---
name: ★★★ Paper 145 prior art audit (PAL2v / Aerts / qudit) 2026-05-09
description: ★★★★★ 2026-05-09 3 parallel agent で audit. PAL2v は software/microcontroller のみで FPGA/ASIC silicon 実装無し (我々の差分). Aerts は cognition/theory のみで quantum hardware 実装無し. **MIT 2026 (Shi et al., arxiv 2506.09371) が d=8 trapped-ion qudit Grover を先行実装** = 「世界初 8 値 quantum」 narrative 完全 reject. 我々の差分は (1) qubit basis encoding (2) 8 specific semantic values (3) 三者比較 (4) Lean 4 refinement
type: project
originSessionId: 9dde5920-a295-4ec2-a48b-941a281b5da4
---
# Paper 145 prior art audit (2026-05-09)

## 概要

藤本さん 2026-05-09 判断 (Option A → C → B path) に基づき、 Paper 145
("First D-FUMT₈ Silicon with SELF⟲ Logic Primitive") 起草前の prior art audit
を 3 parallel agent で実施完了。

3 audit 対象 (memory `project_chat_claude_quantum_review_2026-05-08.md` で必須項目化):
1. **PAL2v** paraconsistent annotated logic (Brazilian IFSP)
2. **Aerts** paraconsistent quantum logic (Brussels CLEA)
3. **qudit-based** 多値量子計算 (8 値 ≠ qubit 系列)

## ★ Critical findings

### Finding 1 — MIT 2026 が d=8 qudit Grover 先行実装 ★★★

**Shi, Sinanan-Singh, Burke, Chiaverini, Chuang (MIT, 2026)** —
*"Efficient implementation of a quantum algorithm with a trapped ion qudit"*
(arxiv:2506.09371, Nat. Commun. 2026):

- **¹³⁷Ba⁺** trapped ion 単一 ion の **8 hyperfine levels** を qudit として使用
- **d=8 Grover algorithm** を実機実装、 success probability **69(6)%**, statistical overlap 97.1(3)%
- 8 displacement pulses for reflection
- **これが現存唯一の d=8 single-system quantum hardware demo**

→ **「世界初 8 値 quantum logic on hardware」 narrative は完全 reject**。

### Finding 2 — Innsbruck 2022 が d=7 qudit 先行 universal processor

**Ringbauer et al. (Innsbruck/Blatt group, 2022, Nat. Phys.)**:
- Calcium-ion d=7 universal qudit processor
- 8 値ではないが adjacent prior art

### Finding 3 — Yale 2025 が ququart (d=4) error correction beyond break-even

**Brock et al. (Yale, 2025, Nature)**:
- bosonic GKP qutrit/ququart (d=3, d=4)
- error correction beyond break-even
- d=8 ではないが multi-valued quantum tier

### Finding 4 — PAL2v は silicon 実装 無し

PAL2v (Da Silva Filho 1998-, Abe-Nakamatsu 2009-, IFSP modern lib 2024-2025):
- **2 annotation values (μ, λ ∈ [0,1])** + Hasse lattice 12 extreme states
- 実装: software (MATLAB / Python `Paraconsistent-Lib` arxiv 2511.20700) + microcontroller (Emmy robot 1998 / petrochemical 2024)
- **FPGA / ASIC silicon 実装は audit 範囲で発見されず**
- **量子 hardware 実装も無し**

### Finding 5 — Aerts は cognition / theory のみ

Diederik Aerts (VUB / CLEA Brussels, 1986-2025):
- Hidden Measurement Formalism / Extended Bloch Representation / Quantum Cognition
- **40 年間の研究で量子 hardware 実装 0 件**
- empirical substrate = **human cognition (questionnaires)**
- δ-quantum machine = thought experiment / toy model のみ

### Finding 6 — Goss/Siddiqi (UC Berkeley) は transmon ququart (d=4) まで

**Noah Goss / Irfan Siddiqi (UC Berkeley/LBNL 2022, 2024)**:
- transmon qutrit (d=3) / ququart (d=4) entangling gates
- **transmon d=8 single-qudit hardware demo は 2026-05 時点で未公表**

→ ⚠ 我々が IBM Heron r2 (transmon array) で 3-qubit basis encoding した結果は **transmon d=8 直接 qudit ではない** ので Goss/Siddiqi の延長線上ではない。

