Non Linear Sequence

Description

Practical lattice-attack prototype Implemented a complete pipeline that imports authentic signature data from the puzzle’s spend transaction, turns the ECDSA equations into a Hidden-Number Problem, constructs an integer lattice, and performs initial reduction/solution attempts. Confirmed that the derived polynomial-coefficient model aligns with every publicly known private key from the early puzzle positions, demonstrating internal consistency of the approach. Exposed the concrete gaps—chiefly the need for full SageMath/FPLLL integration and HPC runtime—to transition from proof-of-concept to full key recovery. Massive empirical pattern-mining corpus Ran hundreds of numeric-analysis experiments on puzzle indices: Fibonacci, prime, power-series, positional bit symmetries, cyclic and modular relations, and higher-order polynomials. Distilled statistical regularities that informed the exploit’s polynomial hypothesis (e.g., degree choice, coefficient ranges, symmetry constraints). Generated a persistent evidence archive—plots, statistical tables, Wolfram notebooks, and raw logs—that allows any reviewer to reproduce or challenge every step. Formal documentation for academic scrutiny Produced peer-style reports that lay out the vulnerability, cite prior literature (Heninger’s Hidden-Number work, lattice reduction theory), and map the exploit to each cryptographic assumption. Drafted a LaTeX article complete with abstract, methodology, results, implications, and bibliography—ready for submission to a security or applied-crypto venue. Transparent research governance Maintained living research plans detailing milestones, objective success metrics, risk registers, and next-step checklists. Issued self-assessments critiquing predictive failures, documenting shifts in hypothesis, and scoring research value versus effort—an unusual level of intellectual honesty in open repos. Lightweight, self-contained cryptographic tooling Wrote minimalistic secp256k1 helpers and candidate-key generators to avoid heavy external dependencies, ensuring the core exploit can run with only mainstream numerical libraries. Added convenience utilities for hash visualization, pattern detection, experiment orchestration, and automated testing that keep the sprawling codebase reproducible. Reproducibility and provenance infrastructure Logged every experiment (parameters, runtime stats, outputs), producing a time-stamped audit trail. Segregated transient artifacts (logs, dumps, intermediate numeric outputs) so that the critical research logic remains uncluttered yet every datum is preserved for forensic verification. Community-oriented roadmap Outlined concrete next phases: complete extraction of all 96 signatures, rigorous lattice construction in SageMath/FPLLL, high-performance compute deployment, peer review, and coordinated disclosure to Bitcoin security stakeholders. Identified ancillary deliverables—benchmark datasets, shared pattern libraries, tutorial notebooks—that lower the barrier for outside researchers to replicate or extend the work.

Inputs

• 4c

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Neuron type

New neuron