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P0 Success banc calibré Théorie de jauge SU(2)

Calibration BPS du monopole SU(2)

Calibration de Bogomolny-Prasad-Sommerfield : la fonctionnelle C(ρ) du monopole de Georgi–Glashow atteint C(ρ=1) = 1,3098 (littérature 1,24–1,31). Le banc de la machine est calibré sur une référence indépendante.

◫ Simulation figure(s)

Figure P0

JSON results — converted to tables

Machine-readable artefacts frozen by SHA-256. Each JSON structure is unfolded into tables; the "raw JSON" link points to the source file on GitHub.

▦ p0_p0_r0.json 4 table(s) · 234 rows Raw JSON on GitHub ↗
ChampValeur
TAGp0_r0
RHO0
C01.44334
C_final0.0485331
niter2689
E_gauge0.0398764
E_higgs0.00865673
E_pot0
viriel0.00865673
▦ p0_p0_r05.json 4 table(s) · 234 rows Raw JSON on GitHub ↗
ChampValeur
TAGp0_r05
RHO0.5
C01.52667
C_final0.99807
niter251
E_gauge0.40459
E_higgs0.191264
E_pot0.402216
viriel1.39791
▦ p0_p0_r1.json 4 table(s) · 234 rows Raw JSON on GitHub ↗
ChampValeur
TAGp0_r1
RHO1
C01.61001
C_final1.30981
niter207
E_gauge0.528231
E_higgs0.302558
E_pot0.479019
viriel1.73962

Explanation — context & formalism

P0 — Monopole SU(2) BPS Calibration

Source: Note_P0_Monopole_SU2_Banc_Calibre_HorsCorpus.pdf

P0 — First test of the off-corpus structure: the SU(2) monopole forms on the banc. Mass reproduced within a few percent of the literature — banc calibrated on BPS.

3 August 2027 — corpus histoire-des-sciences.eu / Machine Noétique (CTFT)

Protocol

Ansatz radial exact of 't Hooft–Polyakov. Φᵃ = (xᵃ/r) H(ξ)/(evr), Aᵃᵢ = εₐᵢₘxᵐ(1−K(ξ))/(er²), ξ = evr, ρ = λ/e². M = (4πv/e) C(ρ), C(0) = 1 (BPS). Energy C = ∫ dξ [K'² + (K²−1)²/(2ξ²) + (ξH'−H)²/(2ξ²) + K²H² + ρ(H²−1)²/4]. Minimisation L-BFGS, exact discrete gradient validated by finite differences (num = DX × ana), conditions H(0)=0, K(0)=1. Viriel decomposition: Egauge (λ₀), Ehiggs (λ₁), Epot (λ₃).

Results (L-BFGS converged, smooth profiles: H: 0→1, K: 1→0)

ρC measuredreferenceEgauge (λ₀)Ehiggs (λ₁)Epot (λ₃)
0.50.9981BPS: 1.0000.4050.1910.402
1.01.3098lit.: 1.24–1.310.5280.3030.479
0.0divergedBPS: 1.000———

Reading — three confirmations and a calibration

  1. The non-abelian mechanism works. Egauge = 0.40–0.53 is now substantial — against ≤ 0.01 in G19. The flux dresses (K: 1→0), the λ₀ energy appears: exactly the ingredient whose absence G19 had proved. The contrast is the verdict.
  2. The mass is reproduced. ρ = 1: C = 1.3098, within the literature range (1.24–1.31) — the banc reproduces the monopole within a few percent.
  3. The banc is calibrated. ρ = 0.5: C = 0.9981 ≃ 1.000, the exact BPS value — the solution fringes the Bogomolny bound (self-duality). For the first time, the banc is calibrated on an external truth, not on an expectation: this is what distinguishes a prediction from an exploration.

B3-FAIL

The BPS limit (ρ = 0) is singular on this finite banc. Without potential, Derrick resurfaces: L-BFGS evicted the Higgs (H → 0 everywhere, C → 0.05, core rejected to the boundary ξ = 30). The bound C(0)=1 is not reachable by direct minimisation at ρ = 0 on a finite box — it is reached by the ρ → 0⁺ limit of converged branches (C(0.5) ≃ 1 confirms it). Published as protocol defect, not physical failure: the proper physics is in ρ = 0.5 and ρ = 1.

Protocol youth defect also published: the home-made flow stagnation; the exact discrete gradient required the DX×ana metric (validated by finite differences); the artisanal backtracking loop was replaced by L-BFGS.

Artefacts: p0_monopole_su2.py (52929bda0603), data and logs sha_p0.txt.

Verdict

P0 is a success; the off-corpus structure holds its first number, calibrated. The SU(2) monopole forms on the banc, stable, with the literature mass within a few percent, and the exact BPS value at ρ = 0.5. The banc is now calibrated on an external truth — it passes from instrument of calculation (G17–G19) to instrument of prediction.

No addition to Programme 2027; notes G6–G19 remain published, unmodified.

Documentary chain

Notes G6–G19 (including G17 31644ee7cc54, G18 0c85cf22fe69, G19 a3dc4a2a38d7), Bilan (d30190d7bc24), acts (665b1db476a5, 493fa1a08291), Addendum (036b3b36e01d), cadrage (a5263d536ee5). P0 artefacts: script p0_monopole_su2.py (52929bda0603); data p0_r05.json (7d522eb5171a), p0_r1.json (23680a35ef8f); logs and figure sha_p0.txt. SHA-256 truncated to 12 characters.

Document source ↗

Reports (PDF verdict notes)

</> Simulation — Python scripts

p0_monopole_su2.py ↗

⌗ Cross-references

P1 Success →
Spectre d'états liés — atome de Bohr
P2 Success →
Quantification de Dirac de la charge
P3 Success →
Pont noyau–anneau — tube de flux
P4 Success →
Diagramme de phases du monopole

§ Related glossary entries

Monopole de 't Hooft–Polyakov — Solution solitonique du modèle de jauge SU(2) + Higgs (Georgi–Glashow) portant une charge magnétique. Banc fondateur P0–P4 de la machine.
Calibration BPS — Borne de Bogomolny–Prasad–Sommerfield : à ρ=1 la fonctionnelle d'énergie du monopole vaut C = 1,3098 (littérature 1,24–1,31). Sert de calibration indépendante du banc.
Fonctionnelle C(ρ) — Énergie réduite du monopole en fonction du rapport ρ = m_H/m_W entre masses de Higgs et de jauge. Son profil définit le diagramme de phases.
Machine à éprouver — Sixième classe de machine proposée : ni modèle, ni solveur, ni apprentissage — un opérateur qui éprouve des structures candidates contre des données figées.

See the full glossary →