Rydberg = GATE + K/E = 13.6 eV. The hydrogen ground state IS the axiom's boundary. 43 quantities from the ring Z/970200Z — one of 108 sharing heartbeat λ=420.
| Name | Value | Error |
|---|
Orbital sublevels count: 2l+1 = {1, 3, 5, 7, 9, 11} = {sigma, K, E, b, K^2, L}
Max electrons per subshell: D*(2l+1) = {2, 6, 10, 14, 18, 22}
s = sigma, p = K, d = E, f = b, g = K², h = L. The chain IS chemistry.
At l=6: denominator = 13 = GATE. Same boundary that stops Cunningham chains, hydrogen degeneracy, and Heegner numbers.
L=11 extends the smooth region by 1 orbital (from 5 to 6). L = error correction = protection.
verify chain in .axOnly d = K = 3 spatial dimensions give closed Keplerian orbits (Bertrand, 1873).
Force law: F ~ 1/r^(K-1) = 1/r^D = 1/r^2. K closes orbits. D shapes decay.
d = K-1 = D: flat (orbits precess, never close). d = K+1 = D^2: collapse (unstable).
Heavy particles (proton) CAN SIT (nucleus). Light particles (electron) MUST ORBIT (ISS strategy). m_p/m_e = D^2*K^3*ESCAPE.
CRT decomposes every integer into 5 independent channels: n → (n%8, n%9, n%25, n%49, n%11).
A mirror pair n and N−n have complementary channels in each modulus. Measuring one channel of n determines that channel of mirror(n).
Channels are independent (CRT), but reconstruction requires all 5. This is not local hidden variables — it is structural correlation through ring membership. Bell violation follows from channel independence + reconstruction necessity.
verify mirror pair in .axEvery integer match (shell capacities, sublevels, noble gas Z) is a structural identity, not a fit. The continuous values have independently tested null models:
GATE = 13 = h(-191): the D-chain class number that gates hydrogen, Cunningham chains, and Heegner numbers. Kolmogorov E/K = h(-47)/h(-23): D-Chain Class Numbers. Shell capacities D*n^2 — the partition function p(n) is smooth for n ≤ 12 = D^2*K, gates at 13: Partitions & the Gate. Ramanujan congruences {E, b, L} = the axiom chain in partition arithmetic: Modular Forms Synthesis.