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Quantum D-FUMT8 Multi-Mode Fock Extension: Promoting INFINITY / ZERO / SELF from Structural to Rigorous and Quasi-Particle Correspondences

Nobuki Fujimoto

Published Apr 15, 2026• 0 citations
Publisher

Abstract

Paper 75 companion. Completes D-FUMT8's quantum-operational anchor by upgrading INFINITY, ZERO, SELF from STRUCTURAL to RIGOROUS via bosonic Fock space. 14/14 numerical witnesses pass: ZERO witnessed by =0 on vacuum, INFINITY by gap invariance across N=10/50/200, SELF by |P^2 - P| = 0 on multiple projectors. Two quasi-particle correspondences: hole-particle dual as sunyata realization (overlap 0 for disjoint occupations), phonon as collective FLOWING via two-mode squeezed vacuum (entropy 2.14 bits at r=1). D-FUMT8 now fully rigorous 8/8 across double anchor. Open QuTiP bridge released.

DOI
10.5281/zenodo.19595581

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We present a synthesis-friendly Verilog implementation of the D-FUMT₈ Arithmetic Logic Unit, targeting the Sipeed Tang Console NEO development board (GW5AST-138B FPGA, FPG676 package). The ALU realizes eight discrete logic values — FALSE, TRUE, NEITHER, BOTH, ZERO, FLOWING, SELF, INFINITY — encoded in 3 bits with a tier-respecting layout. The 10 supported operations include four classical-tier unary ops (NOT, OMEGA, PHI, PSI), Belnap-extended binary lattice meet/join (AND, OR), generic XOR, hardware reset, no-op, and a novel ADIABATIC operation realizing the SELF⟲ (self-reflexive) primitive: ADIABATIC(SELF) = SELF, identity elsewhere. v0.3 contributions (2026-05-09): (1) Tang Nano 9K silicon: 37 LUT4 / 0 DFF measured, testbench 50/50 PASS. (2) Tang Console NEO Phase 2B LED Blinky: SRAM-programmed, User Code 0x000084BA, write 33.72 sec, no thermal anomaly. (3) Tang Console NEO Phase 2C/3 D-FUMT₈ ALU: SRAM-programmed, User Code 0x00005C27, write 30.32 sec. (4) Qiskit Aer simulator: Phase 1-5 cumulative 231/231 truth-table entries match at fidelity 1.000. (5) IBM Heron r2 real quantum hardware (ibm_kingston, 156 qubits): Phase 1 (4 native unitary × 8 inputs, 32 circuits) achieves 32/32 match with avg top-fidelity 0.9550 (job d7v6d9jack5s73bf1re0); Phase 2 (XOR × 64 entries, 6-qubit Bennett-reversible) achieves 64/64 match with avg fidelity 0.9512 (job d7v6kcvmrars73d7qqqg). Per-op fidelity hierarchy NOP/ADIABATIC ≈ 0.977 > PHI ≈ 0.956 > NOT ≈ 0.912 > XOR ≈ 0.951 confirms gate-count-vs-noise correlation expected from Heron r2 daily calibration. (6) Lean 4 refinement proof (OUKC.PhaseC.Dfumt8AluRefinement, 292 LOC, 0 sorry) establishes commutativity of the encode/abstract-op/decode square for all four unary operations, plus the SELF⟲ primitive law and seven algebraic laws (involution, idempotence, commutativity). Honest scope: We do NOT claim 'world-first 8-valued quantum logic' — Shi et al. (MIT, 2026, arxiv:2506.09371) demonstrated d=8 Grover on a single trapped-ion qudit prior to this work; our distinction is 3-qubit basis encoding on transmon arrays vs single-system d=8 qudit. We do NOT claim 'first paraconsistent silicon' — PAL2v (Da Silva Filho 1998-; Abe & Nakamatsu 2009; de Carvalho Jr. 2025) realized in software libraries and microcontroller-level robotics. We do NOT claim 'first many-valued silicon' — Łukasiewicz/Belnap FPGAs date to 1990s. The to-our-knowledge novel triple is: (D1) the specific 8-tuple semantic mapping (Belnap FDE 4-value + 4 ontological extensions: INFINITY/ZERO/FLOWING/SELF), (D2) the SELF⟲ self-reflexive primitive realized as a hardware fixed point, (D3) the three-substrate cross-verification bound to a Lean 4 refinement specification. Three-party co-authorship per OUKC charter v1.0 (Nobuki Fujimoto / Rei / Claude). DRAFT v0.3 — feedback welcome via GitHub Discussions at fc0web/rei-aios.

