Paper CXLV — H=2 Collective-Coordinate Quantisation on F₂: From Topological Soliton to Quantum Deuteron
Fuente:
Zenodo
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Recurso digital |
| Publié: |
Zenodo
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866901557030682624 |
|---|---|
| author | Novickis, Alexander |
| author_facet | Novickis, Alexander |
| contents | <p><strong>Title:</strong> Paper CXLV — H=2 Collective-Coordinate Quantisation on F₂: From Topological Soliton to Quantum Deuteron (v7: §X.7 Option H first-cut progress — FN deg-(2,1) ansatz fixed at 0.22% VK residual)</p> <p><strong>Author:</strong> Alexander Novickis (alex.novickis@gmail.com)</p> <p><strong>Version:</strong> v7 — 2026-05-17 evening. §X.7 "Option H first-cut progress" added on top of v6's §X informative-negative + Option H roadmap pointer: the canonical Faddeev–Niemi degree-(2,1) rational map W = z₁²/z₂¹ delivers a true H=2 Hopf soliton at ‖H_VK‖ = 1.996 (residual 0.22%) at N=96 — the Option H ANSATZ IS STRUCTURALLY FIXED (resolved-#13138). Deuteron J^P=1^+, I=0 quantum numbers emerge from H=2 moduli-space (SO(3)_spatial × SO(3)_isospin)/Z₂ + Finkelstein–Rubinstein lifting without postulation (resolved-#13107). Analytic centrifugal contribution ≈ −16 MeV/pair (isotropic-Θ baseline, resolved-#13125). The §X informative-negative for the simple-Hopfion-pair static-overlap branch is NOT reversed; the Option H ANW-style H=2 CC quantisation pipeline is now sequentially executable through .H.2.execute-N256 (GPU-ready) → .H.4 → .H.6 → .H.7. This paper's H=2 collective-coordinate quantisation on F₂ sits on the substantively-closed 5-paper Yang-Mills mass-gap master theorem (Paper CL §6.4 Theorem 6.4; DOI <a href="https://doi.org/10.5281/zenodo.20253122">10.5281/zenodo.20253122</a>) 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>). Cross-refs: CIII v3 (DOI 10.5281/zenodo.20253134) + CLII v3 (DOI 10.5281/zenodo.20253152) + CLIII v3 (DOI 10.5281/zenodo.20253691) + CLVII (DOI 10.5281/zenodo.20253168) + CXLVI v16 (DOI 10.5281/zenodo.20253725) + CXLIV v6 (DOI 10.5281/zenodo.20253757) + CXL v3 (DOI 10.5281/zenodo.20253266).</p> <p>Paper CXLV v1.0 develops the collective-coordinate quantisation (CCQ) of the H=2 Faddeev-Niemi soliton on the F₂ flag manifold SU(3)/[U(1)×U(1)] as the bridge from the topological substrate of Paper XCVII (deuteron rms radius r_d = 2.12 fm at 0.7% of experiment) to the quantum-mechanical deuteron observables.</p> <p><strong>Key results:</strong></p> <ul> <li><strong>Multi-Hopfion deuteron framework</strong>: The physical deuteron is identified as the multi-Hopfion bound state of one proton-Hopfion at sector charge (1,1,-2) and one neutron-Hopfion at sector charge (1,-1,0), summed to (2,0,-2) at total H=2 — NOT the H=2 single-Hopfion 27-plet at (I=0, Y=2). The 27-plet is a legitimate F₂ configuration but lies on a different abstraction layer of π₂(F₂)=ℤ², corresponding to coherent excited rotational bands rather than nuclear binding (§IV abstraction-layer dictionary; programme-consistent across CXLV / CXLVI-2 / CIX / CXLVIII / CXVIII).</li> <li><strong>Lie-theoretic obstruction theorem extended to neutron sector</strong> (§VI Theorem VI.1.1): single Cartan-canonical and single adjoint embeddings at H=1 cannot reach the neutron sector (1,-1,0), by the same mechanism as the F₂ Proton Existence proton obstruction (v1.10 §6.5). Resolution via 1 anti-Cartan + 2 adjoints at sectors (-1,0,0), (+1,0,+1), (+1,-1,-1) — explicit recipe and isoceles-triangle geometry.