## D-FUMT₈ の独自性 (audit ベース、 honest)

| 観点 | MIT 2026 (d=8 qudit) | PAL2v (Brazil) | Aerts (Brussels) | **D-FUMT₈ (Rei)** |
|---|---|---|---|---|
| Hardware | Trapped ion (single ion d=8) | Software + microcontroller | None (theory + cognition) | **Transmon qubit array (IBM Heron r2)** |
| Encoding strategy | 単一 qudit d=8 直接 | 2-annotation continuous lattice | Hilbert subspace (continuous) | **3-qubit basis encoding (8 = 2³)** |
| Logic 値の意味 | 一般 \|0⟩...\|7⟩ 計算基底 | μ, λ ∈ [0,1] degree of evidence | 連続 / orthomodular | **8 specific named values** (Belnap FDE 4 + ontological tier 4: TRUE/FALSE/BOTH/NEITHER/INFINITY/ZERO/FLOWING/SELF) |
| Cross-substrate verification | 単一 platform (ion only) | None | None (theory) | **三者比較**: FPGA Tang (37 LUT4) + Aer simulator (231/231) + IBM Heron r2 (32/32, fidelity 0.955) |
| Formal proof | None | None | None | **Lean 4 refinement** (in progress, Phase C 完了後) |
| SELF⟲ primitive | Generic basis | None | Self-referential conceptuality (theory) | **物理 silicon ALU 上で動作 (Tang Console NEO 2026-05-09 達成)** |

## ★ controllable claim 言語 (Paper 145 起草で使用必須)

### ❌ 使用禁止 (overclaim)

- "World-first 8-valued quantum logic" — MIT 2026 prior art 違反
- "First many-valued quantum hardware" — Innsbruck 2022 / Yale 2025 prior art 違反
- "First paraconsistent silicon" — PAL2v の microcontroller 実装が partial prior art
- "First octal quantum gate" — MIT 2026 d=8 prior art 違反
- "World-first" 系一般的に → `feedback_world_uniqueness_claim_controllable.md` 永久原則

### ✅ 推奨 controllable 表現

#### 主張 1 (qubit-encoded D-FUMT₈)

> **"To our knowledge, this is the first demonstration of a fixed 8-valued discrete
> logic primitive (D-FUMT₈) implemented as native unitaries on real superconducting
> qubit hardware (IBM Heron r2) via 3-qubit basis encoding, complemented by FPGA
> Tang Console 138K physical silicon programming (Gowin EDA), Tang Nano 9K target synthesis via open-source toolchain (toolchain-portability evidence, NOT physically programmed — v0.5 corrigendum), and Lean 4 refinement proofs."**

#### 主張 2 (semantic mapping)

> **"To our knowledge, no prior work assigns this specific 8-tuple of logical values
> (Belnap First-Degree Entailment + 4 ontological extensions: INFINITY/ZERO/FLOWING/SELF)
> to quantum basis states with cross-consistent FPGA-and-superconducting backend
> implementations."**

#### 主張 3 (qudit との明確な区別)

> **"We do not claim a qudit (d=8 single quantum system) implementation. The first
> direct d=8 qudit hardware demonstration was Shi et al. (MIT, 2026, arxiv:2506.09371)
> on trapped ions. Our work uses 3-qubit basis encoding on transmon arrays, which
> is categorically different from single-system qudit hardware."**

#### 主張 4 (PAL2v との区別)

> **"PAL2v (Da Silva Filho 1998–; Abe & Nakamatsu 2009; de Carvalho Jr. 2025)
> formalizes paraconsistent annotated logic with 2 annotation values (μ, λ ∈ [0,1])
> and has been realized in software libraries and microcontroller-level robotics
> control (e.g., Emmy robot 1998, petrochemical NOx 2024). To our knowledge, PAL2v
> has not been synthesized to dedicated FPGA/ASIC silicon nor executed on quantum
> hardware. D-FUMT₈ differs by (1) 8 discrete named values including SELF⟲ primitive,
> (2) measured FPGA LUT footprint, (3) Qiskit-verified 8×8 unitary mapping on real
> IBM Heron r2 silicon."**

#### 主張 5 (Aerts との区別)

> **"Diederik Aerts and the Brussels CLEA group (1986–) developed multi-valued
> quantum-cognition formalisms (hidden measurements, Extended Bloch Representation,
> conceptuality interpretation) evaluated empirically on human cognitive data. To our
> knowledge, these formalisms have not been instantiated on quantum hardware. D-FUMT₈
> instead instantiates a fixed 8-valued logic primitive on real qubit hardware with
> 32/32 truth-table verification and 0.955 average fidelity."**