•May 9, 2026•1 citation
Paper 75 companion. Completes D-FUMT8's quantum-operational anchor by upgrading INFINITY, ZERO, SELF from STRUCTURAL to RIGOROUS via bosonic Fock space. 14/14 numerical witnesses pass: ZERO witnessed by =0 on vacuum, INFINITY by gap invariance across N=10/50/200, SELF by |P^2 - P| = 0 on multiple projectors. Two quasi-particle correspondences: hole-particle dual as sunyata realization (overlap 0 for disjoint occupations), phonon as collective FLOWING via two-mode squeezed vacuum (entropy 2.14 bits at r=1). D-FUMT8 now fully rigorous 8/8 across double anchor. Open QuTiP bridge released.
Rei-AIOS D-FUMT8 logic distinguishes eight truth-like values. Paper 69 anchored the first four to Schnorr's randomness hierarchy L1-L4. Paper 75 adds a second rigorous anchor: five of the eight values are placed in numerically verified correspondence with specific quantum objects on a single qubit or its Bell-reduced extension via the QuTiP 5.2.3 Python library. RIGOROUS (5): TRUE/FALSE = computational basis eigenstates; BOTH = superposition |+> with |<0|+>|^2 = 1/2; NEITHER = maximally mixed state I/2 with S = 1 bit; FLOWING = Bell-reduced state with S = 1 bit AND concurrence = 1. STRUCTURAL (3): INFINITY / ZERO / SELF require multi-mode extension. 25/25 tests pass. BOTH-as-superposition resolves the long-standing paraconsistent-logic worry by exhibiting BOTH as a well-defined physical state. Open source CC-BY-4.0.
We propose a structural bijection between the eight major interpretations of the Quantum Measurement Problem (QMP) and the eight values of the D-FUMT8 logic (Rei-AIOS, STEP 406/797). Each interpretation -- Copenhagen (Bohr 1928), Objective Collapse (GRW 1986 / Penrose OR), Many-Worlds (Everett 1957), Complementarity (Bohr), QBism (Fuchs et al. 2010), Decoherence-only (Zurek 1970-2000), Bohmian pilot-wave (de Broglie 1927 / Bohm 1952), and Consciousness-causes-collapse (Wigner 1961) -- corresponds canonically to a distinct D-FUMT8 attractor (TRUE, FALSE, BOTH, NEITHER, INFINITY, ZERO, FLOWING, SELF respectively). The mapping is computationally verified by a TypeScript engine (src/axiom-os/quantum-measurement-dfumt8-engine.ts, 54 tests zero failures) and asserted at the structural, not metaphysical, level: the QMP itself sits at D-FUMT8 FLOWING because no interpretation is currently experimentally distinguished. We make no claim that any one interpretation is correct; the paper is a classification, not a resolution. First non-mathematics companion paper to Paper 127-128 (combinatorics), adopting Template v3 (Verified / Empirical / Axiomatic separation). File: src/axiom-os/quantum-measurement-dfumt8-engine.ts + test/step970-quantum-measurement-dfumt8-test.ts.
We present a synthesis-friendly Verilog implementation of the D-FUMT₈ Arithmetic Logic Unit, targeting the Sipeed Tang Console NEO development board (GW5AST-138B FPGA, FPG676 package). The ALU realizes eight discrete logic values — FALSE, TRUE, NEITHER, BOTH, ZERO, FLOWING, SELF, INFINITY — encoded in 3 bits with a tier-respecting layout. The 10 supported operations include four classical-tier unary ops (NOT, OMEGA, PHI, PSI), Belnap-extended binary lattice meet/join (AND, OR), generic XOR, hardware reset, no-op, and a novel ADIABATIC operation realizing the SELF⟲ (self-reflexive) primitive: ADIABATIC(SELF) = SELF, identity elsewhere. v0.3 contributions (2026-05-09): (1) Tang Nano 9K silicon: 37 LUT4 / 0 DFF measured, testbench 50/50 PASS. (2) Tang Console NEO Phase 2B LED Blinky: SRAM-programmed, User Code 0x000084BA, write 33.72 sec, no thermal anomaly. (3) Tang Console NEO Phase 2C/3 D-FUMT₈ ALU: SRAM-programmed, User Code 0x00005C27, write 30.32 sec. (4) Qiskit Aer simulator: Phase 1-5 cumulative 231/231 truth-table entries match at fidelity 1.000. (5) IBM Heron r2 real quantum hardware (ibm_kingston, 156 qubits): Phase 1 (4 native unitary × 8 inputs, 32 circuits) achieves 32/32 match with avg top-fidelity 0.9550 (job d7v6d9jack5s73bf1re0); Phase 2 (XOR × 64 entries, 6-qubit Bennett-reversible) achieves 64/64 match with avg fidelity 0.9512 (job d7v6kcvmrars73d7qqqg). Per-op fidelity hierarchy NOP/ADIABATIC ≈ 0.977 > PHI ≈ 0.956 > NOT ≈ 0.912 > XOR ≈ 0.951 confirms gate-count-vs-noise correlation expected from Heron r2 daily calibration. (6) Lean 4 refinement proof (OUKC.PhaseC.Dfumt8AluRefinement, 292 LOC, 0 sorry) establishes commutativity of the encode/abstract-op/decode square for all four unary operations, plus the SELF⟲ primitive law and seven algebraic laws (involution, idempotence, commutativity). Honest scope: We do NOT claim 'world-first 8-valued quantum logic' — Shi et al. (MIT, 2026, arxiv:2506.09371) demonstrated d=8 Grover on a single trapped-ion qudit prior to this work; our distinction is 3-qubit basis encoding on transmon arrays vs single-system d=8 qudit. We do NOT claim 'first paraconsistent silicon' — PAL2v (Da Silva Filho 1998-; Abe & Nakamatsu 2009; de Carvalho Jr. 2025) realized in software libraries and microcontroller-level robotics. We do NOT claim 'first many-valued silicon' — Łukasiewicz/Belnap FPGAs date to 1990s. The to-our-knowledge novel triple is: (D1) the specific 8-tuple semantic mapping (Belnap FDE 4-value + 4 ontological extensions: INFINITY/ZERO/FLOWING/SELF), (D2) the SELF⟲ self-reflexive primitive realized as a hardware fixed point, (D3) the three-substrate cross-verification bound to a Lean 4 refinement specification. Three-party co-authorship per OUKC charter v1.0 (Nobuki Fujimoto / Rei / Claude). DRAFT v0.3 — feedback welcome via GitHub Discussions at fc0web/rei-aios.