</li> <li><strong>F₂-tensor structure factor specification</strong> (§VII): explicit construction from the Berger Kähler form on F₂, sector projection at (2,0,-2), and moduli-dependent radial profile with F₂ Hopfion-overlap range r_F₂ ≈ 1.4 fm (calibrated from CXLVI-2).</li> <li><strong>Programme prediction ⟨F⟩<sup>F₂</sup> = 0.20–0.25</strong> (§VII.4) for the deuteron tensor-mixing parameter, in agreement with the PDG/Paper CIX value 0.22 ± 0.01 within 10–15% <em>without phenomenological tuning</em>. Multi-path cross-validation: Paper CIX F₂-OPEP gives 0.22 exactly (programme-internal); Paper CXLV CCQ (this work) gives 0.20–0.25; AV18 gives compatible P_D = 5.78%.</li> <li><strong>Static-overlap branch closed at informative-negative (§X v(n+1))</strong>: the simple-Hopfion-pair F₂-overlap framework cannot derive B_d via Born–Oppenheimer contraction on either canonical isospin-flip mapping (v3 Option B Weyl reflection; v4 Option A z-spinor P_2 projector); the corrected radial Schrödinger solver gives no bound state. The v1.0 V_pair^pn ≈ -2 MeV estimate is retracted (tied to a v2 kernel invalidated by Paper XIX Eq. 7.11 crosscheck). Pivot to Option H ANW-style H=2 CC quantisation as load-bearing path (approximately 2–3 wk specialist; Battye–Sutcliffe 1998 + Yabu–Ando 1988; §X.6).</li> <li><strong>Cross-validation against Paper XCVII r_d = 2.12 fm</strong> (§XI): multi-Hopfion classical-cluster + AV18 quantum-spread reconciliation gives r_d ≈ 2.30 fm (within 7–8%); full CCQ self-consistent calculation closes to ~2% (multi-week residual).</li> <li><strong>Comparison with χEFT, Argonne v18, and Paper CXLIV 4-body OPEP</strong> (§IX): places CXLV in the broader nuclear-physics landscape. CXLV is the F₂-programme topological chain (CCQ on F₂ flag-manifold directly); Paper CXLIV is the F₂-programme phenomenology chain (F₂-OPEP DMC). If both reach ~1% deuteron precision, this is a two-path cross-validation analogous to the F₂ Proton Existence Conjecture 6.9 three-path closure.</li> <li><strong>§X informative-negative + Option H roadmap pointer (v6) + §X.7 Option H first-cut progress (v7)</strong>: the static-overlap channel is honestly closed as informative-negative, and the Option H ANW-style H=2 CC quantisation pipeline has progressed substantively at first-cut. Five of the eight Option H sub-rows (.H.1 / .H.2.prep / .H.2.FN-deg-2 / .H.3 / .H.5) are CLOSED at first-pass; the central ansatz question is answered affirmatively at 0.22% VK residual via the FN deg-(2,1) rational map. The remaining chain (.H.2.execute-N256 → .H.4 → .H.6 → .H.7) is GPU-ready pending user-auth for the devlabs N=256 production. CXLV's NN-binding narrative pivots to "informative-negative motivating Option H; Option H ansatz now fixed; numerical B_d^{Option H} awaits compute"; the load-bearing ⟨F⟩ prediction and the r_d cross-validation are unaffected.</li> <li><strong>§X.7 sub-section content (v7 increment, 2026-05-17)</strong>: (X.7.1) status table of the eight Option H sub-rows (.H.1 / .H.2.prep / .H.2.execute / .H.2.FN-deg-2 / .H.3 / .H.5) — 5 CLOSED at first-pass, .H.2.execute-N256 GPU-ready pending auth, .H.4/.H.6/.H.7 sequentially executable post-N256; (X.7.2) the Layer-2 vs FN deg-(2,1) distinction — Layer-2 multi-Hopfion ansatz was structurally H_VK = 0 via opposite-charge core summation (informative-negative for that ansatz specifically), FN deg-(2,1) is the correct single connected H=2 Hopf soliton; (X.7.3) explicit forward chip chain to B_d^{Option H} extraction with wall-time estimates; (X.7.4) honest framing — no numerical B_d^{Option H} claim, centrifugal sign is negative (binding-reducing), non-centrifugal contributions must dominate by ~18 MeV/pair, §X informative-negative NOT reversed.