research(proximity): add G318 n64 rank-six norm guard

[OxBenji]

Adds G318 cyclotomic norm guard for n=64,r=6 at p=111*2^128+1. The guard shows any coefficient-a relation with a in {1,2}, |A|=6, |B|=5 has l1 <= 14, so any nonzero 64th-cyclotomic relation has norm bounded by 14^32 < p and cannot vanish mod p. Therefore the finite-field count is forced to equal the antipodal-model count, giving coefficient 1 dot=0 and coefficient 2 dot=20331698688. Verification: python scripts/probes/g318_n64_r6_norm_guard.py; git diff --check; python scripts/forbidden_tokens.py. Known pre-existing Windows docs issue: python scripts/check-docs-integrity.py reports CLAUDE.md must be a symlink to AGENTS.md.

[coopertweak]

Reproduced scripts/probes/g318_n64_r6_norm_guard.py locally. The Proth-prime certificate, p > 14^32 margin, adjacent total, and constants match the PR:

• coefficient 1: dot=0, A=-2341449599010471936
• coefficient 2: dot=20331698688, A=+767955559391433686463300268059000302726608177666560

I also wrote an independent antipodal-pair DP check that does not import the probe. It counts the folded 32 antipodal pairs directly and gets:

• a=1: base count 0, dot 0
• a=2: base count 317682792; multiplying by the 64 cyclic placements gives 20331698688

git diff --check origin/research/proximity-prize...HEAD is clean. python3 scripts/forbidden_tokens.py is clean modulo the repo's 9 allowlisted residual axioms.

Only minor note: the prose says "Combining this guard with the G316 formula" / "emits the G316 rank-six dot/A constants" in a couple places. Given this is G318 and G316 is a different depth-3 floor PR, that looks like a wording typo rather than a math issue.

[shane9coy]

Independent verification on file from coopertweak (2026-08-02 15:10):
he reproduced the probe locally, verified the Proth-prime/witness
check, the p > 14^32 margin, the adjacent total, and the constants
(coeff-1 dot=0, A=-2341449599010471936; coeff-2 dot=20331698688,
A huge positive). He also wrote a separate antipodal-pair DP that
counts the folded 32 antipodal pairs directly and gets the coeff-2
base count as 317,682,792 (matches the 20,331,698,688 dot when
multiplied by 64 cyclic placements). git diff --check clean,
forbidden_tokens.py clean modulo the allowlist. One minor note
from coopertweak: the probe docstring confuses "G318" with "G316"
in a couple places (says "Combining this guard with the G316
formula" / "emits the G316 rank-six dot/A constants"). A wording
typo, not a math issue. Concur.