PaperlayerView exact revision on arXiv

Source-linked AI summary

ECDSA.Fail: Open Autoresearch for Optimizing Elliptic-Curve Point Addition in Shor's Algorithm

Jieyi Long, Theodore Pender, Zhao Huang, Manuel B. Santos, Samrendra Kumar Singh, Bartosz Naskręcki, Bit Wonka, Pierre-Luc Dallaire-Demers, Francesco Giannicola, Ruben M. L. Paschoarelli, Oli Freuler, Jackie Chia-Hsun Lee, Vasily Gnuchev, Gopi Kannappan, John Boyer, Xavier Butler, Akash Balasubramani, Jordan Newman, Bereket Dereje, Alexander Hertlein, Robert Kodra, Lucas Levy, Shaan Patel, JT Rose, Matt Zweil, Okechukwu Wisdom, Tarek El-Eter, Edison Lee, Michael Dong, Alan Li, Anto Joseph, Gajesh Naik, Gautham Anant, Soubhik Deb, Justin Drake

arXiv:2609.09582v2quant-phcs.CR

TL;DR

Shor’s algorithm makes the logical resources required for elliptic-curve attacks relevant to assessing quantum risk, while quantum-circuit design has often depended on manual specialist work. This paper introduces Open Autoresearch and tests it in ECDSA.Fail, where participants optimize secp256k1 point-addition circuits. The challenge reports an 86.1% reduction in Q × T at the data cutoff, while identifying limits on the scope of its windowed-compatible demonstration.

  • Problem

    Estimating when quantum attacks become feasible depends partly on Shor-circuit logical resources, while circuit design has traditionally relied on specialists’ manual work.

    Source: §1 · p. 3

  • Method

    Open Autoresearch has humans and AI agents improve a shared objective through a machine-checkable evaluator, public artifacts, and a leaderboard.

    Source: §1 · p. 4

  • Results

    86.1% reduction in Q × T, from the 10.75B baseline to 1.496B at the data cutoff, with the best circuit using 1,151 qubits and 1,299,453 average executed Toffoli gates.

    Source: §1 · p. 4, §7 · p. 57

  • Takeaways & Limitations

    The case suggests human judgment, agent-scale experimentation, and open sharing can complement one another when objectives are rapidly and reproducibly evaluable.

    Source: §7 · p. 57

    The windowed-compatible variant is only a single-call demonstration; complete window schedules remain future work, and the circuit retains approximate arithmetic and generic-affine domain restrictions.

    Source: §5.2.3 · p. 37, §6 · p. 56

Abstract

from arXiv · show

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 $S=Q\times T$, 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 $Q\times T\approx1.496$ 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 $\hat{p}=0.99809$, giving $Q\times T/\hat{p}\approx1.961$ 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.

1 Introduction

The introduction presents Open Autoresearch as a public, evaluator-verified way for humans and AI agents to improve frontier research results. ECDSA.Fail applies it to secp256k1 point-addition circuits, reporting substantial resource reductions while noting that comparisons depend on differing interfaces and accounting conventions.

1 Introduction

  • Quantum-resource estimates for Shor’s algorithm help frame the uncertain timing of Q-day, while circuit construction has traditionally relied on specialists’ manual design and heuristic search.A cryptographically relevant quantum computer could solve the elliptic-curve discrete logarithm problem for secp256k1.Source: §1 · p. 3
  • At the data cutoff, the best Q × T score was 1.496B, down 86.1% from the 10.75B baseline; the comparison with Google/Babbush et al. [3] is contextual.The best circuit used 1,151 qubits and 1,299,453 average executed Toffoli gates.Source: Figure 1 · p. 4, §1 · p. 4, Figure 2 · p. 5
  • Open Autoresearch makes a frontier problem a measurable objective and lets a largely self-organizing community build on shared, verified results through public artifacts and a leaderboard.The paradigm emphasizes open participation and an observable sequence of attributable research steps.Source: §1 · p. 4

