Quantum Spin-1/2 Phosphorus in Posner Molecules: A 64-Dimensional Qubit Substrate — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Fisher's quantum cognition hypothesis centers on nuclear spin-1/2 phosphorus-31 (³¹P) as a qubit substrate, with coherence protected by the Posner molecule (Ca₉(PO₄)₆) — a crystallographic cluster with octahedral symmetry. | MATH: ³¹P has nuclear spin I = 1/2 (two-level system, qubit). Posner molecule: Ca₉(PO₄)₆ — 9 Ca²⁺, 6 PO₄³⁻. The 6 phosphate groups form an octahedral arrangement (O_h point group, order 48). Each Posner carries 6 phosphorus nuclei → 2⁶ = 64-dimensional Hilbert space. Key decoherence shield: the molecule's symmetry forbids certain dipole-dipole couplings between ³¹P spins due to inversion symmetry — the dipolar Hamiltonian vanishes under parity for pairs related by inversion. Fisher's proposed quantum error correction: nuclear spin singlet states (|↑↓⟩ − |↓↑⟩)/√2 have zero net magnetic moment, immune to external field fluctuations. | CONNECTION: The Posner molecule's octahedral symmetry is a crystallographic point group (O_h) — same symmetry class as the cu
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026quantum,
title = {{Quantum Spin-1/2 Phosphorus in Posner Molecules: A 64-Dimensional Qubit Substrate — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23526236},
url = {https://zenodo.org/records/23526236},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Spin-1/2 Phosphorus in Posner Molecules: A 64-Dimensional Qubit Substrate — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23526236
UR - https://zenodo.org/records/23526236
AB - FINDING: Fisher's quantum cognition hypothesis centers on nuclear spin-1/2 phosphorus-31 (³¹P) as a qubit substrate, with coherence protected by the Posner molecule (Ca₉(PO₄)₆) — a crystallographic cluster with octahedral symmetry. | MATH: ³¹P has nuclear spin I = 1/2 (two-level system, qubit). Posner molecule: Ca₉(PO₄)₆ — 9 Ca²⁺, 6 PO₄³⁻. The 6 phosphate groups form an octahedral arrangement (O_h point group, order 48). Each Posner carries 6 phosphorus nuclei → 2⁶ = 64-dimensional Hilbert space. Key decoherence shield: the molecule's symmetry forbids certain dipole-dipole couplings between ³¹P spins due to inversion symmetry — the dipolar Hamiltonian vanishes under parity for pairs related by inversion. Fisher's proposed quantum error correction: nuclear spin singlet states (|↑↓⟩ − |↓↑⟩)/√2 have zero net magnetic moment, immune to external field fluctuations. | CONNECTION: The Posner molecule's octahedral symmetry is a crystallographic point group (O_h) — same symmetry class as the cu Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -