two high axes. Each such call records two completed_swap_oracle entries, charged as T_old rather than a fixed-tape transition count. The forward shear records none.

The selected conditional exponent stays 781451/250000000. This does not admit P3, implement the transposition, or change the frontier.

Task and overlap

Base: 2485805a6d47f36ea83ddde6327d453ac82d44dc, priority revision 8.

Task card: supplier-boundary-audit, refined. The request is handoff #1166 comment 19137812. Later packages on this base already schedule the route (research/bit-row-route-generator), price unit scale (research/signed-dyadic-scaling), and price the later-target shear (research/fixed-tape-ordered-shear, research/fixed-tape-affine-shear, research/inplace-runtime-affine). Those write-ups leave the earlier-target / reversed-field half open. No open upstream PR body found for that remainder.

Scope status: refined. The handoff asks for a full N-dimensional stock/owner/route generator satisfying P1–P3. This package takes only the remaining earlier-target contract and stops at the oracle gap.

Validation

python3 -B scripts/research_package.py --package research/earlier-target-shift-gap --check-only
python3.12 -B scripts/research_package.py --package research/earlier-target-shift-gap

Local result: PASS_PACKAGE_METADATA_AND_PINS and PASS_EARLIER_TARGET_SHIFT_GAP earlier=64*f^2 later=160*f^2 oracle_calls=2, including the optimized command. The checker matches both committed route directions, checks f = 1, 2, 3, runs three conjugation fixtures, and requires two failing controls to fire.

Not run: a fixed-tape transposition, helper-462 owner replay, P3 admission, Lean, Docker, or the selected cold replay. The oracle records are not converted into a transition count.

Credit

Route schedule: Chris R / Clear1nsight, PR #4957 / #4989. Stream lemma and completed-swap oracle: Jose Manuel. Earlier-target remainder and the priced neighboring classes: JoyboyBrian. Ordinary API handoff: ai-nanachi. Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. Compile one high-axis transposition into the forward shear's local instruction model and give its all-extent transition and visited-cell bill. The source oracle is still direct indexing charged as T_old.
2. Charge that bill twice on each of the 64 f² sites, together with low-cache lifetime and ROW padding. Owner-bank installation and P3 remain open.