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| Formato: | Recurso digital |
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Zenodo
2026
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| Acceso en línea: | https://doi.org/10.5281/zenodo.19200440 |
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- <p>We present a first-principles derivation of the complete periodic table of elements through Oganesson (Z≤118)—including the Aufbau filling sequence, the 7-period structure with capacities {2,8,8,18,18,32,32}, the noble gas atomic numbers {2,10,18,36,54,86,118}, the IUPAC 18-group column structure, the s/p/d/f block decomposition, chemical family classification, and ionic bonding with stoichiometric ratios—from the Recognition Composition Law (RCL) with zero continuously adjustable parameters. Within the certified chemistry scope Z≤118, equivalently the 19-candidate subshell set 1≤n≤7, 0≤ℓ<n, ℓ≤3, n+ℓ≤8, the derivation proceeds through a nine-module Lean 4 chain: (i) D=3 spatial dimensions are forced (T8), giving orbital degeneracy 2ℓ+1 via symmetric traceless tensor counting; (ii) the RS bridge fixes spin degeneracy 2 at the physical dimension; (iii) φ>1 (T6) makes the RS rank code R(n,ℓ)=8(n+ℓ)+n strictly monotone, so sorting the certified candidate set generates the canonical Aufbau sequence; (iv) scanning the generated sequence for s-block restarts produces exactly 7 periods with algorithmically derived boundaries; (v) cumulative sums and the derived closure engine yield the noble gas positions; (vi) block, period, and group assignments are computed from the generated sequence; (vii) chemical families emerge from the derived group/block structure; (viii) periodicity theorems prove same-group block/valence invariants; (ix) three global closure theorems (completeness, exclusivity, inevitability) close the derivation. All structural claims are machine-verified in Lean 4 with Mathlib (9 modules, 0 sorry). A 23-component provenance audit (4 FORCED + 19 DERIVED + 0 calibration + 0 convention) is assembled in Theorem 9.1. Eight sharp falsification criteria are verified in Theorem 11.1. Experimental confrontation is separated cleanly from the derivation chain: period capacities, closure positions, the 18-column structure, and audited family counts agree exactly with the conventional table, while comparison against NIST ground-state configurations yields 98 exact strict-Aufbau matches and 20 explicit frontier-shell anomalies. Every ingredient is labelled as FORCED, DERIVED, or comparison-only.</p>