feat(L-S37): PhiPriorQuantCorrect — Coq formal proof of phi-prior quantizer#794
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…correctness Closes #793 Adds formal Coq proof for L-S37 φ-prior on-chip weight quantizer correctness. Theorems proved (all Qed, no Admitted): - quantize_ternary: forall w, quantize w = TPos \/ TZero \/ TNeg - quantize_zero_region: forall w, |w| < phi_inv_sq -> quantize w = TZero - quantize_positive_region: phi_inv_sq <= w -> quantize w = TPos - quantize_negative_region: w <= -phi_inv_sq -> quantize w = TNeg - quantize_at_pos_boundary, quantize_just_below_pos_boundary - quantize_at_neg_boundary, quantize_just_below_neg_boundary - quantize_zero: quantize 0 = TZero - quantize_q115_complete: Q1.15 range completeness - quantize_symmetric_pos/neg/zero: anti-symmetry - phi_inv_sq_positive, phi_inv_sq_in_range, ternary_encoding_smaller Verification: coqc 8.20.1 exit 0 phi_inv_sq = 12533 (Q1.15 threshold) DOI: 10.5281/zenodo.19227877 Apache-2.0, no vendor IP
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Closes #793
L-S37: φ-prior Weight Quantizer — Coq Formal Proof
Summary
Adds
docs/phd/theorems/igla/PhiPriorQuantCorrect.v: a self-contained Coq 8.20.1 formal proof of correctness for the L-S37 φ-prior on-chip weight quantizer.Quantizer Rule
Theorems Proved (all Qed, zero Admitted)
quantize_ternaryforall w, quantize w = TPos \/ TZero \/ TNegquantize_zero_regionforall w, Z.abs w < phi_inv_sq -> quantize w = TZeroquantize_positive_regionphi_inv_sq <= w -> quantize w = TPosquantize_negative_regionw <= -phi_inv_sq -> quantize w = TNegquantize_at_pos_boundaryquantize phi_inv_sq = TPosquantize_just_below_pos_boundaryquantize (phi_inv_sq - 1) = TZeroquantize_at_neg_boundaryquantize (- phi_inv_sq) = TNegquantize_just_below_neg_boundaryquantize (-(phi_inv_sq-1)) = TZeroquantize_zeroquantize 0 = TZeroquantize_q115_completequantize_symmetric_pos/neg/zeroVerification
Coq version: 8.20.1
Anchor
φ² + φ⁻² = 3 ; phi_inv_sq = 12533 ; DOI: 10.5281/zenodo.19227877
Apache-2.0, no vendor IP, Author: Dmitrii Vasilev admin@t27.ai