https://w3id.org/np/RA5EUDtbN2g-vIoxWM6O1kvhkENxQbRP0fR4SM3uhSwKk/Head https://w3id.org/np/RA5EUDtbN2g-vIoxWM6O1kvhkENxQbRP0fR4SM3uhSwKk http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RA5EUDtbN2g-vIoxWM6O1kvhkENxQbRP0fR4SM3uhSwKk/assertion https://w3id.org/np/RA5EUDtbN2g-vIoxWM6O1kvhkENxQbRP0fR4SM3uhSwKk http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RA5EUDtbN2g-vIoxWM6O1kvhkENxQbRP0fR4SM3uhSwKk/provenance https://w3id.org/np/RA5EUDtbN2g-vIoxWM6O1kvhkENxQbRP0fR4SM3uhSwKk http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RA5EUDtbN2g-vIoxWM6O1kvhkENxQbRP0fR4SM3uhSwKk/pubinfo https://w3id.org/np/RA5EUDtbN2g-vIoxWM6O1kvhkENxQbRP0fR4SM3uhSwKk http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RA5EUDtbN2g-vIoxWM6O1kvhkENxQbRP0fR4SM3uhSwKk/assertion https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d http://purl.org/dc/terms/description Written before the simulation was run. Model: u_t = a - u + u^2 v + D_u u_xx, v_t = b - u^2 v + D_v v_xx; steady state u* = a + b, v* = b / (a + b)^2; Jacobian entries f_u = -1 + 2b/(a+b), f_v = (a+b)^2, g_u = -2b/(a+b), g_v = -(a+b)^2. d_c is the smallest D_v satisfying D_v f_u + D_u g_v = 2 sqrt(D_u D_v det J); k_c^2 = sqrt(det J / (D_u d_c)). Grid: 16 points per lambda_c. Seeds: 20261102, 20261103, 20261104. Domain lengths for the scaling runs are fixed at 80 lambda_c(s = 1) so the quantisation error is at most 1/(2 n) with n >= 40 waves. https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/Assessment https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d http://www.w3.org/2000/01/rdf-schema#comment Measured: 0.9877 lambda_measured / lambda_c at L = 80 lambda_c, D_v = 1.05 d_c (n = 27, wavelength quantised to L/n: step 1/81 (1.2%) at L = 80 lambda_c; 3 seeds per condition agree to within one quantum). Interpretation: This tests the formal statement as written, on its own assumptions (two species, near onset, domain large compared with the wavelength). A pass shows the onset formula predicts the simulated pattern in that regime; it says nothing about organisms, where Sheth et al. 2012 (10.1126/science.1226804) already show Hox dose changes digit period. The far-from-onset control measures how quickly the formula stops applying, which is the claim's own caveat. https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d http://www.w3.org/2000/01/rdf-schema#label Claim test of turing-wavelength (schnakenberg-1d): supports, confidence 0.9 https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d http://www.w3.org/2000/01/rdf-schema#seeAlso https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/math-bio-claims/turing-wavelength/schnakenberg-1d/result.json https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/admissibleDatasets No external dataset; only seeded output of the simulation in analysis.py. The onset values d_c, k_c and lambda_c are computed from the Jacobian, not fitted. https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/dataKind computational https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/disconfirmingObservation Nonlinear selection moves the wavelength away from lambda_c by more than 20% even 5% above onset, or the wavelength tracks the domain length, or the slope against D departs from 1/2. https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/evidenceAgainst A computational test of a model theorem: it checks the theorem's stated regime (two species, near onset, large domain) in one kinetic scheme (Schnakenberg), not biology, and not other kinetics. Sheth et al. 2012 (10.1126/science.1226804) is the organism-level evidence and is cited, not reproduced. https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/evidenceAgainst All three pre-registered criteria passed: onset ratio 0.988 (pass band within 10%), domain spread 1.8% over L in {20, 40, 80} lambda_c (pass band 5%), slope 0.495 (pass band [0.45, 0.55]). No deviation from the pre-registration. https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/evidenceAgainst The far-from-onset control at D_v = 2 d_c still gave lambda / lambda_c = 0.973 for this scheme, so the 'near onset' assumption was not stressed here; mass-conserving systems are known to select differently far from onset (PMID 38243507). https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/evidenceAgainst The wavelength is quantised by the periodic domain (n waves in L); seeds at L = 20 lambda_c landed on 19, 20 and 21 waves, which is the whole of the 1.8% spread. https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/expectedObservation The saturated pattern's dominant wavenumber sits at the linearly fastest-growing mode, so lambda tracks lambda_c, does not move with L beyond the quantisation 2 pi n / L, and goes as sqrt(D). https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/failCriterion Any one: |lambda_measured / lambda_c - 1| > 0.20; spread over L > 0.10; slope outside [0.40, 0.60]. Results between the pass and fail bands on any criterion give a mixed verdict. https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/hasConfidence 0.9 https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/hasEvidence http://www.w3.org/1999/02/22-rdf-syntax-ns#nil https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/hasVerdict supports https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/hypothesis In a two-species Schnakenberg reaction-diffusion system (a = 0.1, b = 0.9, D_u = 1) simulated on a one-dimensional periodic domain just above the Turing threshold (D_v = 1.05 d_c), the dominant wavelength of the saturated pattern (i) equals the onset wavelength lambda_c = 2 pi / k_c with k_c^2 = sqrt(det J / (D_u D_v)) to within 10%, (ii) is independent of domain length L in {20, 40, 80} lambda_c to within a 5% spread, and (iii) scales as sqrt(s) when both diffusivities are multiplied by s in {0.25, 0.5, 1, 2, 4}, with a log-log slope in [0.45, 0.55]. https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/inferenceMethod Semi-implicit Fourier (IMEX) integration from a homogeneous steady state plus seeded noise of amplitude 1e-3, to t = 20,000 in model time; dominant wavenumber from the peak of |FFT(u - mean u)| at the final time (the peak is a multiple of 2 pi / L, so lambda_measured is quantised to L / n). A far-from-onset control at D_v = 2 d_c is run and reported but is not part of the verdict. https://w3id.org/delphi/resource/assessment/turing-wavelength--claim-test--schnakenberg-1d https://w3id.org/delphi/ontology/passCriterion All three: |lambda_measured / lambda_c - 1| <= 0.10 at L = 80 lambda_c; (max - min) / mean of lambda over L in {20, 40, 80} lambda_c <= 0.05; least-squares slope of log lambda against log s in [0.45, 0.55]. 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