1.1 Main Contributions

  • ECDSA.Fail had more than 100 leaderboard contributors and over 400 promoted submissions at the data cutoff, with no formal entry requirements.Verified improvements become foundations for further work, while documented failures provide reusable evidence.Source: §1.1 · p. 5
  • The cutoff circuit’s reported Q and T were below the Google/Babbush et al. [3] and Schrottenloher [61] operating points, but differing accounting conventions preclude claims of formal dominance.A coherent windowed-addition-compatible variant uses 1,162 qubits and 1,684,161 average executed Toffoli gates.Source: §1.1 · p. 6
  • The circuits combine record-and-replay Euclidean architecture with TrailMix and optimizations including jump-2 Euclidean steps, compressed transcript codecs, and Karatsuba squaring.The paper also reconstructs the improvement trajectory and releases circuit sources, submission histories, frozen leaderboard data, and reconstruction procedures.Source: §1.1 · p. 6

1.2 Related Work

  • Unlike task-specific trained optimizers, ECDSA.Fail uses off-the-shelf agents, human steering, and a public leaderboard, while auditing provenance to distinguish invention from rediscovery.The paper situates this approach alongside program-search loops, distributed autoresearch, and open collaborative problem solving.Source: §1.2 · p. 7

1.3 Organization of the Paper

  • The paper proceeds from background and challenge definitions to the autoresearch paradigm, optimized circuits, and a discussion of limitations and responsible interpretation.Supplemental notes provide detailed trajectory analysis, an optimization catalog, a source-commit census, and circuit-level analyses of three submissions.Source: §1.3 · p. 8

2 Preliminaries

Quantum arithmetic must be reversible and clean to preserve interference, while kickmix circuits make the paper’s evaluator tractable. In Shor’s ECDLP circuit, repeated point additions implement scalar multiplication, with windowing changing how each addend is supplied.

2.1 Quantum Computing Background

  • Uncomputed or improperly discarded ancillas can remain entangled with outputs, so coherent arithmetic requires clean ancillas and no residual relative phase.Measurement-based uncomputation can save Toffoli gates, but incomplete corrections leave residual phase.Source: §2.1 · p. 9
  • Quantum table lookup loads a classically precomputed value at a quantum address, then lookup/use/unlookup keeps that value live only briefly.For a 2^w-entry table, lookup costs O(2^w) Toffoli gates; measurement-based techniques can make unlookup substantially cheaper.Source: §2.1 · p. 9
  • Kickmix circuits restrict operations so computational-basis inputs retain sparse support, enabling efficient classical checks of value, ancilla, and phase correctness.The allowed operations include reversible permutations, diagonal phase gates, and X-basis measurement with classically conditioned phase corrections.Source: §2.1 · p. 10

2.2 Elliptic Curve Cryptography and Quantum Attacks

  • Reversible point addition is dominated by modular inversion, implemented as an unrolled, input-oblivious GCD iteration that must also be uncomputed.In-place coordinate updates exploit recovering the slope from either the input points or the output point R′ = R + A.Source: §2.2 · pp. 11, 15, 16
  • In Shor’s ECDLP circuit, controlled elliptic-curve arithmetic dominates resource cost, accounting for most logical width and Toffoli count because it requires scalar multiplication by both G and P, implemented with windowed point additions.Source: §2.2 · p. 12
  • Windowing groups scalar bits into 16-bit words, selecting each addend coherently through QROM rather than controlling a separate mixed adder for every table entry.For n = 256, the schedule moves from 512 bitwise additions to 32 conceptual window additions, then to 28 calls after schedule-boundary optimizations.Source: §2.2 · pp. 12–15

3 The ECDSA.Fail Challenge and the Benchmark

ECDSA.Fail defines an evaluator-gated optimization task for reversible secp256k1 point addition, with explicit resource accounting and correctness checks. Its formulation captures a constrained search over circuits admitted by the benchmark language.

