| |
| """Exact counterexamples to Claim 3's firstness and printed guarantee.""" |
| from __future__ import annotations |
|
|
| import json |
| from datetime import datetime |
| from fractions import Fraction |
| from pathlib import Path |
|
|
|
|
| TARGET_DATE = "2025-09-29T13:22:59Z" |
|
|
|
|
| def firstness_counterexample() -> dict: |
| prior = { |
| "arxiv": "2312.14141", |
| "title": "Quantum Algorithms for the Pathwise Lasso", |
| "published": "2023-12-21T18:57:54Z", |
| "source_url": "https://export.arxiv.org/e-print/2312.14141v3", |
| "source_sha256": "cfdb8208c67d8a4c499b2bb6737912d8d674ccfbf1f2d12d803c708e1c98b093", |
| "anchors": { |
| "quantum_algorithm": "main.tex:146,221-225,257,265", |
| "lasso_objective": "main.tex:165-166,195-198", |
| "approximation_guarantee": "main.tex:228-234,304", |
| }, |
| "quantum_algorithm_present": True, |
| "penalized_squared_loss_l1_objective": True, |
| "classical_lasso_solution_output": True, |
| } |
| earlier = { |
| "arxiv": "2110.13086", |
| "title": "Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints", |
| "published": "2021-10-25T16:26:37Z", |
| "source_url": "https://export.arxiv.org/e-print/2110.13086v2", |
| "source_sha256": "d6d120eb60829e5120b2700f8776dd35030d10a8e884522db11a7e592ce9b1cc", |
| "anchors": { |
| "penalty_equivalence": "LassoRidge22.tex:169", |
| "quantum_lasso_runtime": "LassoRidge22.tex:203,806-843", |
| }, |
| "quantum_algorithm_present": True, |
| "lasso_problem_present": True, |
| } |
|
|
| target_timestamp = datetime.fromisoformat(TARGET_DATE.replace("Z", "+00:00")) |
| prior_timestamp = datetime.fromisoformat(prior["published"].replace("Z", "+00:00")) |
| earlier_timestamp = datetime.fromisoformat(earlier["published"].replace("Z", "+00:00")) |
| same_objective_family = ( |
| prior["penalized_squared_loss_l1_objective"] |
| and prior["classical_lasso_solution_output"] |
| ) |
| return { |
| "claim_id": "C3", |
| "claim_component": "first quantum algorithm for Lasso regression", |
| "target": { |
| "arxiv": "2509.24757", |
| "published": TARGET_DATE, |
| "source_sha256": "bd48105ab08395ba1edbdb3a407eee9f2e1a8464521d7d67dbe5b6e96edf2549", |
| "objective_anchor": "arxiv-version.tex:1164-1167", |
| "own_prior_art_acknowledgement": "arxiv-version.tex:329-330", |
| }, |
| "prior_art": [prior, earlier], |
| "objective_mapping": { |
| "prior": "(1/2)||y-X beta||_2^2 + lambda_prior ||beta||_1", |
| "multiply_by": 2, |
| "target": "||A x-b||_2^2 + lambda_target ||x||_1", |
| "parameter_bijection": "lambda_target = 2*lambda_prior", |
| "preserves_argmin": True, |
| }, |
| "checks": { |
| "pathwise_lasso_predates_target": prior_timestamp < target_timestamp, |
| "chen_dewolf_predates_target": earlier_timestamp < target_timestamp, |
| "same_penalized_objective_family": same_objective_family, |
| "prior_quantum_algorithm_present": prior["quantum_algorithm_present"], |
| "firstness_contradicted": ( |
| prior_timestamp < target_timestamp |
| and same_objective_family |
| and prior["quantum_algorithm_present"] |
| ), |
| }, |
| "negative_controls": { |
| "later_matching_work": { |
| "published": "2026-01-01T00:00:00Z", |
| "semantic_match": True, |
| "contradicts_firstness": False, |
| }, |
| "earlier_ridge_only_work": { |
| "published": "2021-01-01T00:00:00Z", |
| "semantic_match": False, |
| "contradicts_firstness": False, |
| }, |
| }, |
| } |
|
|
|
|
| def build_counterexample() -> dict: |
| epsilon = Fraction(1, 10) |
| left_minimum = Fraction(1) |
| right_minimand = Fraction(3, 4) |
| right_bound = (1 + epsilon) * right_minimand |
| gap = left_minimum - right_bound |
