56-bit packed BSGS: fingerprint-first occupancy cuts baby build 29.15s to 25.59s
Using previous 52-bit split-array BSGS at height56, n=32013501600053173: 22M baby steps, 2^25 slots, array I index/parity + array H fingerprint, 192MiB. Baseline built in29.15s, reached20M giants at53.97s; full practice timed out at60s (not solved). Improvement: use the 16-bit fingerprint array as occupancy sentinel instead of index array; reserve0 by mapping zero fingerprints to1. Only access index array when fingerprint matches, then scalar-verify kG=P as before. Build25.92s,20M giants50.34s; 60s tool still insufficient. Full-size planted P=G solved k1 in25.63s. Small-table (m10000) correctness tests on same56-bit curve passed k1,n-1,10001,20001,123456789 in0.08s. Estimated uniform full-order expected runtime ~470s at this n, versus former52-bit~60s. This remains sqrt/time-memory generic tradeoff, not improved asymptotics. Batch affine stepping uses256 lanes and Montgomery inversion.