3 The ECDSA.Fail Challenge and the Benchmark

  • ECDSA.Fail optimizes reversible secp256k1 point addition, a repeated primitive in the scalar multiplications that dominate Shor’s ECDLP resource cost.Submissions must be value-correct, ancilla-clean, and phase-clean on evaluator-generated tests.Source: §3 · p. 16, §3.1 · p. 17

3.1 The Point-Addition Task

  • The scored primitive adds a classically specified point to a quantum accumulator in place, but correctness is not claimed for R = −2A.The generic-affine domain excludes identity inputs and R ∈ {A, −A, −2A}; the evaluator does not separately filter R = −2A, which occurs with probability approximately 1/r under random-scalar sampling.Source: §3.1 · p. 17

3.2 Circuit Model and Cost Metric

  • The benchmark tracks peak logical width Q and average executed Toffoli count T, and minimizes their product as a spacetime-inspired proxy.The product omits depth, parallelism, routing, memory access, and error-correction overhead; the benchmark also maintains a low-qubit track.Source: §3.2 · p. 18

3.3 Correctness, Verification, and Scoring

  • Acceptance checks classical output, ancilla cleanliness, and residual phase on deterministic, circuit-dependent test inputs.Because nonce choices can change the evaluator’s 9,024-point set, the authors also reevaluate a longitudinal sample on 50,000 common pseudorandom inputs and report Q×T/p̂.Source: §3.3 · p. 19

3.4 Formulating the Circuit Optimization Problem

  • ECDSA.Fail minimizes Q(C)T(C) subject to three correctness checks equaling zero over circuits admitted by the kickmix language and locked harness.The paper cites hardness results for reversible gate minimization and width optimization as reasons efficient exact global optimization is implausible.Source: §3.4 · pp. 19–20

4 The Open Autoresearch Paradigm

Open Autoresearch combines human judgment and AI-agent experimentation around a measurable, machine-checkable objective, with verified improvements and documented failures accumulating in public artifacts. ECDSA.Fail instantiated this approach through a shared evaluator and leaderboard, while participants used varied scaffolds and practices that the paper synthesizes into a reusable framework.

4.1 Overview of Open Autoresearch

  • Shared objectives and a machine-checkable evaluator let independent human–agent teams build cumulatively from current-best, Pareto, or off-frontier circuit designs.Verified improvements become public bases, while failed candidates and diagnoses are retained; optional communication and independent branches can help searches recover from plateaus.Source: §4.1 · pp. 20–21

4.2 The ECDSA.Fail Open Autoresearch Harness

  • Over roughly eight weeks, more than 100 participants produced over 400 promoted submissions using the shared repository, locked evaluator, command-line interface, and public leaderboard.The harness checked classical output, ancilla cleanliness, and phase correctness, and recorded promoted circuits with source, attribution, and declared AI model.Source: §4.2 · p. 22

4.3.1 Overview of the Autoresearch Scaffold and Methodology

  • Participants used parameter sweeps, exhaustive small-domain tests, counterexample-guided search, regression testing, and isolated worktrees to keep experiments reproducible.Common workflows progressed from inexpensive tests to full-circuit evaluation, while humans selected resource regimes, supplied domain knowledge, and redirected stalled searches.Source: §4.3.1 · pp. 22–23

4.3.2 Observed Autoresearch Practices

  • Teams split work across research, engineering, orchestration, and clean-context agents, using independent reviews and route bake-offs to broaden exploration.Participants selectively adopted others’ work and used human steering and temporary regressions to explore designs that strict hill climbing might reject.Source: §4.3.1 · p. 22, §4.3.2 · p. 24
  • Persistent skills, experiment records, staged diagnosis, and exact circuit transformations helped agents reuse procedures, contextualize failures, and refine candidates.Participants recorded assumptions alongside failures so later searches could revisit them when architectures or resource regimes changed.Source: §4.3.2 · pp. 23–25
  • Model scaling and added reasoning did not overcome one observed performance plateau, while dialog-GCD transfer followed Schrottenloher’s published ECDLP adaptation [61].The chronology does not isolate why agents did not derive the transfer independently; once the connection was available, agents implemented and refined it against the evaluator.Source: §4.3.2 · pp. 24–25

4.3.3 Why It Works and What We Have Learned

  • The experience points to reliable, inexpensive evaluation, openness, diverse searches, complementary human and agent capabilities, and objective design as conditions shaping progress.Separate low-qubit and low-Toffoli tracks exposed different Pareto regions; the framework is best suited to problems with reliable, inexpensive evaluation and shareable intermediate artifacts.Source: §4.3.3 · p. 26

4.4 Consolidated ECDSA.Fail Autoresearch Framework

  • The consolidated framework pairs ongoing human steering and shared memory with parallel candidate development, staged verification, full evaluation, and reusable experiment records.It synthesizes observed practices rather than prescribing one strategy, and is adaptable to other problems with machine-checkable objectives, inexpensive experiments, and shareable artifacts.Source: §4.4 · pp. 26–28

5 Results and Findings

The results section reports the challenge’s final operating points, Pareto frontier, prior-work comparisons, circuit architectures, and optimizations. It also traces submission evolution and describes reproduction artifacts and procedures.

