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{
"claim": "Theorem 1.2 / 3.4",
"constant": {
"abs_err_vs_paper_rounding": 3.333333333333313e-05,
"eps_prime_exact": "11/750",
"eps_prime_float": 0.014666666666666666,
"implied_rho_slope_1_over_eps_prime": 68.18181818181819,
"matches_paper_rounding": true,
"paper_states": 0.0147,
"rounds_to_4dp": 0.014666667208075523
},
"constant_provenance": {
"0.088_admissible_strictly_below_threshold": true,
"bernasconi_normalisation_divisor": 6,
"conclusion": "0.088/6 is a valid (slightly conservative) instantiation: 0.088 < 2*sqrt(73)-17 = 0.0880075, so the strict inequality of Pure-Circuit Thm 4.4 is respected with only 7.5e-6 of slack. Neither cited paper states the value 0.088/6 itself; it must be composed from Bernasconi's *proof*.",
"difference": 1.2484391770559572e-06,
"eps_prime_from_exact_threshold": 0.014667915105843723,
"eps_prime_from_rounded_0.088": 0.014666666666666666,
"margin": 7.490635062335743e-06,
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"pure_circuit_threshold_exact": "-17 + 2*sqrt(73)",
"pure_circuit_threshold_float": 0.08800749063506233,
"reason_for_6": "degree-3 graph and alpha_ij in [-2,2] give row/column absolute sums <= 6; dividing the operator by 6 enforces ||D||_1, ||D||_inf <= 1 and rescales the additive error by the same factor (rho* = eps*/6)."
},
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],
"symbolic": {
"equals_c_times_F": true,
"grad_simplifies_to": "c*(a*xstar + b)",
"solve_c_for_eps_prime_target": "[epsilon/epsilon_prime]"
},
"verdict": {
"constant_arithmetic_correct": true,
"note": "PPAD-hardness itself is inherited from Lemma 3.3 (Bernasconi et al. 2024) and is not executable; what is verified here is that the reduction of Theorem 3.4 is solution-preserving in both directions with the stated rho bound.",
"reduction_correct": true
}
}

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