RELEASE_V99.88_GAUSSIAN_FACTORING.md

PrMers v4.20.77-alpha-v99.88 — Gaussian-Mersenne P-1/ECM lift

Added

• -gm-pm1: exact P-1 Stage 1 and low-memory product-exponent Stage 2 for G_p = 2^p - (2/p)2^((p+1)/2) + 1.
• Structural 4p multiplier in the Stage 1 exponent.
• -gm-ecm: Suyama Montgomery ECM with GPU projective x/z ladders.
• CPU projection, GCD and inversion strictly modulo G_p at stage/chunk boundaries.
• -gm-factor-chunk-bits for P-1 and ECM Stage 2 batching.
• Atomic CRC32 Stage 1 and Stage 2 checkpoints.
• -gm-safe independent P-1 block/chunk replay and ECM Stage 1/chunk replay.
• Deterministic mathematical tests and four small GPU validation cases.

Isolation

The new implementation is contained in src/modes/RunGaussianMersenneFactor.cpp plus CLI/dispatch declarations. No file under third_party/aevum, kernels/marin.cl or kernels/prmers.cl was modified relative to the working v99.87 Gaussian-Mersenne bundle.

Deliberate limitation

Stage 2 is a safe product-exponent continuation rather than the ordinary Mersenne V-trace/BSGS implementation. Those implementations assume arithmetic and inversions directly modulo the tested Mersenne number; applying them unchanged to 2^(4p)-1 could be obstructed by the unrelated lift cofactor.