Spectroscopic Circuits: Selection Rules as Excluded Volume Conditions in the Origami ISA
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CORRECTION NOTICE (2026-08). Section 1.2 asserts that the 6j symbol {1 1 1; 1 1 1} equals −1/3 and builds a “universality of −1/3” argument on it. The correct value is +1/6. A further item in that list, “17/36 ≈ −1/3 + 1/2”, is arithmetically false (17/36 = 0.472; −1/3 + 1/2 = 0.167). The section’s central claim does not stand. Files are restricted pending revision.
PENDING QUALITY AUDIT (2026-08). The file is restricted while this record is reviewed as part of a systematic audit of the author's corpus. It has not yet been assessed. Metadata and DOI remain public, and access can be requested.
Every physical system governed by a Hamiltonian H is running a quantum algorithm. The time-evolution operator e^{-iHt} is the circuit; the eigenstates are the registers; the transition amplitudes measured by spectroscopy are the outputs. Written in the Origami Instruction Set Architecture, this circuit is remarkably small: between 3 and 21 qubits and depth 10–50 for all the spectroscopic systems studied. Every one is classically emulable on a laptop today.
The key structural insight: spectroscopic selection rules are Excluded Volume Principle (EVP) conditions in the symplectic polar space W(5,2). A transition |i⟩ → |f⟩ is allowed if and only if the transition operator bridges two distinct Fano orbit sectors — exactly the condition that the operator is non-isotropic with respect to both states. Allowed transitions are SPLIT;SPLAT sequences in the Origami ISA; forbidden transitions are identity operations in disguise.
Five spectroscopic systems are identified as instances of the same Origami ISA algorithm family: nuclear three-body recoupling, X(3872) C-parity selection, CO₂ Q-branch vibrational selection, FMO energy routing, and ribosome A-site decoding. The Pandya recoupling in nuclear physics and the CS Magic Composition Theorem in quantum computing are identical algorithms: both evaluate the 6j symbol of Z₂³ with the same numerical answer (−1/3) for the same physical reason.
Keywords
Spectroscopic Selection Rules, Excluded Volume Principle, Origami ISA, Symplectic Polar Space, W(5,2), Fano Orbit, 6j Symbol, Nuclear Spectroscopy, Pandya Transform, X(3872), C-Parity, CO₂ Vibrational Spectroscopy, FMO Complex, Ribosome A-Site, Quantum Circuit, SPLIT Opcode, SPLAT Opcode, Classical Emulation, Quantum Algorithm, Fano Plane, PG(2,2), CS Magic Composition Theorem, Z₂³, Adelic Simplicial Architecture
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