This repository contains the source files, manuscript, and supplemental materials for:

Deterministic Resolution of the Quantum State via a Discrete Prime‑Indexed Manifold

Author: Neil Crago (SpaceTCO)
Date: May 16, 2026

The work proposes a deterministic substrate beneath the standard quantum wave function, replacing probabilistic collapse with a mathematically rigid, prime‑indexed manifold that enforces unique state finalization.

Standard quantum mechanics represents physical states using a continuous complex amplitude.
This project introduces a deterministic alternative based on a triadic state vector:

$S(A) = (T_{\mathrm{total}},,E_{\mathrm{grid}},,\phi_{\mathrm{geom}})$

where:

• Ttotal — total geometric tension
• Egrid — grid efficiency (tension per nucleon)
• φgeom — geometric phase (modulo the hydrogen mass unit)

Quantum phase evolution becomes a discrete sawtooth, and state finalization is governed by a 12‑prime manifold:

[ M_{46} = {13,17,19,23,29,31,37,41,43,47,53,59} ]

The absence of integer midpoints between primes eliminates symmetric superposition, producing a deterministic “Proximity Snap” to the nearest prime anchor.

The model replaces stochastic wave‑function collapse with a nearest‑anchor minimization rule:

$$ P^{*} = \arg\min_{p \in M_{46}} \lvert x - p \rvert $$

This yields a unique, computable final state for any geometric‑phase coordinate.

The geometric‑phase bandwidth is shown to be uniquely fixed at 60 units by:

• maximal geometric divisibility,
• embedding of 12 prime anchors,
• and torsional symmetry of the Generator Field.

The repository includes:

• Lagrangian formulation
• Hamiltonian formulation
• Operator algebra for deterministic evolution
• Tensor‑field interpretation of the Generator Field

Appendix H provides explicit, testable predictions:

• phase discontinuities at one hydrogen mass unit
• 12 discrete stability basins
• instability peak at coordinate 46
• quantized latent‑heat release
• deterministic GHZ correlations
• non‑Gaussian phase noise
• anchor‑dependent decoherence rates
• tensor‑strain prediction of the muon (g-2) anomaly

Includes:

• full 60‑unit coordinate table
• geometric‑phase sawtooth diagrams
• energy‑shear landscape
• deterministic finalization flowchart
• formal proofs (Appendices A–C)

/
├── shrodinger.pdf        # Main manuscript (recommended for publication)
├── README.md             # This file
├── CITATION.cff          # Citation Information
└── LICENSE-MIT           # License information

If you use this work in academic research, please cite:

Crago, N. (2026). Deterministic Resolution of the Quantum State via a Discrete Prime‑Indexed Manifold. SpaceTCO.

doi: DOI: 10.5281/zenodo.20270178

For questions, collaboration, or discussion:

Author: Neil Crago
Affiliation: SpaceTCO
Location: Bury St Edmunds, UK

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