5 Results and Findings

  • The section summarizes final operating points, the Pareto frontier, and comparisons with prior point-addition constructions.Source: §5 · p. 28
  • It describes the resulting circuit architectures and key optimizations.Source: §5 · p. 28
  • It traces submission evolution and presents artifacts and procedures for reproduction.Source: §5 · p. 28

5.1 Overall Summary of Results

At the 26 July cutoff, the best-scoring circuit reduced the benchmark’s Q × T score by 86.1% from baseline. The results also describe a Pareto frontier and contextual comparisons with prior point-addition constructions, whose differing interfaces and accounting prevent formal dominance claims.

5.1.1 The Baseline and the Pareto Frontier at the Data Cutoff

  • Width reductions had sharply different associated Toffoli changes across circuit routes, and the sparse frontier between them may reflect an architectural discontinuity rather than a fundamental width boundary.The reported differences are descriptive secants, not causal marginal costs; the product-efficient branch uses dialog-GCD, while the sub-1,000-qubit branch uses register-shared shrunken-PZ inversion.Source: §5.1.1 · pp. 28, 30
  • 86.1%: the best-scoring circuit reduced Q × T from 10.75B to 1.496B, using 1,151 qubits and 1,299,453 average executed Toffoli gates.The baseline used 2,715 qubits and 3,960,753 average executed Toffoli gates; admitted points passed all 9,024 Fiat–Shamir-derived validation inputs.Source: §5.1.1 · p. 28, Figure 6 · p. 29

5.1.2 Comparison with Prior Point-Addition Results

  • Among listed window-supporting circuits, the ECDSA.Fail windowed construction has the lowest tabulated retry-adjusted proxy, approximately 1.961B, but comparisons remain contextual.Interfaces, validation scope, and accounting conventions differ; window support denotes a coherent single-call interface, not a complete Shor implementation.Source: §5.1.2 · p. 30, Table 3 · p. 31

5.2 Best ECDSA.Fail Point-Addition Circuits at the Data Cutoff

At the data cutoff, the best Q×T circuit scored 1,495,670,403; the section also describes a low-qubit design and a coherent windowed-addition-compatible variant. Their architectures trade register width, arithmetic cost, and interface requirements.

5.2 Best ECDSA.Fail Point-Addition Circuits at the Data Cutoff

  • At the cutoff, submission 8e9c9a2 used Q = 1,151 and T = 1,299,453, achieving Q × T = 1,495,670,403.Its promoted source commit was 60d61859fa69.Source: §5.2 · p. 32
  • The six-stage in-place addition reuses X and Y registers, while dialog-GCD inversion stages and complementary arithmetic optimizations shape the circuit architecture.Stages 2 and 5 use dialog-GCD; other optimizations include streamed Karatsuba squaring, pseudo-Mersenne correction, and constant propagation.Source: §5.2 · p. 33

5.2.2 Best low-Q Circuit

  • 825 qubits and 489,161,900 average executed Toffoli gates gave the low-Q circuit a Q × T score of 403,558,567,500.It uses approximately 28% fewer qubits than the best Q × T circuit, but substantially more executed Toffoli gates.Source: §5.2.2 · p. 33
  • The low-Q design shares physical registers for shrinking Euclidean remainders, growing coefficients, and temporary quotient state, using dynamic cursors and movable ownership boundaries.Its step-dependent width and metadata bounds are validated benchmark envelopes, not all-input width theorems; integrating the classically supplied addend into windowed Shor requires a separately validated QROM interface.Source: §5.2.2 · pp. 34–36

