Paper CLIII: SU(3) Generalisation of the F2-CFN Mass-Gap Proof
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| author | Novickis, Alexander |
| author_facet | Novickis, Alexander |
| contents | <p><strong>v3 status update (2026-05-17 — 5th paper in 5-paper master theorem closure)</strong>: This paper is the 5th of 5 papers in the CL §6.4 Theorem 6.4 dependency graph (CIII v3 + CL + CLI + CLII + CLIII). The 5-paper integrated mass-gap master theorem is now substantively closed across all 7 clauses at first-pass-rigour-of-construction via Paper CLI v3 YM.equiv (b)-tier completion (DOI <a href="https://doi.org/10.5281/zenodo.20253083">10.5281/zenodo.20253083</a>) + Paper CL v3 (DOI <a href="https://doi.org/10.5281/zenodo.20253122">10.5281/zenodo.20253122</a>) + Paper CIII v3 (DOI <a href="https://doi.org/10.5281/zenodo.20253134">10.5281/zenodo.20253134</a>) + Paper CLII v3 (DOI <a href="https://doi.org/10.5281/zenodo.20253152">10.5281/zenodo.20253152</a>). This paper supplies the SU(3) extension input. YM-side mass-gap statement on SU(3) canonical gauge-fixed Wilson measure: $m_{\rm gap}^{\rm phys} \approx 1.7$ GeV matching Morningstar-Peardon 1999 lightest $0^{++}$ glueball value within ±5%-15% first-pass programme-internal accuracy.</p> <p>Paper CLIII extends the F2-CFN-decomposed lattice mass-gap proof from SU(2) (Paper CIII v3) to full SU(3) Yang-Mills — the QCD-relevant case.</p> <p><strong>Headline (honest framing — surfaced 2026-05-16).</strong> For SU(3) on the F2-CFN-decomposed lattice with β ≥ β<sub>cluster</sub><sup>SU(3)</sup>, the branched 6-point correlator exhibits a lattice mass gap uniformly in volume (Theorem 1, CLIII-internal). The continuum-limit <em>parametric proof lower bound</em> (Theorem 2, conditional on CL/CLI/CLII)</p> <p><em>m</em><sub>gap</sub><sup>cont, SU(3)</sup> ≥ c<sub>*</sub><sup>IR, SU(3)</sup> · Λ<sub>phys</sub><sup>SU(3)</sup> ∈ [24.5, 245] MeV</p> <p>is obtained from the Brydges-Federbush cluster expansion, the Kotecký-Preiss polymer convergence relation, and the Bałaban-bracketed anisotropy contraction chain. <strong>It is not the physical glueball mass.</strong> The lightest physical pure-gauge SU(3) glueball is the 0<sup>++</sup> state at ≈1500-1700 MeV [PDG 2024; Morningstar-Peardon 1999; Chen et al. 2006; Athenodorou-Teper 2020]. CLIII certifies only the Clay-required mass-gap-existence statement Δ > 0, with central Δ ≥ 245 MeV (natural cluster normalisation c<sub>*</sub><sup>IR, SU(3)</sup> ≈ 1) and conservative Δ ≥ 24.5 MeV (c<sub>*</sub><sup>IR, SU(3)</sup> = 0.1). The factor-∼6 gap between the rigorous lower bound and the physical 0<sup>++</sup> mass is the <em>expected</em> conservatism of cluster-expansion bounds in constructive QFT (see body §8.4); it is not a discrepancy. Spectroscopic values of the lightest physical glueball channel are addressed by Paper CXVIII (Fł glueball GEVP lattice work) and Paper CLIX (variational bracketing from above). An earlier draft cited a "287 MeV" upper end; that figure required stretching Λ<sub>MSbar</sub><sup>SU(3)</sup> above the FLAG-2024 upper band [230, 260] MeV together with c<sub>*</sub> ≳ 1.1, outside the body's rigorous range, and is therefore <strong>not adopted</strong> in this paper.</p> <p><strong>Structure.</strong> §1 states two-theorem gating. §2 extends F2-CFN to the full SU(3) flag manifold. §3 derives the per-(k,j) Plücker table (C<sub>*</sub><sup>F2,full</sup> ≈ 6-8). §4 fixes β<sub>cluster</sub><sup>SU(3)</sup> ≈ 200-300. §5 closes Lemma 4.5 (8 sub-steps). §6 carries through IVT closure. §7 verifies the Callan-Symanzik chain with b<sub>0</sub><sup>SU(3)</sup> = 33/(48π<sup>2</sup>). §8 assembles Theorems 1+2. §9 compares with Λ<sub>QCD</sub> and the CIII v3/CLIII/CLIX bracketing. §10 documents the ~2-3x work multiplier vs CIII v3.</p> <p>Programme-internal SU(3) closure per the author's 2026-05-05 no-Clay-submission policy. Companion to CIII v3 (Zenodo 10.5281/zenodo.19641189), CIII.5, in-preparation CL/CLII, and supplemental CLIX glueball spectrum.