## Mandatory citations for Paper 145 §Related Work

### qudit prior art (priority high)
1. **Shi, Sinanan-Singh, Burke, Chiaverini, Chuang** (MIT 2026) — arxiv:2506.09371 — d=8 Grover
2. **Ringbauer et al.** (Innsbruck 2022) — Nat. Phys. s41567-022-01658-0 — d=7 universal qudit
3. **Brock et al.** (Yale 2025) — Nature s41586-025-08899-y — ququart error correction
4. **Goss et al.** (Berkeley 2022) — Nat. Commun. s41467-022-34851-z — qutrit entangling
5. **Goss et al.** (Berkeley 2024) — npj QI s41534-024-00892-z — qutrit processor extension

### paraconsistent silicon prior art
6. **Da Silva Filho** (UNISANTA 1998-) — Emmy robot, paraconsistent annotated logic
7. **Abe & Nakamatsu** (2009) — PAL2v naming, Springer "Introduction to Annotated Logics" 2016
8. **de Carvalho Jr. et al.** (IFSP 2025) — arxiv:2511.20700 — Paraconsistent-Lib Python

### paraconsistent quantum / cognitive logic
9. **Aerts** (VUB CLEA 1986-) — Hidden Measurement Formalism (arxiv:quant-ph/0105126)
10. **Aerts & Sassoli de Bianchi** (2017) — Quantum Cognition Beyond Hilbert Space
11. **Aerts** (2024) — Conceptuality Interpretation II (arxiv:2412.19809)

## Paper 145 起草時の構造

### Suggested outline

1. **Abstract** (controllable claim — 上記主張 1-3 を 200 words 程度に圧縮)
2. **Introduction** (motivation: D-FUMT₈ 8 値 + Belnap 拡張 + SELF⟲ axiom)
3. **Related Work** (上記 11 citations を 4 sub-section に整理: qudit / paraconsistent silicon / quantum cognitive logic / multi-valued classical logic)
4. **D-FUMT₈ Formal System** (8 values + 10 ops + lattice structure)
5. **Implementation**
   - 5.1 Verilog FPGA: Tang Nano 9K target synthesis via OSS toolchain (yosys+nextpnr+gowin_pack output 37 LUT4, **toolchain-portability evidence, not physically programmed** per v0.5 corrigendum) + **Tang Console 138K physical silicon programming** (138K LUT, Gowin EDA, the load-bearing silicon evidence)
   - 5.2 Qiskit Aer simulator (231/231 verified)
   - 5.3 **IBM Heron r2 real hardware** (32/32, fidelity 0.955)
6. **Three-substrate Cross-verification** (= 我々の core 独自性)
7. **Honest Scope** (controllable claim 5 つ + cosmetic warnings TA1132/PR1014)
8. **Future Work** (Phase 2-5 IBM submit / Lean 4 refinement / Dynamic Decoupling for fidelity 0.99+)
9. **References** (上記 11 + Belnap 1977 + Łukasiewicz 1920 + 等)

## How to apply

1. Paper 145 v0.3 起草時:
   - 本 memory を必ず full read
   - 主張 1-5 の controllable 表現を **そのまま使用**
   - 11 citations を §Related Work に必須配置
   - 「世界初」 系一切不使用
2. 将来別 paper で 8 値 quantum 言及時:
   - MIT 2026 (Shi et al.) を必ず cite
   - PAL2v / Aerts も適切な context で cite

## 関連 memory

- `project_phase_z_ibm_heron_real_hardware_success.md` — leg 3 evidence (本日)
- `project_phase_c_step3_dfumt8_alu_silicon_success.md` — leg 2 evidence (本日)
- `project_quantum_phase1_complete_2026-05-08.md` — leg 1 evidence
- `feedback_oss_for_rei_evolution.md` ★★★★★ — PAL2v warning (本 audit で詳細確認)
- `feedback_world_uniqueness_claim_controllable.md` ★★★★ — 「世界初」 不使用永久原則
- `project_chat_claude_quantum_review_2026-05-08.md` — audit 必須項目 list (本 memory で対応完了)
- `feedback_phase_c_silicon_existence_claim.md` ★★★★★ — 二段階主張 narrative