|
|
| control_left = right_minimand |
| control_passes = control_left <= right_bound |
| return { |
| "claim_id": "C3", |
| "assumptions_satisfied": True, |
| "counterexample": { |
| "A": [[1]], |
| "b": [1], |
| "m": 1, |
| "n": 1, |
| "r": 1, |
| "lambda": 100, |
| "epsilon": "1/10", |
| }, |
| "exact_values": { |
| "left_global_minimum": str(left_minimum), |
| "left_minimizer": "0", |
| "right_minimand_minimum": str(right_minimand), |
| "right_minimand_minimizer": "1/2", |
| "right_bound": str(right_bound), |
| "gap": str(gap), |
| }, |
| "finding": { |
| "all_outputs_violate_corollary": gap > 0, |
| "literal_corollary_falsified": gap > 0, |
| "headline_claim_resolved": True, |
| }, |
| "negative_control": { |
| "lambda": 1, |
| "output_x": "1/2", |
| "left_value": str(control_left), |
| "right_bound": str(right_bound), |
| "passes": control_passes, |
| }, |
| } |
|
|
|
|
| def headline_routes() -> dict: |
| return { |
| "claim_id": "C3", |
| "headline_status": "FALSIFIED", |
| "routes_completed": 4, |
| "routes": [ |
| { |
| "route": 1, |
| "method": "Exact source and quantifier audit", |
| "result": ( |
| "Corollary 26 states a high-probability Lasso runtime of " |
| "O~(r*sqrt(mn)/epsilon+n^3/epsilon^2), while its displayed " |
| "right minimand omits lambda." |
| ), |
| "resolution": "The display is defective; this route alone does not resolve firstness.", |
| }, |
| { |
| "route": 2, |
| "method": "Independent symbolic counterexample to the printed display", |
| "result": "The source-valid scalar instance has exact impossibility gap 7/40.", |
| "resolution": "Independently falsifies the literal approximation display.", |
| }, |
| { |
| "route": 3, |
| "method": "Primary-source prior-art audit", |
| "result": ( |
| "arXiv:2312.14141 was published in 2023, writes the same penalized " |
| "squared-loss Lasso family, and gives quantum LARS algorithms." |
| ), |
| "resolution": "Contradicts the claimed firstness before the target's 2025 publication.", |
| }, |
| { |
| "route": 4, |
| "method": "Independent earlier-paper cross-check", |
| "result": ( |
| "arXiv:2110.13086 was published in 2021, proves a quantum Lasso " |
| "algorithm, and explicitly relates constrained and penalized Lasso." |
| ), |
| "resolution": "A second independent pre-target quantum Lasso result confirms falsification.", |
| }, |
| ], |
| } |
|
|
|
|
| def write_counterexample(root: Path) -> dict: |
| result = build_counterexample() |
| firstness = firstness_counterexample() |
| assert result["assumptions_satisfied"] |
| assert result["finding"]["literal_corollary_falsified"] |
| assert result["negative_control"]["passes"] |
| assert firstness["checks"]["firstness_contradicted"] |
| assert not firstness["negative_controls"]["later_matching_work"]["contradicts_firstness"] |
| assert not firstness["negative_controls"]["earlier_ridge_only_work"]["contradicts_firstness"] |
| raw = root / ".openresearch" / "artifacts" / "claim_3" / "raw" |
| raw.mkdir(parents=True, exist_ok=True) |
| raw.joinpath("counterexample.json").write_text( |
| json.dumps(result, indent=2, sort_keys=True) + "\n" |
| ) |
| raw.joinpath("routes.json").write_text( |
| json.dumps(headline_routes(), indent=2, sort_keys=True) + "\n" |
| ) |
| raw.joinpath("firstness_counterexample.json").write_text( |
| json.dumps(firstness, indent=2, sort_keys=True) + "\n" |
| ) |
| print("C3_LITERAL_COUNTEREXAMPLE") |
| print(json.dumps(result, sort_keys=True)) |
| print("C3_FIRSTNESS_COUNTEREXAMPLE") |
| print(json.dumps(firstness, sort_keys=True)) |
| return {"literal": result, "firstness": firstness} |
|
|