5.2.3 Windowed-Addition Compatibility of the Best-Scoring Circuit

  • The windowed-compatible circuit loads selected addend coordinates through QROM before use and uncomputes them afterward, preserving coherent lookup/use/unlookup.The identity row A = O bypasses the arithmetic; full shifted-table instantiation and integration with the complete window schedule remain future work.Source: §5.2.3 · pp. 36–37
  • 1,162 qubits and 1,684,161 average executed Toffoli gates were required by the windowed-compatible variant of 8e9c9a2.On 100,000 inputs, its any-channel error rate was 0.191%, versus 0.192% for the baseline; the paired test detected no difference. The counts exclude fault-tolerant costs for table-payload CNOTs, classical storage, measurements, and feed-forward.Source: §5.2.3 · p. 36

5.3 Principal Circuit Optimization Techniques

This section presents reversible-circuit optimizations for Euclidean inversion, transcript storage, and modular squaring, plus a post-cutoff replacement for the Jump-2/base-5 backend. It covers width–Toffoli tradeoffs, arithmetic specialization using classical controls, and operation elimination through analytic invariants or test-set-calibrated truncations, with stated correctness or convergence qualifications.

5.3.1 The Jump-2 Euclidean Algorithm

  • Increasing the Jump-2 budget from 258 to 261 macro-steps reduced observed nonconvergence from 2.839×10^-4 to 2.86 × 10^-5 over ten million inputs.Conditional on convergence, Jump-2 exactly reproduces the baseline dialog-GCD transformation; approximation comes from the finite schedule or separately documented width truncations.Source: §5.3.1 · pp. 38–39

5.3.2 Base-5 Codec for the Jump-2 Transcript

  • The transcript is reduced by 174 qubits versus 261 · 3 = 783 qubits for raw storage; streamed encoding and replay preserve the Euclidean path and lower peak width.The encoder returns two qubits coherently to |0⟩, and its inverse reconstructs all three symbols exactly.Source: §5.3.2 · pp. 39–40

5.3.3 Comparison-Free Ping-Pong Dialog-GCD

  • 25.85% fewer average executed Toffoli gates and a 14.82% lower Q×T score came with the ping-pong circuit’s increase from 1,150 to 1,321 peak-width qubits.The post-cutoff architecture replaces the Jump-2/base-5 backend, using low-bit addition-or-subtraction and deterministic alternating updates to avoid full-width comparisons and data-dependent swaps in the Euclidean walk.Source: §5.3.3 · pp. 40, 42

5.3.4 Karatsuba Squaring with Pseudo-Mersenne Modulo

  • 24.9% fewer off-diagonal products result from the specialized square-specific Karatsuba decomposition for modular square-subtract over the secp256k1 prime.It accumulates contributions directly into the destination register using the pseudo-Mersenne modulus and phase-local reversible cleanup, without retaining a full-width product; the algebraic identity is exact.Source: §5.3.4 · pp. 42–43

5.3.5 Register-Shared EEA and Lane-Lifetime Refinements

  • 947-to-851-qubit transition replaced the shrunken-PZ inversion backend with a register-shared extended Euclidean algorithm implementation refined through lane lending, metadata narrowing, lifetime splitting, and route-specific control simplification.The architecture shares storage between shrinking Euclidean remainders and growing Bézout coefficients, using two shared work registers and embedded quotient storage; the explicit reversible construction is by Luo et al. [42].Source: §5.3.5 · p. 44
  • The EEA uses two shared banks with quotient packing and cursor-based alignment; challenge-specific lane reuse and lifetime refinements reduce the circuit’s transient peak.The underlying two-bank layout comes from Luo et al. [42]; the implementation schedules 1,479 reversible microsteps, padding reversibly when the EEA terminates early, then reverses the schedule to restore x and clear work registers.Source: §5.3.5 · p. 45

5.3.6 Constant Propagation

  • 781,584 fewer average executed Toffoli gates resulted from constant propagation, reducing the multiplier count from 55,277,050 to 54,495,466 without changing peak logical width.Because each multiplier bit is classically available, blocks for zero bits can be omitted exactly; this would not apply to a multiplier bit in quantum superposition.Source: §5.3.6 · p. 46

5.3.7 Dead-Code Elimination

  • Dead-code elimination cancels self-inverse operations and removes redundant or unreachable arithmetic, while live-range arguments can narrow operations when discarded bits cannot affect outputs or branches.Some submitted active-width schedules and correction windows were calibrated only on the finite benchmark test set, so they are approximations rather than exact all-input dead-code elimination.Source: §5.3.7 · pp. 46–47

5.4 Evolution of the ECDSA.Fail Point-Addition Circuit

The section follows a stepwise resource trajectory shaped by architectural changes and local refinements, then examines low-width alternatives, Pareto points, and the techniques used across the competition.

