Analysis of March 2026 Google Quantum AI and Oratomic papers on Shor's algorithm resource estimates for secp256k1 elliptic curve cryptography. Covers ZK-proof censorship, Schrottenloher's independent rediscovery (arXiv:2606.02235), the ecdsa.fail crowdsourced optimization challenge (15.1% improvement over Google), Justin Drake's Q-Day estimates (50% by 2032), and Ethereum Foundation's leanVM post-quantum migration plan.
Analysis of March 2026 Google Quantum AI and Oratomic papers on Shor's algorithm resource estimates for secp256k1 elliptic curve cryptography. Covers ZK-proof censorship, Schrottenloher's independent rediscovery (arXiv:2606.02235), the ecdsa.fail crowdsourced optimization challenge (15.1% improvement over Google), Justin Drake's Q-Day estimates (50% by 2032), and Ethereum Foundation's leanVM post-quantum migration plan.
[v2.0 — Full QWAV Thermodynamic Integration] Analysis of March 2026 Google Quantum AI and Oratomic papers on Shor's algorithm resource estimates for secp256k1 elliptic curve cryptography, presented alongside QWAV's published thermodynamic critique of Shor scalability. CONTENTS: - Resource estimates: Google (≤1,200 logical qubits, ≤90M Toffoli gates; <500K physical qubits superconducting) and Oratomic (10K physical qubits, neutral atoms) - ZK-proof censorship: First use in academic publishing; hidden optimizations independently rediscovered by Schrottenloher (arXiv:2606.02235) within two months - ecdsa.fail: Crowdsourced optimization challenge achieving 15.1% improvement over Google's classified circuit (135 submissions, 35 solvers) - Q-Day timeline: Justin Drake 50% by 2032 vs. QWAV "never" (thermodynamic impossibility) - QWAV THERMODYNAMIC CRITIQUE (new in v2.0): Full analysis of Landauer-limited QEC scaling, precision scaling problem, five false assumptions in Shor's algorithm, Feynman-Shor quantum bifurcation - Post-quantum migration: Ethereum Foundation's leanVM, 2029 target, Proximity Prize, Poseidon Initiative - UNRESOLVED DEBATE: Is Shor's algorithm physically viable at cryptographically relevant scales? Google/Oratomic: yes (engineering). QWAV: no (thermodynamic). No experimental resolution at scale exists. QWAV prior work integrated: Feynman-Shor Quantum Bifurcation (DOI: 10.5281/zenodo.17977869), Post-Quantum Synthesis (DOI: 10.5281/zenodo.17184229), SHORS IS BUSTED internal analysis.
Quantum computing poses a real, broad-based, but bounded and substantially mitigable threat to Bitcoin and Ethereum. We separate the two quantum algorithms that public discussion routinely conflates: Shor's algorithm breaks the elliptic-curve signatures (ECDSA over secp256k1, BLS over BLS12-381) that authorize spending, whereas Grover's algorithm does not meaningfully threaten proof-of-work mining, which is protected by a merely quadratic speedup, fault-tolerant per-operation costs, a square-root parallelization wall, and difficulty adjustment. Folding hardware scaling, the falling resource requirement, a fault-tolerance readiness lag, and expert surveys into a single Monte-Carlo forecast yields a wide, bimodal arrival distribution for a cryptographically relevant quantum computer: about a one-in-six chance by 2035, near 30% by 2040, and about 60% by 2050. Exposure is concentrated and mostly migratable: of Bitcoin's roughly six million quantum-exposed coins only about 2.3 million are irreducibly at risk, while 50 to 65% of Ether sits at key-revealed accounts that can adopt post-quantum signatures. A timely migration beats even an optimistic 2035 machine, so the binding constraint is governance, not technology. A survey of the top twenty cryptocurrencies finds none fully post-quantum. Reproducible models accompany every quantitative claim.
[v3.0 — Ultrametric Synthesis] Complete analysis integrating three research threads: 1. Google Quantum AI and Oratomic's March 2026 Shor resource estimates for secp256k1 ECDLP 2. The ecdsa.fail crowdsourced optimization challenge (QWAV participation: scored 2,535,067,306, submitted to leaderboard) 3. QWAV's thermodynamic critique (Feynman-Shor Quantum Bifurcation, Post-Quantum Synthesis, SHORS IS BUSTED) NEW IN v3.0 (Section 10-11): Proposes ultrametric quantum computation as the alternative to Shor's algorithm. Introduces the Monna map (p-adic to real number readout), hierarchical error confinement via ultrametric topology, and prime factorization via geometric reconstruction instead of phase estimation. Proposes an ultrametric benchmark — p-adic modular exponentiation scored by branch operations × tree depth — as the next step for the field. Prior versions: v2.0 (DOI: 10.5281/zenodo.20517291), v1.1 (DOI: 10.5281/zenodo.20517264), v1.0 (DOI: 10.5281/zenodo.20517217).
