Vol3 Sections 258, 261, 269 · P-QM-1 through P-QM-10

Quantum Mechanics as Lattice Address Substitution

G1 = m_e·c²·α²/2 exact at 0.000 ppm. All hydrogen levels E_n = G1/n². Schrödinger = dimensional addressing

QC Theorem
G1 = m_e·c²·α²/2
exact, 0.000 ppm
·
Level n=2,3,5
denom = 2²,3²,5²
FOT prime squares
·
Propositions
10
P-QM-1 to P-QM-10
The Quantum Consistency Theorem

G1, m_e·c², and α are one lattice identity

G1 = m_e·c²·α_FOT²/2 exactly. The π⁴ and 5⁶ cancel algebraically. Given any two of G1, m_e·c², α_FOT, the third is determined exactly by {2,3} arithmetic alone.

P-QM-1
G1 = m_e·c²·α_FOT²/2 [0.000 ppm]
Proof: [2⁹×3⁸×5⁶×π⁴×10⁻⁷] × [3⁴/(5⁶π⁴)] / 2 = 2⁸×3¹²×10⁻⁷ = G1
π⁴ and 5⁶ cancel exactly
Registered Propositions

Key Results

P-QM-1

Quantum Consistency Theorem: G1 = m_e·c²·α²/2 exact. π⁴ and 5⁶ cancel. Three projections of one lattice identity.

P-QM-3

E_n = −G1/n². Denominators at n=2,3,5: 2²,3²,5² — squares of the {2,3,5} lattice. n=7 has no clean {2,3,5,π} node — it falls off the lattice, as in musical dissonance.

P-QM-10

De Broglie closure: n·λ_dB = 2π·r_n exact. Bohr quantisation and de Broglie wave mechanics are the same {2,π} statement.

Cross-references: Vol3 Sections 258, 261, 269 | P-ACOUS-2 (7 off-lattice)