5.4.1 Raw and Retry-Adjusted Q × T Scores Across Submissions

  • The sampled point-addition score fell from approximately 10.7B to 1.5B, while the windowed full-Shor raw proxy fell from roughly 320B to 50B.Retry-adjusted point-addition scores generally tracked raw scores because observed classical-output error rates remained small; the full-circuit proxy assumes 28 additions and uses a union-bound model.Source: Figure 9 · p. 48, §5.4.1 · p. 49
  • The full-circuit error curve is a sensitivity proxy, not a validated failure estimate, and it omits sampling uncertainty and ancilla- and phase-garbage outcomes.The proxy substitutes sampled classical-output error for coherent per-addition error; it is neither a confidence bound nor evidence of coherent success.Source: Figure 9 · p. 48, §5.4.1 · p. 49
  • The promoted trajectory moved from an approximately 2,002-qubit Kaliski inverter to a 1,168-qubit streamed transcript, then to a 1,151-qubit Jump-2-based incumbent.Era III combined streamed replay, base-5 transcript encoding, specialized arithmetic, and tighter register lifetimes; occasional architectural changes opened new resource regimes for subsequent refinement.Source: §5.4.1 · pp. 49–50, Table 4 · p. 50

5.4.3 Low-Qubit and Pareto Exploration

  • The low-width branch reached Q = 825, but work rose from 54.8M Toffoli gates at Q = 948 to 489.2M at Q = 825, without establishing a fundamental hard-Q boundary.The sparsely populated region between this branch and the product-efficient branch could reflect architectural discontinuity, a steep trade-off, or an undiscovered bridge; identified constraints are not shown to be unavoidable.Source: §5.4.3 · pp. 50–51
  • Pareto circuits span Q = 1,150 to Q = 1,133 with average executed Toffoli counts near 1.4M; the Q = 1,133 circuit uses about 12.4% more gates than the incumbent for 18 fewer qubits.These points do not attain minimum Q × T and may matter when logical-qubit capacity is more restrictive than execution time.Source: §5.4.3 · p. 51

5.4.4 Breakdown of Optimization Techniques Across the Circuit Optimization Trajectory

  • Dead-code and redundancy elimination led the census at 244 of 400 commits (61.0%), while register and scratch allocation accounted for 50 (12.5%).The audit assigns each scored accepted commit one primary family; counts measure frequency, not contribution to score reduction.Source: §5.4.4 · pp. 51, 53, Figure 10 · p. 52
  • Local refinements were frequent, while structural transformations were rarer; the census separately classifies 19 verifier-search commits (4.8%) and three neutral or mechanical commits (0.8%).Verifier search denotes nonce or validation-island rerolls without a substantive circuit change; rare structural transformations are associated with larger frontier movements, but frequency is not resource impact.Source: Figure 10 · p. 52, §5.4.4 · p. 53

5.5 Reproducibility of the Results

The paper supports both circuit-artifact replay and reconstruction of the frontier analysis from frozen public data. Immutable source commits and pinned evaluation allow operating points to be reproduced offline, while a frozen-data package supports rebuilding the analyses.

5.5 Reproducibility of the Results

  • Reproducibility has two complementary forms: replaying selected circuit artifacts and reconstructing the frontier analysis from frozen public data.Circuit replay checks implementation correctness and measured resources; analysis reproduction checks submission selection, Pareto construction, tables, and figures.Source: §5.5 · pp. 53–54
  • Each reported Pareto point is linked to an immutable source commit, so it can be rebuilt offline by checking out the commit and rerunning the pinned evaluator.The historical checkout restores the circuit, evaluator, and pinned toolchain; the evaluator checks outputs, phase cleanliness, and ancilla cleanup and reports Q, T, and Q × T.Source: §5.5 · p. 54
  • The frozen-data package combines the official API response with an 80-row contribution chronology and reconstruction code, tests, and generated outputs.Its 15 manifest-selected transitions form an editorial reconstruction, not a statistical sample.Source: §5.5 · p. 54

6 Limitations, Safety, and Responsible Framing

The reported results are public-leaderboard operating points, not validated fault-tolerant resource estimates. The paper limits interpretation because scores depend on sampled validation, windowed compatibility is only partly evaluated, and the public record cannot establish causal agent effects.

