Entity Catalog — Atomic Physics

Entities are the real-world quantities that become channels in the trace vector. Each maps to [0,1]ⁿ through the embedding.

118 elements across 11 modules — the complete periodic table through the GCD kernel

8-Channel Property Kernel

Every element maps to an 8-channel trace vector with equal weights (w_i = 1/8):

Channel	Formula	Physical Basis
`Z_norm`	Z / 118	Atomic number position
`EN`	electronegativity / 4.0	Pauling scale (max ≈ 4.0)
`radius`	1 − r_pm / r_max	Inverted: smaller radius → higher c
`IE`	IE_eV / IE_max	First ionization energy
`EA`	\|EA_eV\| / EA_max	Electron affinity magnitude
`T_melt`	T_melt_K / T_max_K	Melting point
`T_boil`	T_boil_K / T_max_K	Boiling point
`density`	log(ρ+1) / log(ρ_max+1)	Logarithmic density

Cross-Scale Kernel (12 Channels)

Source: closures/atomic_physics/cross_scale_kernel.py

Bridges subatomic → atomic scales:

Category	Channels
Nuclear (4)	Z_norm, N/Z ratio, binding_per_nucleon (Bethe-Weizsäcker), magic_proximity
Electronic (2)	valence_electrons, block_ordinal (s=1, p=2, d=3, f=4)
Bulk (6)	EN, radius_inv, IE, EA, T_melt, density_log

Key finding: magic_proximity is the #1 IC killer (39% contribution). d-block has highest ⟨F⟩ = 0.589.

Representative Elements

Z	Element	Block	Key Regime	Notes
1	Hydrogen	s	Stable	Simplest: Rydberg exact (AX-AT1)
2	Helium	s	Stable	Noble gas — shell closure attractor
6	Carbon	p	Stable	High fidelity, balanced channels
10	Neon	p	Stable	Noble gas — shell closure
11	Sodium	s	Watch	Alkali — single outer electron
26	Iron	d	Watch	Peak binding energy region
28	Nickel	d	Stable	IC/F = 0.9573 — restored coherence
29	Copper	d	Watch	d→s electron transition
36	Krypton	p	Stable	Noble gas — shell closure
47	Silver	d	Watch	Anomalous electron configuration
54	Xenon	p	Stable	Noble gas — shell closure
79	Gold	d	Watch	Relativistic effects significant
86	Radon	p	Stable	Noble gas — shell closure
92	Uranium	f	Collapse	f-block — complex shell structure
118	Oganesson	p	Collapse	Superheavy — edge of periodic table

Module Catalog

Module	Purpose	Entities
`periodic_kernel.py`	118-element periodic table kernel	118 elements
`cross_scale_kernel.py`	12-channel nuclear-informed analysis	118 elements × 12 channels
`tier1_proof.py`	Exhaustive Tier-1 proof	10,162 tests, 0 failures
`electron_config.py`	Electron configuration analysis	Shell filling patterns
`fine_structure.py`	Fine structure constant α = 1/137	Energy-level splitting
`ionization_energy.py`	Ionization energy closures	All 118 elements
`spectral_lines.py`	Spectral line analysis	Emission/absorption
`selection_rules.py`	Quantum selection rules	Δl = ±1 transitions
`zeeman_stark.py`	Zeeman and Stark effects	Field-induced splitting
`recursive_instantiation.py`	Recursive instantiation	Structural self-similarity

Shell Closure Attractors

Noble gases (Z = 2, 10, 18, 36, 54, 86) are shell-closure attractors per AX-AT0. They consistently occupy Stable regime with high IC/F, because complete electron shells produce homogeneous trace vectors — all channels are simultaneously high, minimizing the heterogeneity gap Δ = F − IC.

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