p11: transfer-matrix sub-frontier reproduction (n<=14 exact) + honest resource model for n=25..28

[LightChainr]

Fixes #11 (partial — sub-frontier portion; see scope below). Draft, do not merge.

Full Matching-One repository CI has not been run for this commit.

What this PR adds

Reproduction of the Mertens-2022 square-site percolation transfer-matrix
sequence on free-boundary n×n grids, plus an honest resource model for
n=25..28. Per the ticket's acceptance rule ("先复现已发表宽度与位数"), the
reproduction is pinned to the published table
data/mertens_2022_square_site_estimators.csv digit-by-digit before any
extension.

Reproduced (exact)

• Two independent encodings of the connectivity states — label-based DP
  carrying exact integer polynomials (p11_square_dp.py) and exhaustive
  2^(nm) union-find enumeration (p11_bruteforce.{py,cpp}) — agree
  bit-for-bit on A(k) for every width both reach (n=2..5).
• Path A reproduces published p_med to all 30 printed decimals for n=2..10
  (p_cell checked n=2..5).
• An independent C++ cell-sweep engine (p11_exact_dp.cpp) with CRT over
  verified 30-bit primes reproduces p_med/p_cell for n=11,12,13 to 32
  leading digits (all 30 published digits) on ARM containers; n=14/15 runs
  and per-pass checkpoints are included as telemetry.
• State counts equal Mertens' S_n exactly at every width (…29964, 83304,
  232323, 649845, 1815992…), an independent confirmation of the encoding.
• Deterministic checkpoint/restart: row-7 state-map dumps (SHA-256 recorded)
  restart to bit-identical A(k) mod p at n=14 on container.

Binary128 audit

aarch64 long double (IEEE binary128) Newton root-finding with derivative
DP and 1e-25 bracket verification reproduces all 30 published digits (32
actual) at every audited width n=5..10. f128 runs at n=16..18 carry no
exact cross-check and are explicitly labelled uncertified.

Jacobsen cylinder sequence — negative result

An independent strip-sector implementation of the open/closed eigenvalue
identity matches p_c(1)=1/2 but gives p_c(2)=0.5200209… vs published
0.5651977…; diagnosis (paper's sectors live on periodic-TL s=0 reduced
states, not strip connectivity states) and the 3×3 sector matrices are in
p11_cylinder_sectors.py. We claim no cylinder width beyond n=1.

Resource model for n=25..28 (model-based, labelled, not measured)

Log-linear fits over measured widths n=11..13 (max relative residual ≤
3.5e-3): states b=2.7845, peak RSS b=3.1106, wall (10 CRT primes) b=4.4573.
Extrapolation: n=25 needs ~499 TiB RSS / 2.4e10 s; n=28 ~15.0 PiB / 2.2e12 s
— 4–5 orders of magnitude beyond 10×32GiB containers, which is why the
deliverable for 25–28 is this model rather than numbers. Widths 19–24 were
not attempted.

Bugs found and fixed along the way (each would silently corrupt results)

1. Drop rule: non-top finished clusters were wrongly dropped (found by
   brute-force mismatch at n=5, k=11).
2. Union-find did not encode old-row label connectivity.
3. Canonical relabeling gap when a label's last cell empties (first fires n=6).
4. Class-merge relabel missed new-row cells (first fires n=6).
5. CRT "prime" list contained composites sharing factor 7; now sympy-verified
   with a pairwise-coprimality assert.

Files

• scripts/p11_*.py, scripts/p11_exact_dp.cpp, scripts/p11_bruteforce.*
• notes/p11-transfer-subfrontier-20260913.md
• results/transfer-subfrontier-20260913/ (REPORT.md, metadata.json,
  commands.txt, raw/ telemetry, roots, audits, resource model)

No existing files under analysis/, results/, docs/STATUS.md, ROADMAP or
RESEARCH-FRONTIER are modified. Draft PR — never merged by the author.