[jwr404]

Change and mathematical scope

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

PR #4328 absorbs the sparse repair when L ≤ p. PR #4646 reuses that hypothesis to reach r ≤ p/19200 and the constant 1/6400. This package reads one production plan from PR #4174.

The caller is Layout(6 * L, 24, widths) with d = 65536 and widths alternating 24, 23. The first plan (level 1, partition 0, batch 0, axes (1, 3, 5, 7, 9)) has address length L = 1540096 and p = 9240576 = 6L. So L ≤ p, and r_max = 5 ≤ p/19200.

The same constructor accepts p = 2, ell = 2, and 65,536 widths of 1. There L = 65536 > p and r_max = 2 > p/19200. L ≤ p is true for the production choice p = 6L. It is not an invariant of every #4174 layout.

Task and overlap

• Base: canonical main 624de9dc66858af0945e5f8a0942488d62280d43, fetched 2026-10-22T23:43:14Z, priority revision 7.
• Card: formal-interface-lemma, scope refined. This is the open question of PR Record the sharp-window two-target macro on K-separated guards (no new κ) #4904.
• Predecessor: Hiroki KUMAZAKI, PR Audit CRT reservoir placement and split-axis coordinate descriptors #4174. The hypothesis is PR 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. The constant 1/6400 is PR Compare the sharp compact-switch window with CRT.md's repair room. #4646. PR Decide #4100 CRT.md's guard premise: mod-K coloring needs (K-1)-bit guards; vacuous on #4174's production plans (no new κ) #4329 already prints this production row, including p = 6L, for the guard-coloring premise.
• Package: research/crt-reservoir-length-hypothesis/.
• Overlap at 2026-10-22T23:42:46Z: this package, and PR Decide #4100 CRT.md's guard premise: mod-K coloring needs (K-1)-bit guards; vacuous on #4174's production plans (no new κ) #4329's production row. No package tests a Audit CRT reservoir placement and split-axis coordinate descriptors #4174 layout with L > p.

Validation

Python 3.12, standard library only:

python3.12 -B scripts/research_package.py --package research/crt-reservoir-length-hypothesis

Observed PASS_CRT_RESERVOIR_LENGTH_HYPOTHESIS production_L=1540096 production_p=9240576 longer_L=65536 longer_p=2, then PASS_REGISTERED_RESEARCH_PACKAGE research/crt-reservoir-length-hypothesis outcome=completed.

Not run: the 104,864-plan census, the repair-tariff fixtures, Lean, and Docker.

Credit

Hiroki KUMAZAKI, PR #4174, for the constructor and the recorded constants. PR #4329 for the same production row. PR #4328 for the L ≤ p hypothesis. PR #4646 for the constant 1/6400. Cinna Davis, PR #4100, for the CRT parameters.

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. On the admitted layout p = 2, ell = 2, L = 65536, what constant replaces 1/6400 in r (2/B + β) ≤ C p 2^{-G}? First step: evaluate that one inequality at r = r_max.