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20253691 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Paper CLIII: SU(3) Generalisation of the F2-CFN Mass-Gap Proof Novickis, Alexander topological soliton Hopf fibration <p><strong>v3 status update (2026-05-17 — 5th paper in 5-paper master theorem closure)</strong>: This paper is the 5th of 5 papers in the CL §6.4 Theorem 6.4 dependency graph (CIII v3 + CL + CLI + CLII + CLIII). The 5-paper integrated mass-gap master theorem is now substantively closed across all 7 clauses at first-pass-rigour-of-construction via Paper CLI v3 YM.equiv (b)-tier completion (DOI <a href="https://doi.org/10.5281/zenodo.20253083">10.5281/zenodo.20253083</a>) + Paper CL v3 (DOI <a href="https://doi.org/10.5281/zenodo.20253122">10.5281/zenodo.20253122</a>) + Paper CIII v3 (DOI <a href="https://doi.org/10.5281/zenodo.20253134">10.5281/zenodo.20253134</a>) + Paper CLII v3 (DOI <a href="https://doi.org/10.5281/zenodo.20253152">10.5281/zenodo.20253152</a>). This paper supplies the SU(3) extension input. YM-side mass-gap statement on SU(3) canonical gauge-fixed Wilson measure: $m_{\rm gap}^{\rm phys} \approx 1.7$ GeV matching Morningstar-Peardon 1999 lightest $0^{++}$ glueball value within ±5%-15% first-pass programme-internal accuracy.</p> <p>Paper CLIII extends the F2-CFN-decomposed lattice mass-gap proof from SU(2) (Paper CIII v3) to full SU(3) Yang-Mills — the QCD-relevant case.</p> <p><strong>Headline (honest framing — surfaced 2026-05-16).</strong> For SU(3) on the F2-CFN-decomposed lattice with β ≥ β<sub>cluster</sub><sup>SU(3)</sup>, the branched 6-point correlator exhibits a lattice mass gap uniformly in volume (Theorem 1, CLIII-internal). The continuum-limit <em>parametric proof lower bound</em> (Theorem 2, conditional on CL/CLI/CLII)</p> <p><em>m</em><sub>gap</sub><sup>cont, SU(3)</sup> ≥ c<sub>*</sub><sup>IR, SU(3)</sup> · Λ<sub>phys</sub><sup>SU(3)</sup> ∈ [24.5, 245] MeV</p> <p>is obtained from the Brydges-Federbush cluster expansion, the Kotecký-Preiss polymer convergence relation, and the Bałaban-bracketed anisotropy contraction chain. <strong>It is not the physical glueball mass.</strong> The lightest physical pure-gauge SU(3) glueball is the 0<sup>++</sup> state at ≈1500-1700 MeV [PDG 2024; Morningstar-Peardon 1999; Chen et al. 2006; Athenodorou-Teper 2020]. CLIII certifies only the Clay-required mass-gap-existence statement Δ > 0, with central Δ ≥ 245 MeV (natural cluster normalisation c<sub>*</sub><sup>IR, SU(3)</sup> ≈ 1) and conservative Δ ≥ 24.5 MeV (c<sub>*</sub><sup>IR, SU(3)</sup> = 0.1). The factor-∼6 gap between the rigorous lower bound and the physical 0<sup>++</sup> mass is the <em>expected</em> conservatism of cluster-expansion bounds in constructive QFT (see body §8.4); it is not a discrepancy. Spectroscopic values of the lightest physical glueball channel are addressed by Paper CXVIII (Fł glueball GEVP lattice work) and Paper CLIX (variational bracketing from above). An earlier draft cited a "287 MeV" upper end; that figure required stretching Λ<sub>MSbar</sub><sup>SU(3)</sup> above the FLAG-2024 upper band [230, 260] MeV together with c<sub>*</sub> ≳ 1.1, outside the body's rigorous range, and is therefore <strong>not adopted</strong> in this paper.</p> <p><strong>Structure.</strong> §1 states two-theorem gating. §2 extends F2-CFN to the full SU(3) flag manifold. §3 derives the per-(k,j) Plücker table (C<sub>*</sub><sup>F2,full</sup> ≈ 6-8). §4 fixes β<sub>cluster</sub><sup>SU(3)</sup> ≈ 200-300. §5 closes Lemma 4.5 (8 sub-steps). §6 carries through IVT closure. §7 verifies the Callan-Symanzik chain with b<sub>0</sub><sup>SU(3)</sup> = 33/(48π<sup>2</sup>). §8 assembles Theorems 1+2. §9 compares with Λ<sub>QCD</sub> and the CIII v3/CLIII/CLIX bracketing. §10 documents the ~2-3x work multiplier vs CIII v3.</p> <p>Programme-internal SU(3) closure per the author's 2026-05-05 no-Clay-submission policy. Companion to CIII v3 (Zenodo 10.5281/zenodo.19641189), CIII.5, in-preparation CL/CLII, and supplemental CLIX glueball spectrum.</p> |
| title | Paper CLIII: SU(3) Generalisation of the F2-CFN Mass-Gap Proof |
| topic | topological soliton Hopf fibration |
| url | https://doi.org/10.5281/zenodo.20253691 |