The Baryon Resonance Ladder from a Discrete C8 Boundary: Holographic Dimensional Reduction, the Bipartite Winding Theorem, and the S3 × Z2 Partition Rule

The baryon resonance spectrum — the nucleon N (939), the ∆(1232), the Roper N (1440), the negative-parity orbital states N (1520) and N (1535), the higher-k resonances, and the established 4-star PDG cluster at the∼ 1500–1700 MeV level — emerges as the boundary conformal-field-theory trace of a closed topological string on the C8 matter octagon, the 2D boundary of the canonical Holographic Circlette Q3 matter cell after Fisher-Information- Action minimization squeezes the 3D bulk wavefunction onto the boundary. Five substrate- level ingredients combine to generate the complete coarse spectrum at zero free parameters once the chiral scale ΛQCD = 332 MeV is anchored: (i) the Virasoro descendant ladder with cos(kπ/8)Λ prefactor per level, giving cluster centres at Mk = (2√2+ k j=1 cos(jπ/8))ΛQCD; (ii) the bipartite winding theorem, a graph-theoretic corollary forcing closed loops on the C8 ring to have even step count, which deterministically generates the k-parity isospin alternation rule (even k → I = 1/2, odd k → I = 3/2); (iii) the ΛQCD/3 ≈ 110.6 MeV spin-orbit splitting from the S3 color-link hop cost, producing the ±100 MeV fine- structure envelope around each Virasoro cluster centre as a literal geometric path-length difference between parallel and anti-parallel orbital-spin alignments; (iv) the ∆n = 2 pair- quantization of radial excitations as cyclic bulk-breathing modes off the C8 boundary into the Q3 interior, identifying the Roper N (1440) as the substrate’s pure-radial (L, s, n) = (0, 0, 2) partition; (v) the S3 × Z2 partition rule with the induced-representation decom- position IndS3 S2 (1) = 1S ⊕ 2M supplying sub-leading multiplets within each cluster, de- riving N (1535) and N (1650) as the 2M component of the (1, 1, 0) orbital-plus-spin par- tition at the k = 2 Virasoro level. All seven PDG 4-star nucleon states at k = 2— N (1440), N (1520), N (1535), N (1650), N (1675), N (1680), N (1720) — are accounted for com- binatorially by three partitions of the k = 2 excitation number among the three substrate degrees of freedom (orbital, spin-injection, radial). The framework predicts a finite palin- dromic baryon ladder of exactly eight levels, in contrast to the infinite Regge trajectories of continuum string theory, with the saturation tied to the C8 ring’s eight-fold symmetry. The substrate’s baryon resonance count is structurally bounded, not extensible to arbitrary mass. 2026-06-20 legacy erratum: This version adds a canon erratum note to the legacy paper. Matter/spectroscopy mostly held but needs canon status check The body is preserved as a historical derivation trail; the erratum note identifies the current ANCHOR/DRIFT status and superseded claims. 2026-06-21 canon refresh: This version incorporates the 2026-06-21 ANCHOR/DRIFT/PTMS canon refresh and rebuilt local PDF.