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"""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}
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