[jwr404]

Change and mathematical scope

Scoped finite check. No new κ. The selected conditional exponent stays 60403/20000000, and PR #4100 is not accepted.

CRT.md's simultaneous carry argument assumes the published margin 2B ≤ W < 2^m − 2B. The isolated step also holds for 0 ≤ W ≤ 2^m − B + 1. This package runs the live two-target macro, two post-increment steps with a load of f between them, at those sharp edges on positions (0, K) with K = m + 1.

Both control words return, and the data word ends as the XOR of the two source bits, on:

• B = 4, m = 5: 5,184 independent edge pairs, plus 648 window-bit sources
• B = 2, m = 5: 32 matched-edge pairs
• B = 8, m = 6: 76,832 matched-edge pairs

One step past the edge, (u, t, y) = (1, 2, 60) with first window 30, ends at (1, 10, 60). A source that reads the target bits, and the overlapping positions (0, 1), also fail the ideal restoration.

This does not prove every base or every placement, and it does not move the simultaneous argument off the 2B margin. The twelve paid H-bit exchanges are not replayed.

Task and overlap

• Base: canonical main 624de9dc66858af0945e5f8a0942488d62280d43, fetched 2026-10-22T23:29:09Z, priority revision 7.
• Card: formal-interface-lemma, scope refined. This is open question 1 of PR Compare the sharp compact-switch window with CRT.md's repair room. #4646.
• Predecessor: Cinna Davis, PR Propose unconditional κ = 0.00173097911567079247276057 via batched CRT #4100. The live-digit lemma is PR Audit the compact-switch coefficient and guard contract. #4321. The density comparison is PR Compare the sharp compact-switch window with CRT.md's repair room. #4646.
• Package: research/compact-switch-sharp-two-target/.
• Overlap at 2026-10-22T23:29:00Z: the matches are this package, Audit the compact-switch coefficient and guard contract. #4321, and Compare the sharp compact-switch window with CRT.md's repair room. #4646's open question. No other package runs the pair on these edges.

Validation

Python 3.12, standard library only:

python3.12 -B scripts/research_package.py --package research/compact-switch-sharp-two-target

Observed PASS_COMPACT_SWITCH_SHARP_TWO_TARGET b4_m5=5184 b2_m5=32 b8_m6=76832 window_sources=648, then PASS_REGISTERED_RESEARCH_PACKAGE research/compact-switch-sharp-two-target outcome=completed.

Not run: Lean, Docker, the selected cold replay, the twelve H-bit exchanges, and the tape repair.

Credit

Cinna Davis, PR #4100, for CRT.md. PR #4321 for the live-digit lemma and the published-margin pair sweep. PR #4646 for the density comparison that left this macro open. PR #4328 for the L ≤ p hypothesis, which remains open.

Prepared by James Reed with substantial Cursor Grok 4.7 assistance. Apache-2.0. No independent human review and no formal-kernel acceptance are claimed.

Open next questions

1. Is L ≤ p true for a real Audit CRT reservoir placement and split-axis coordinate descriptors #4174 placement, or only a sufficient hypothesis inherited from Audit #4100 CRT.md's sparse exception repair tariff at Θ(p)-bit records: O(V) dense, o(V) sparse at every p (no new κ) #4328? First step: read one production plan's address length against its p.