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.
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.
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.
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.
It is argued that a fuzzy version of 4-truth-valued paraconsistent logic (with truth values corresponding to True, False, Both and Neither) can be approximately isomorphically mapped into the complex-number algebra of quantum probabilities. I.e., p-bits (paraconsistent bits) can be transformed into close approximations of qubits. The approximation error can be made arbitrarily small, at least in a formal sense, and can be related to the degree of irreducible "evidential error" assumed to plague an observer's observations. This logical correspondence manifests itself in program space via an approximate mapping between probabilistic and quantum types in programming languages.
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.
Are there quantum objects? What are they if they are neither given nor resemble anything familiar? To answer these questions we have to abstract from the substantive features of familiar things, delineate the pure logical forms by which we acknowledge objects and show how the forms are fulfilled in quantum theories. We have to explicate, in general terms and without resorting to the given, what we mean by objects. The clear criteria will enable us to affirm the objectivity of quantum theories. Auyang 1995, p. 5 Introduction Cantor, famously, defined a set as ‘… collections into a whole of definite, distinct objects of our intuition or of our thought’ (Cantor 1955, p. 85, our emphasis). On this basis the standard formulations of set theory, and consequently much of contemporary mathematics, are erected. Reflecting upon this definition, and the underlying ontological presuppositions, the question immediately arises, how are we to treat, mathematically, collections of objects which are not distinct individuals? This question becomes particularly acute in the quantum mechanical context, of course. As Yu. I. Manin noted at the 1974 American Mathematical Society Congress on the Hilbert Problems, We should consider possibilities of developing a totally new language to speak about infinity [that is, axioms for set theory]. Classical critics of Cantor (Brouwer et al. ) argue that, say, the general choice is an illicit extrapolation of the finite case.