An open-science investigation of the trans-categorical isomorphisms between the Riemann Hypothesis and nuclear shell stability, validated on real quantum hardware.
| Pillar | Observable | Result | Evidence |
|---|---|---|---|
1 — PT-symmetric Im(H_PT) |
5 sequential 1-Pub VQE on ibm_fez |
all |bias| < 0.005, mean −0.0001, std 0.0019 | A+ |
| 3 — Schmidt entropy scaling | QPU single-shot tomography, N ≤ 127 |
α_QPU = 0.348 (vs α_Aer = 0.272) | A− |
| 3 — Asymptotic Sub-RH | statevector, N ∈ [10⁴, 10⁶] |
α(10⁶) = 0.223, monotonically decreasing | A− |
The Latorre–Sierra prediction of linear entanglement scaling (α → 1) is empirically excluded in N ∈ [10³, 10⁶]. See LATORE_TENSION_NOTE.md §11.
All conclusions are graded using the SciMind 4.0 Evidence Grading Scale (A–F) with the Steelman Mandate, Ockham's Quantified Razor, and Anti-Sharpshooter Protocol. See PRIMARY_HYPOTHESIS_AUDIT.md for the formal RH-orthogonality audit.
git clone https://github.com/bartman081523/riemann-nuclear-synthesis.git
cd riemann-nuclear-synthesis
python3 -m venv .venv && source .venv/bin/activate
pip install qiskit>=1.0 qiskit-aer>=0.13 qiskit-ibm-runtime numpy scipy matplotlib pytest
# Credentials (DO NOT commit)
echo "IBMQ_TOKEN=your_token_here" > .env
echo "IBMQ_TOKEN2=your_second_token_here" >> .env
# Run the test suite
python3 -m pytest tests/ -q # 173/173 passing
# Reproduce the asymptotic scaling (statevector, no QPU cost)
python3 pt_asymptotic_N1e6.py # alpha(N=10^6) = 0.223For QPU reproduction details, see Reproducibility in the primary research repository.
| Account | Backend | Status | Last run |
|---|---|---|---|
IBMQ_TOKEN |
ibm_fez (156 qb) |
✅ Open (post 2026-07-01 reset) | 2026-07-21 |
IBMQ_TOKEN2 |
ibm_fez (156 qb) |
✅ Open | 2026-06-17 |
Update 2026-07-21: Both accounts now open after the 1.7.2026 quota reset. ERSTER echter QPU-VQE+VQD-Lauf Fez/TOKEN1 since 31 Tagen (Job d9fidihhtsac739fg3n0, E_0 = 2.1398, bias_PT_re = −0.0119, H1/H3 QPU-confirmed). Three-path consistency: Fez/TOKEN2 Singleshot 2026-06-10 + Statevector VQE-opt + Fez/TOKEN1 VQE+VQD. See SYNTHESIS_2026_06_10.md §W.
Operational policy: QPU time is scarce — all statevector-first validations must precede any QPU submission. Preregistration before main() is required for every QPU script (Anti-Sharpshooter Protocol).
| Document | Status | Role |
|---|---|---|
CLAUDE.md |
Reference | SciMind 4.0/5.0 methodology manifest |
RIEMANN_HYPOTHESIS_AND_NUCLEAR_STRUCTURE.md |
Primary | Theory (§1–9) + Operational Findings Log (§10) |
SYNTHESIS_2026_06_10.md |
Master | SciMind verdicts, strategic vectors |
QUANTUM_ARCHITECTURE_IMPLEMENTATION.md |
Master | Statevector-first architecture + QPU-update log |
LATORE_TENSION_NOTE.md |
Pre-print | Latorre–Sierra tension + §11 asymptotics |
PRIMARY_HYPOTHESIS_AUDIT.md |
Current | Theorem audit + RH-orthogonality + multi-observable convergence |
INVESTIGATION_PLAN.md |
Reference | Mermaid flowchart of investigation paths |
PLAN.md |
Historical | Phases 1–3 done, Phase 4 active |
QUANTUM_ARCHITECTURE_BRIDGE.md |
Superseded | Architecture rationale (frozen 6/8) |
SAEULE1_FEZ_BLOCKED.md |
Superseded | Fez quota block (resolved 6/17) |
QUANTUM_COMPUTING_AND_PRIMES_RESEARCH.md |
Reference | External research literature survey (95 KB) |
See the Cross-Reference Index in the primary research repository for the canonical detail.
@misc{riemann-nuclear-synthesis-2026,
author = {Julian H. and Claude},
title = {Riemann--Nuclear Synthesis: A Four-Pillar TDD-Validated
Quantum-Spectral Investigation of the Trans-Categorical
Isomorphisms between the Riemann Hypothesis and Nuclear
Shell Stability},
year = {2026},
month = jun,
howpublished = {\url{https://github.com/bartman081523/riemann-nuclear-synthesis}},
note = {QPU-validated on ibm\_fez, SciMind 4.0/5.0 graded}
}CC-BY 4.0. See LICENSE.
IBM Quantum (Open Plan, ibm_fez); Latorre & Sierra (2013/2020) for the Prime State framework; Zeraoulia (2012) for the PT-symmetric Jacobi operator; the SciMind 4.0/5.0 cognitive architectures.