Guardat en:
| Autor principal: | |
|---|---|
| Format: | Recurso digital |
| Idioma: | anglès |
| Publicat: |
Zenodo
2026
|
| Matèries: | |
| Accés en línia: | https://doi.org/10.5281/zenodo.20106768 |
| Etiquetes: |
Afegir etiqueta
Sense etiquetes, Sigues el primer a etiquetar aquest registre!
|
Taula de continguts:
- <p>We show that the combinatorial structure of the complete graph on five vertices (K₅, the pentachoron) encodes both the atom and the origin of temperature. A binary colouring of vertices yields, with zero free parameters: (1) the alpha particle as the unique nucleus within one tetrahedron [T1]; (2) the nuclear mass number A = 4k − s and maximum charge Z_max = 2k for assemblies of k pentachores [T1]; (3) the α-conjugate sequence A = 4k, Z = N = 2k saturating Z_max (⁴He, ⁸Be, ¹²C, ¹⁶O, ²⁰Ne, ²⁴Mg, ²⁸Si, ³²S, ³⁶Ar, ⁴⁰Ca for k = 1–10) [T1]; the doubly-magic subset (⁴He, ¹⁶O, ⁴⁰Ca) follows by intersection with the shell-model magic numbers {2, 8, 20} accepted as external input [T2]; (4) all stable isotopes from H to Ne reproduced from colourings of k = 1–5 pentachores [T1] (with ⁶Li located in the A = 6 structural gap of the chain topology); (5) electron shell capacities 2(l+1)² from the uniqueness of d = 4 [T1]; (6) valences 1, 0, 1, 2, 3, 4, 3, 2, 1, 0 for H–Ne, exact 10/10, from the distance to the nearest noble gas Z = 2k_noble [T2]; (7) chemical bonding as shared tetrahedral faces between pentachoric assemblies [T2]; (8) temperature as total reconstruction conflict: T(S) ∝ exp(+α* · C(S)), where the integer C(S) = Σ_v n_v counts the simultaneous reconstruction attempts at shared vertices, dual to mass m_k/m_e = u^(n_k²) (u = exp(α*/4), P2) where n² counts spectral channels [T1, mass formula from P2]. The instability of ⁸Be is derived as a theorem: two nuclear tetrahedra sharing zero triangular faces (the α-conjugate at k = 2) fragment into 2α despite saturating Z_max. Mass and temperature share the same coupling α* = 1/(4 ln 2) and the same positive exponential structure: mass counts what must be built per mode, temperature counts disagreements to resolve per assembly. The K₅ thermal scale k_B T* τ₀/ℏ = ρ* follows from P15 and anchors T(S) on the fundamental tick without free parameters. Every quantitative claim is verified by a companion script (P12_circuit_v4.py); the α-conjugate sequence is verified by exhaustive enumeration up to k = 7 (²⁸Si). No continuous free parameter enters the construction.</p>