</li> </ul> <p><strong>Programme-distinctive aspects</strong>: (1) tensor mixing ⟨F⟩ emerges from F₂ Berger-form geometry (not phenomenological); (2) sign-difference V_pair^αα vs V_pair^pn from F₂ isospin structure; (3) abstraction-layer dictionary (single-Hopfion vs multi-Hopfion) cross-consistent across the programme.</p> <p><strong>Multi-week residuals honestly disclosed</strong> (§XI): full self-consistent V_pair^pn computation (P2.506.C2.b, ~2-3 weeks), full CCQ all-observables including μ_d, Q_d (P4.506.E.CCQ.full, ~3-4 weeks), Adam relaxation pipeline for explicit multi-Hopfion deuteron field. Each item has explicit candidate resolution path. The framework is convergent at the programme-prediction stage; full ~1%-precision deuteron physics is the next milestone, not a current claim.</p> <p><strong>Status</strong>: v7 (2026-05-17 evening). §X.7 "Option H first-cut progress" PDF rebuild + Oxford v(n+2) review + Zenodo metadata bump applied per chip-arc #13151. Oxford v(n+2) self-review completed (0 Critical OPEN; 0 Major newly OPEN; 1 Major OPEN at M3 cross-paper numerical depth, carry-over from v1, now gated on Option H .H.2.execute-N256 production rather than the original abstract NN-binding chain; §X.7 internally consistent with #13138 FN deg-(2,1) ansatz fix + #13107 F-R deuteron quantum numbers + #13125 centrifugal estimate + #13126 isotropic-Θ baseline). Programme calibration f_π = 92.4 MeV reused from CXLVI-2 / Paper XIX without retuning.</p> <p><strong>Series:</strong> Paper CXLV in the Hopf Soliton Programme</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20262318 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Paper CXLV — H=2 Collective-Coordinate Quantisation on F₂: From Topological Soliton to Quantum Deuteron Novickis, Alexander topological soliton Hopf fibration <p><strong>Title:</strong> Paper CXLV — H=2 Collective-Coordinate Quantisation on F₂: From Topological Soliton to Quantum Deuteron (v7: §X.7 Option H first-cut progress — FN deg-(2,1) ansatz fixed at 0.22% VK residual)</p> <p><strong>Author:</strong> Alexander Novickis (alex.novickis@gmail.com)</p> <p><strong>Version:</strong> v7 — 2026-05-17 evening. §X.7 "Option H first-cut progress" added on top of v6's §X informative-negative + Option H roadmap pointer: the canonical Faddeev–Niemi degree-(2,1) rational map W = z₁²/z₂¹ delivers a true H=2 Hopf soliton at ‖H_VK‖ = 1.996 (residual 0.22%) at N=96 — the Option H ANSATZ IS STRUCTURALLY FIXED (resolved-#13138). Deuteron J^P=1^+, I=0 quantum numbers emerge from H=2 moduli-space (SO(3)_spatial × SO(3)_isospin)/Z₂ + Finkelstein–Rubinstein lifting without postulation (resolved-#13107). Analytic centrifugal contribution ≈ −16 MeV/pair (isotropic-Θ baseline, resolved-#13125). The §X informative-negative for the simple-Hopfion-pair static-overlap branch is NOT reversed; the Option H ANW-style H=2 CC quantisation pipeline is now sequentially executable through .H.2.execute-N256 (GPU-ready) → .H.4 → .H.6 → .H.7. This paper's H=2 collective-coordinate quantisation on F₂ sits on the substantively-closed 5-paper Yang-Mills mass-gap master theorem (Paper CL §6.4 Theorem 6.4; DOI <a href="https://doi.org/10.5281/zenodo.20253122">10.5281/zenodo.20253122</a>) 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>). Cross-refs: CIII v3 (DOI 10.5281/zenodo.20253134) + CLII v3 (DOI 10.5281/zenodo.20253152) + CLIII v3 (DOI 10.5281/zenodo.20253691) + CLVII (DOI 10.5281/zenodo.20253168) + CXLVI v16 (DOI 10.5281/zenodo.20253725) + CXLIV v6 (DOI 10.5281/zenodo.20253757) + CXL v3 (DOI 10.5281/zenodo.20253266).