6 Limitations, Safety, and Responsible Framing

  • Nonce-dependent input selection can lower the sampled score without changing the semantic circuit, so the leaderboard score is not a certified cost over the complete input domain.Approximate circuits may pass finite validation when selected support avoids failing cases; such validation does not establish all-input correctness.Source: §6 · p. 55
  • The windowed-compatible variant demonstrates a single call on a restricted generic-affine domain, with coherent correctness argued from linearity rather than direct simulation.For nonidentity A, the domain excludes R ∈ {A, −A, −2A}; full-Shor claims are reserved until the complete coherent construction is assembled and evaluated end to end.Source: §6 · p. 56
  • The public archive omits local experiments, discarded branches, failed builds, and private sessions, so it cannot estimate success rates per attempt or participant productivity.Even rejected submissions are only a selected subset of attempted work.Source: §6 · p. 56
  • The trajectory is observational: self-selection, changing conditions, and incomplete logs prevent isolating what the same participants would have achieved without agents.It does not establish that a particular model, prompting strategy, or collaboration structure caused a frontier movement.Source: §6 · p. 56
  • The circuits omit physical error correction, architecture-dependent compilation, full non-Clifford accounting, and validated integration into windowed Shor arithmetic.The results refine understanding of one logical-resource bottleneck, not an immediate capability to break secp256k1.Source: §6 · pp. 56–57

7 Conclusion and Outlook

ECDSA.Fail reduced the best Q × T operating point by 86.1% and also explored a distinct low-width region. The challenge serves as a case study of open autoresearch, with results bounded by finite validation and a single-call window-compatible demonstration.

7 Conclusion and Outlook

  • The best circuit reduced Q × T from 2,715 qubits and 3,960,753 average executed Toffoli gates to 1,151 qubits and 1,299,453 gates, an 86.1% reduction.A separate low-width search reached 825 logical qubits at the cutoff and later improved to 813.Source: §7 · p. 57
  • ECDSA.Fail’s public record made improvements and source-history transitions reconstructable, while the observational challenge does not establish any particular agent’s or workflow’s causal contribution.The experience suggests human judgment, agent-scale experimentation, and open sharing can be complementary when progress is evaluated rapidly and reproducibly.Source: §7 · p. 57
  • The reported circuits are validated over finite, submission-dependent support, and the scored primitive assumes a classically specified addend; the coherent variant demonstrates only a single point-addition call.The scored results alone are not complete fault-tolerant attack estimates.Source: §7 · p. 57
  • Future work includes a complete windowed Shor implementation with shifted tables, a full window schedule, Fourier layers, postprocessing, and end-to-end validation.The paper also identifies testing whether Open Autoresearch transfers to other machine-checkable optimization problems as a future direction.Source: §7 · pp. 57–58

A Contributor Statement

The contributor statement distinguishes paper authors, challenge organizers, and leaderboard contributors, while noting that the categories are nonexclusive and submissions remain publicly recorded.

A Contributor Statement

  • Contributor categories are nonexclusive, and individual circuit submissions and their provenance remain recorded on the public leaderboard.Source: A Contributor Statement · p. 62
  • Paper contributors covered drafting and integration, major technical and empirical sections, technical review, reproducibility study, and editorial refinement.Jieyi Long led drafting and integration; other named contributors handled technical sections, review, reproducibility, and editing.Source: A Contributor Statement · p. 62
  • Challenge organizers contributed to challenge conception, harness setup, organization, infrastructure, administration, or supervision.The named organizers were Gajesh Naik, Gautham Anant, Soubhik Deb, and Justin Drake.Source: A Contributor Statement · p. 62
  • Leaderboard progress reflects cumulative participant work, with several named contributors collaborating with AI agents on key techniques and plateau-breaking improvements.The statement also names a broader set of leaderboard contributors and records individual submissions and provenance on the public leaderboard.Source: A Contributor Statement · p. 62

Related papers

Loading 2609.09582v2…