PDL_D59_script1.py: Verification of the Five Lemmas Establishing the Fundamental Representation 3 of SU(3)_c from the PDL Axioms C1–C4 — Supplementary material to PDL Document D59

Supplementary verification script for PDL Document D59 (Physical Identification of SU(3)_c and the Fundamental Representation 3 from the PDL Axioms C1–C4, Projective Dynamic Logo Framework). The script verifies five lemmas (L1–L5) and one documented negative result (NEG) by exhaustive exact-integer arithmetic, using only the Python standard library (itertools, fractions). No floating-point arithmetic is introduced. All verifications return PASSED; the negative result returns VERIFIED. Lemmas verified: L1 — S3 = S4/V4 acts faithfully and transitively on V4{e} (recalled from D58, re-verified here). L2 — Character decomposition of the permutation representation: χ_π = χ_trivial + χ_standard; verified over all 24 elements of S4. L3 — The trace-zero plane W = {a+b+c=0} ⊂ C³ is the unique S3-invariant complement of C(1,1,1); 6 distinct 2×2 integer matrices with |det|=1 confirmed. L4 — The A2 root system is realised in W: 6 roots of squared norm 2, single S3-orbit, Cartan matrix [[2,−1],[−1,2]] confirmed by exact integer inner products. L5 — The isospin asymmetry Δn = n_d − n_u = 4 > 0 (unconditional theorem of C4, D47) selects orientation 3 over 3-bar; canonical order k1 < k2 < k3 and ratio k3/(k1+k2) = R_e = 6 verified exactly. NEG — No non-trivial S3 permutation fixes the ordered triple (k1, k2, k3); the bijection (T2)↔(T3) is physically motivated, not S4-equivariant. Executed independently in Google Colab (Python 3.12+) under python -W error PDL_D59_script1.py before LaTeX drafting of D59 began (PDL verrouillage protocol). Dependencies: Python standard library only (itertools, fractions). No numpy, no networkx required. PDL corpus: D01–D58 + DS01 + DL01–DL02 + N01 + D-exp series. Community: pdl-framework.