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conformance: promote gf512 + gf1024 -> strict SW-bitexact (paired, 74/1/8) - #1381
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…act (paired, 74/1/8)
gf512 (S1 E195 M316, BIAS=2^194-1, u512_software) and gf1024 (S1 E391 M632,
BIAS=2^390-1, u1024_software; lowest phi-distance in the ladder) promoted paired
from bitexact_selfconsistent to strict bitexact. M=316/632 > 52 -> no FP lowering;
every finite value is an EXACT dyadic odd*2^k (parametric separation-bound, same
lemma as gf96/gf128). E/M/BIAS verified vs SSOT formats_catalog.t27.
Three witnesses each (all abs_error=0):
1. independent dyadic normalizer (gf_wide_independent_witness.py, parametric) 15/15;
2. golden Fraction oracle (conformance/witness/gf{512,1024}/..._decode_ref.py) 15/15;
3. analytic separation-bound (SEPARATION_BOUND.md, zero rounding over 2^512 / 2^1024).
Cross-check dyadic==Fraction: 201512 representative codes (seed=512 / seed=1024) agree.
OOM-safe (+-2^194 / +-2^390 exponent kept symbolic, numerators <= ~2^318 / ~2^634).
INDEX: bitexact 72 -> 74, selfconsistent 3 -> 1 (only gf256 remains), structural 8.
Status [verified SW] -- NOT on-silicon Tier-E (HW [REQUIRES USER ACTION], #199). Catalog=83.
Closes #1380
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This was referenced Jul 6, 2026
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Paired promotion of gf512 (S1 E195 M316, BIAS=2^194-1) + gf1024 (S1 E391 M632, BIAS=2^390-1; lowest phi-distance in the ladder). M>52 -> no FP lowering; exact dyadic odd*2^k (parametric separation-bound, same lemma as gf96/gf128). E/M/BIAS verified vs SSOT.
Witnesses (each, abs_error=0): dyadic normalizer 15/15; Fraction oracle 15/15; analytic separation-bound. Cross-check dyadic==Fraction: 201512 codes (seed=512/1024) agree. OOM-safe (+-2^194/+-2^390 symbolic).
INDEX: bitexact 72->74, selfconsistent 3->1 (only gf256 remains), structural 8. Status [verified SW] -- NOT Tier-E (HW [REQUIRES USER ACTION], trinity-fpga #199). Catalog=83.
Closes #1380.