Research

Abstract

A cross-prover verified core for the golden ratio, Fibonacci and Lucas identities, Cassini's identity, and Binet's formula. Eighteen theorems are proven in Lean 4 with zero sorry and zero custom axioms (Mathlib only), with complete ports to Coq and Isabelle/HOL spanning three distinct logical foundations. Includes KerrShield, a phi-derived PRNG. Verified core complete; manuscript in preparation (target: CPP / ITP / JAR).

Findings

• 18 theorems in Lean 4 - zero sorry, zero custom axioms (Mathlib-only)
• Coq port complete: Binet, Cassini, Pell-Lucas, matrix formulation, golden-power identity
• Isabelle/HOL port complete: phi^2, psi^2, phi+psi, phi*psi, phi-psi identities
• KerrShield PRNG passes NIST SP 800-22 at 93.3% (all critical tests pass)

Abstract

A systematic study of knowledge distillation from a BERT-base teacher (92.32%, 420MB) to sub-2MB student models for binary sentiment classification on SST-2. Through eight controlled experiments with 5-seed evaluations, we observe that 82–83% accuracy appears to represent a Pareto frontier for models under 2MB on this task.

Findings

• Best student achieves 83.03% accuracy in 1.46MB (288× compression from teacher)
• Three negative results: spectral compression, progressive distillation, and transformer students all underperform the linear CNN baseline
• CNN inductive bias outperforms transformers at sub-2MB scale across all 5 seeds
• All experiments use 5-seed evaluation with standard deviations reported

Abstract

An investigation of whether the Berry phase—a geometric phase quantity computed from the instantaneous phase evolution of multichannel EEG—can serve as a pre-ictal biomarker in epilepsy. Analyzed 177 seizures from 24 subjects in the CHB-MIT Scalp EEG Database. Results are from a single retrospective dataset and require prospective validation before any clinical application.

Findings

• Pre-ictal Berry phase 87% higher than baseline (Cohen’s d = 1.599, p = 1.16 × 10⁻³⁹)
• Ictal Berry phase not significantly different from baseline (d = −0.092, p = 0.389)
• Consistent temporal profile across 24 subjects: baseline → pre-ictal surge → ictal drop → post-ictal elevation
• GPU-accelerated pipeline processes 177 seizures in 24.5 minutes

Abstract

A publicly released, multi-prover formal verification of Fibonacci matrix diagonalization and the associated golden-ratio identities - the open subset of the Constant Framework core. All proofs are machine-checked with no gaps.

Findings

• 18 Lean 4 theorems (zero sorry)
• Coq port: 100% (no admit)
• Isabelle/HOL port verified
• Public on GitHub: github.com/QuantQJ/Fibonacci-Formal

Abstract

An Ed25519 plus RFC-8785 canonical-JSON signing tool for AI artifact provenance: sign a model, then verify its integrity and chain of custody before deployment. Public and in production use.

Findings

• Ed25519 signatures over RFC-8785 canonical JSON
• Verifies model integrity and chain of custody pre-deployment
• Public on GitHub: github.com/QuantQJ/modelsign
• Published to PyPI (modelsign v1.0.1)

Abstract

A negative result comparing a variational quantum circuit (VQC) against a classical Random Forest baseline on the QM7 atomization energy prediction task. Rather than obscure these results, we present them as a contribution: an honest dissection of why quantum underperforms in this regime and what would be needed to close the gap.

Findings

• Classical Random Forest achieves 3× lower error than VQC and trains 80× faster
• Bottleneck traced to PCA compression (529→4 features, retaining only 46.4% of variance)
• Single variational layer with 4 trainable parameters is fundamentally underpowered
• Identifies specific conditions needed before quantum advantage should be expected

Abstract

We present AURE, a family of sovereign language models engineered for edge deployment across financial, legal, and regulatory domains. Production inference runs entirely on local hardware with a vector-augmented retrieval pipeline, demonstrating that practical generative edge AI does not require datacenter-scale resources. Prepared for Edge AI San Diego 2026.

Findings

• Distillation pipeline spanning four orders of magnitude (14B → 1.5MB)
• FinSense achieves 96.1% accuracy for financial sentiment at edge scale
• 82–83% accuracy observed as Pareto frontier for sub-2MB NLP models
• Production inference on prosumer hardware with zero cloud dependency

Abstract

A formally verified framework for measuring system coherence via the Sφ metric—a normalized φ-permutation symmetry deviation. Applied to 26 human neural recordings (DBS-LFP), we observe statistically significant discrimination between healthy controls and Parkinson’s disease patients. The framework is backed by 6 theorems proven in Lean 4. Sample sizes are small and results require independent validation.

Findings

• Healthy subjects: phase accumulation 22.16° ± 3.4°, Sφ = 0.53 ± 0.04
• Parkinson’s patients: phase accumulation 41.81° ± 5.2°, Sφ = 0.65 ± 0.05
• Difference achieves p < 0.001 with effect size d = 0.92
• 6 theorems proven in Lean 4; cross-validated against 208 independent measurements

Abstract

A deep learning framework combining 1D convolutional networks with φ-weighted attention mechanisms to extract phase accumulation from neural PSD. Evaluated on three publicly available datasets: Parkinson’s DBS-LFP (n=6), CHB-MIT epilepsy EEG (n=10), and BCI motor imagery (n=9 healthy controls). Sample sizes are small; classification results should not be generalized without larger validation studies.

Findings

• Parkinson’s tremor differentiation: d = 2.14 (F(5,34) = 187.2, p < 0.001)
• Epileptic seizure variance collapse observed (baseline SD = 97.1° vs ictal SD = 3.1°)
• Healthy motor imagery shows no significant differences — serving as negative control
• Real-time capable at <50ms inference latency

Abstract

A translational synthesis exploring whether the same cross-frequency coupling coherence framework applies across radically different diseases—cancer (methylation patterns) and neurology (neural oscillations). Uses TCGA-BRCA dataset (200 patients, 50,714 CpG sites) with quantum circuit on IonQ hardware. This is an early-stage cross-domain synthesis, not a validated clinical result.

Findings

• Quantum circuit achieves 99.2% confidence on one high-risk patient (200-fold discrimination)
• Average confidence across patients is 51.8% — above random but modest
• Same mathematical framework applied to both cancer methylation and neural oscillation data
• 6-qubit, 40-gate circuit designed for IonQ Forte native architecture

Abstract

Exploratory observations of numerical agreement between the φ-spectral entropy barrier (E ≈ 6φ⁴) and transition points in three independent datasets. These results are exploratory and require independent verification, null model comparison, and rigorous statistical analysis before any claims of universality can be made.

Findings

• Hurricanes (1,930 storms, 172 years): 3.79% error relative to predicted barrier
• Earthquakes (17,024 events, 70 years): 3.82% error
• Primes (10M gaps): 3.82% error
• All three datasets within 0.03% of each other — intriguing but unconfirmed