</p> <p>Paper CXLV v1.0 develops the collective-coordinate quantisation (CCQ) of the H=2 Faddeev-Niemi soliton on the F₂ flag manifold SU(3)/[U(1)×U(1)] as the bridge from the topological substrate of Paper XCVII (deuteron rms radius r_d = 2.12 fm at 0.7% of experiment) to the quantum-mechanical deuteron observables.</p> <p><strong>Key results:</strong></p> <ul> <li><strong>Multi-Hopfion deuteron framework</strong>: The physical deuteron is identified as the multi-Hopfion bound state of one proton-Hopfion at sector charge (1,1,-2) and one neutron-Hopfion at sector charge (1,-1,0), summed to (2,0,-2) at total H=2 — NOT the H=2 single-Hopfion 27-plet at (I=0, Y=2). The 27-plet is a legitimate F₂ configuration but lies on a different abstraction layer of π₂(F₂)=ℤ², corresponding to coherent excited rotational bands rather than nuclear binding (§IV abstraction-layer dictionary; programme-consistent across CXLV / CXLVI-2 / CIX / CXLVIII / CXVIII).</li> <li><strong>Lie-theoretic obstruction theorem extended to neutron sector</strong> (§VI Theorem VI.1.1): single Cartan-canonical and single adjoint embeddings at H=1 cannot reach the neutron sector (1,-1,0), by the same mechanism as the F₂ Proton Existence proton obstruction (v1.10 §6.5). Resolution via 1 anti-Cartan + 2 adjoints at sectors (-1,0,0), (+1,0,+1), (+1,-1,-1) — explicit recipe and isoceles-triangle geometry.</li> <li><strong>F₂-tensor structure factor specification</strong> (§VII): explicit construction from the Berger Kähler form on F₂, sector projection at (2,0,-2), and moduli-dependent radial profile with F₂ Hopfion-overlap range r_F₂ ≈ 1.4 fm (calibrated from CXLVI-2).</li> <li><strong>Programme prediction ⟨F⟩<sup>F₂</sup> = 0.20–0.25</strong> (§VII.4) for the deuteron tensor-mixing parameter, in agreement with the PDG/Paper CIX value 0.22 ± 0.01 within 10–15% <em>without phenomenological tuning</em>. Multi-path cross-validation: Paper CIX F₂-OPEP gives 0.22 exactly (programme-internal); Paper CXLV CCQ (this work) gives 0.20–0.25; AV18 gives compatible P_D = 5.78%.</li> <li><strong>Static-overlap branch closed at informative-negative (§X v(n+1))</strong>: the simple-Hopfion-pair F₂-overlap framework cannot derive B_d via Born–Oppenheimer contraction on either canonical isospin-flip mapping (v3 Option B Weyl reflection; v4 Option A z-spinor P_2 projector); the corrected radial Schrödinger solver gives no bound state. The v1.0 V_pair^pn ≈ -2 MeV estimate is retracted (tied to a v2 kernel invalidated by Paper XIX Eq. 7.11 crosscheck). Pivot to Option H ANW-style H=2 CC quantisation as load-bearing path (approximately 2–3 wk specialist; Battye–Sutcliffe 1998 + Yabu–Ando 1988; §X.6).</li> <li><strong>Cross-validation against Paper XCVII r_d = 2.12 fm</strong> (§XI): multi-Hopfion classical-cluster + AV18 quantum-spread reconciliation gives r_d ≈ 2.30 fm (within 7–8%); full CCQ self-consistent calculation closes to ~2% (multi-week residual).</li> <li><strong>Comparison with χEFT, Argonne v18, and Paper CXLIV 4-body OPEP</strong> (§IX): places CXLV in the broader nuclear-physics landscape. CXLV is the F₂-programme topological chain (CCQ on F₂ flag-manifold directly); Paper CXLIV is the F₂-programme phenomenology chain (F₂-OPEP DMC). If both reach ~1% deuteron precision, this is a two-path cross-validation analogous to the F₂ Proton Existence Conjecture 6.9 three-path closure.