. . . . "Seed 470003 was fixed before execution. Because no n=3 census existed in the repository, all 3^9 sign patterns and all seven non-empty diffusion supports were first searched with 200 draws per pattern-support pair. Nonzero reaction magnitudes and positive diffusion coefficients were sampled log-uniformly on [0.01, 100], and 121 wave numbers were swept logarithmically on [0.001, 1000]. Then 2,000 distinct n=4 sign patterns were sampled uniformly conditional on a directed cycle, one non-empty support was sampled uniformly for each, and 100 parameter draws were tested. Strict cubic and quartic Routh-Hurwitz inequalities defined stability; capability required stable J and non-Hurwitz J-k^2D at some tested k > 0." . . "Measured: 0.196 detected-capable fraction (n = 2000, exact two-sided Clopper-Pearson 95% interval [0.1788079205547995, 0.21408794619692778]). Interpretation: This operationalizes topology capability as detection within fixed bounded rate, diffusion, and wave-number searches. It directly tests the stated Monte Carlo approach, but non-detection is not a proof that no parameters exist." . "Claim test of turing-topology-genericity (overnight-turing-n4): refutes, confidence 0.95" . . . "No external dataset; only seeded computational output from the enumerated n=3 and sampled n=4 sign-pattern ensembles." . "claim-test/0.1.0" . "computational" . "The exact 95% binomial interval for the detected-capable fraction lies entirely below 0.9." . "A finite random parameter search has false negatives for existential capability; consequently this result does not settle or rigorously refute the mathematical conjecture that parameters exist for almost all cyclic topologies." . "The exact interval lies far below 0.9 and therefore refutes the pre-registered operational n=4 detection claim." . "The n=3 baseline exhausts sign patterns and diffusion supports but not the continuous parameter domain, so it is not the interval-certified exact census proposed in the approach file." . "The sample can refute the threshold under this fixed procedure but cannot prove 'almost all'; even a detected fraction above 0.9 would only support, not prove, the claim." . "More than 90% of sampled cyclic n=4 sign patterns are detected as Turing-capable by the fixed finite parameter and wave-number search." . "A two-sided exact Clopper-Pearson 95% interval for the detected Turing-capable fraction lying entirely below 0.9 refutes the pre-registered n=4 operational claim." . "0.95"^^ . . "refutes" . "Among uniformly sampled four-species interaction sign patterns whose directed interaction graph contains at least one feedback cycle, more than 90% are detected as admitting a diffusion-driven linear instability for at least one of 100 sampled parameter realizations and one non-empty diffusion support." . "Count a topology once any sampled stable Jacobian becomes non-Hurwitz after diagonal diffusion at a tested positive wave number; apply a two-sided 95% Clopper-Pearson interval to the n=4 detected-capable count." . "A detected Turing-capable fraction greater than 0.9 supports the operational 'almost all' claim; because this is a finite Monte Carlo parameter search, it cannot prove the existential topological claim." . "false"^^ . . . "delphisci claim tester (gpt-5.6-sol; turing-capable-network-topologies--grok-4-7--3)" . . . "gpt-5.6-sol" . . . . . . . . . "2026-11-08T16:24:31.887Z"^^ . . . . . "Claim test of turing-topology-genericity (overnight-turing-n4): refutes, confidence 0.95" . . "RSA" . "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" . "Z8REVArNNjI4w/xNvWMbnGc8BMSpkWTd4BVo1qz8oejT8r4P4wyI/Xxa3+Dmm1mu2QAeEnvJu8cHQDYFOk9g20km5qhVnoUYxrzXppkfrCPcJ49div1KYx6Qs97sEgNkX6aXXBCR7B0gY02Z+NHskkUY+nHsnSbvRK9zP4nO5PDgW6dWOxzDoSVANNiQuU5Lhd7emNbApztgfPVaxkE2K96ny3A03MMH+VGtgHQ2vHOh7BfZXq5idDL+xdXLh4YN53kyVtzqQTeHwaFstrAwa5ncmeRXB7boADU+w2hYt6OdksEPvqqqQH3+eoLRoxO9eymgb8IavE4WBPFHB4qhnw==" . . .