RQDAY-001 documents the Q-Day compression curve confirmation — two independent papers landing simultaneously on March 31, 2026. Google Quantum AI established fewer than 500,000 physical qubits can break ECDLP-256, a 20-fold reduction from prior estimates, with a Bitcoin private key derivable in approximately 9 minutes inside Bitcoin's block window. Oratomic/Caltech pushed the threshold to 10,000 qubits via neutral atom architecture. Five orders of magnitude compressed in two decades. The SASA sovereign stack documented the quantum compute threshold architecture before these papers published. Timestamped records under Clow4485 establish the sequence. Store-now-decrypt-later attacks are already active. The compression curve implications for sovereign architecture are vaulted. The dots are visible. The countermeasure stays here. 🔥🔒⟡
We propose Open Autoresearch, a paradigm in which humans and AI agents publish evaluator-verified improvements to a public leaderboard. We instantiate it in ECDSA.Fail, optimizing reversible secp256k1 point-addition circuits, a bottleneck in Shor's algorithm for elliptic-curve cryptography. The benchmark minimizes the spacetime-inspired score S=Q×T, where Q is peak logical qubit width and T is average executed Toffoli count. Participants reduced S by 86.1%. At the data cutoff (26 July 2026), the best-scoring circuit uses 1,151 qubits and 1,299,453 average executed Toffoli gates, giving Q×T≈1.496 billion. This is more than 50% below Google's published point-addition score thresholds (arXiv:2603.28846), under different accounting conventions. Because the benchmark supplies one addend classically, we construct a coherent windowed-addition-compatible variant implementing the single-call interface required by windowed Shor. It uses 1,162 qubits and 1,684,161 average executed Toffoli gates. On 100,000 random inputs, its empirical success probability is p^=0.99809, giving Q×T/p^≈1.961 billion under an independently rerunnable per-call sensitivity model, not a full-Shor success estimate. Its qubit and Toffoli counts lie below Google's published thresholds and Schrottenloher's reported operating points (arXiv:2606.02235), although differing interfaces, accounting conventions, and validation scope preclude formal dominance. After the cutoff, the score was further reduced to 1.259 billion, while a separate low-width circuit reached 813 qubits. The public record shows AI agents complementing human judgment, providing evidence for open autoresearch on efficiently evaluable, machine-checkable objectives.
Recent advancements, specifically the 2026 whitepaper by Google Quantum AI, Stanford University, and the Ethereum Foundation (arXiv:2603.28846), have demonstrated the resource feasibility of breaking secp256k1 elliptic curve cryptography using fault-tolerant quantum computation (≤ 1200 logical qubits and ≤ 90 million Toffoli gates). While their work validates this capability via zero-knowledge STARK proofs without disclosing explicit circuits, we provide the continuous operator-theoretic framework that explains the exact physical collapse mechanism underlying their discrete resource results. By modeling cryptographic hardness as a stable, invariant computational manifold, we show that quantum vulnerability is a manifestation of a Birman-Schwinger instability. We prove that, within this model, the introduction of a transverse quantum operator (e.g., Shor's algorithm implemented via Quantum Phase Estimation) forces a resolvent singularity in the classical generator when the resource perturbation parameter crosses a critical threshold (μ_c). We establish a strict Hardness Phase Transition, demonstrating that cryptographic security is equivalent to the point 1 remaining outside the spectrum of the Birman-Schwinger kernel. Furthermore, we formalize zero-knowledge proofs (such as the Groth16-wrapped STARK artifacts published by Babbush et al.) as highly constrained Boolean projectors. We show that these proofs trigger an epistemic spectral collapse via Zeno stabilization, certifying the non-invertible regime without decohering the raw computational state into the public domain. The manuscript includes an exact analytic toy model demonstrating bound-state collapse into the continuum, explicitly mapping the destruction of exponential cryptographic isolation to a polynomial scattering state. This formalization transitions cryptographic failure from a domain of discrete computational estimates to a continuous framework of operator-theoretic necessity.