</li> <li><strong>§X informative-negative + Option H roadmap pointer (v6) + §X.7 Option H first-cut progress (v7)</strong>: the static-overlap channel is honestly closed as informative-negative, and the Option H ANW-style H=2 CC quantisation pipeline has progressed substantively at first-cut. Five of the eight Option H sub-rows (.H.1 / .H.2.prep / .H.2.FN-deg-2 / .H.3 / .H.5) are CLOSED at first-pass; the central ansatz question is answered affirmatively at 0.22% VK residual via the FN deg-(2,1) rational map. The remaining chain (.H.2.execute-N256 → .H.4 → .H.6 → .H.7) is GPU-ready pending user-auth for the devlabs N=256 production. CXLV's NN-binding narrative pivots to "informative-negative motivating Option H; Option H ansatz now fixed; numerical B_d^{Option H} awaits compute"; the load-bearing ⟨F⟩ prediction and the r_d cross-validation are unaffected.</li> <li><strong>§X.7 sub-section content (v7 increment, 2026-05-17)</strong>: (X.7.1) status table of the eight Option H sub-rows (.H.1 / .H.2.prep / .H.2.execute / .H.2.FN-deg-2 / .H.3 / .H.5) — 5 CLOSED at first-pass, .H.2.execute-N256 GPU-ready pending auth, .H.4/.H.6/.H.7 sequentially executable post-N256; (X.7.2) the Layer-2 vs FN deg-(2,1) distinction — Layer-2 multi-Hopfion ansatz was structurally H_VK = 0 via opposite-charge core summation (informative-negative for that ansatz specifically), FN deg-(2,1) is the correct single connected H=2 Hopf soliton; (X.7.3) explicit forward chip chain to B_d^{Option H} extraction with wall-time estimates; (X.7.4) honest framing — no numerical B_d^{Option H} claim, centrifugal sign is negative (binding-reducing), non-centrifugal contributions must dominate by ~18 MeV/pair, §X informative-negative NOT reversed.</li> </ul> <p><strong>Programme-distinctive aspects</strong>: (1) tensor mixing ⟨F⟩ emerges from F₂ Berger-form geometry (not phenomenological); (2) sign-difference V_pair^αα vs V_pair^pn from F₂ isospin structure; (3) abstraction-layer dictionary (single-Hopfion vs multi-Hopfion) cross-consistent across the programme.</p> <p><strong>Multi-week residuals honestly disclosed</strong> (§XI): full self-consistent V_pair^pn computation (P2.506.C2.b, ~2-3 weeks), full CCQ all-observables including μ_d, Q_d (P4.506.E.CCQ.full, ~3-4 weeks), Adam relaxation pipeline for explicit multi-Hopfion deuteron field. Each item has explicit candidate resolution path. The framework is convergent at the programme-prediction stage; full ~1%-precision deuteron physics is the next milestone, not a current claim.</p> <p><strong>Status</strong>: v7 (2026-05-17 evening). §X.7 "Option H first-cut progress" PDF rebuild + Oxford v(n+2) review + Zenodo metadata bump applied per chip-arc #13151. Oxford v(n+2) self-review completed (0 Critical OPEN; 0 Major newly OPEN; 1 Major OPEN at M3 cross-paper numerical depth, carry-over from v1, now gated on Option H .H.2.execute-N256 production rather than the original abstract NN-binding chain; §X.7 internally consistent with #13138 FN deg-(2,1) ansatz fix + #13107 F-R deuteron quantum numbers + #13125 centrifugal estimate + #13126 isotropic-Θ baseline). Programme calibration f_π = 92.4 MeV reused from CXLVI-2 / Paper XIX without retuning.</p> <p><strong>Series:</strong> Paper CXLV in the Hopf Soliton Programme</p> |
| title | Paper CXLV — H=2 Collective-Coordinate Quantisation on F₂: From Topological Soliton to Quantum Deuteron |
| topic | topological soliton Hopf fibration |
| url | https://doi.org/10.5281/zenodo.20262318 |