https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/Head https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI http://www.nanopub.org/nschema#hasAssertion https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/assertion https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI http://www.nanopub.org/nschema#hasProvenance https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/provenance https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/pubinfo https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/assertion https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test http://purl.org/dc/terms/description For 145 gastropod specimens (>= 5 apertures) the series sqrt(aperture area in mm^2) versus angle (0, pi, 2pi, ...) and for 179 ammonoid species the series conch diameter versus whorl angle were each fitted by nonlinear least squares with a logarithmic spiral a e^(b theta), an Archimedean spiral a + b theta and a Fermat spiral a sqrt(theta + theta0); the model with the lowest RMSE was recorded per series and the median RMSE ratios Archimedean/logarithmic and Fermat/logarithmic computed per group. Pre-registered thresholds were then applied. https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/Assessment https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test http://www.w3.org/2000/01/rdf-schema#comment Measured: 0.676 fraction of gastropod specimens for which the logarithmic spiral has the lowest RMSE (ammonoids: 1.000) (n = 324, gastropods n = 145 specimens / 21 species; ammonoids n = 179 species). Interpretation: Thompson's statement is a universal over four classes of structure plus a stated exception (the cordate leaf). Public coordinate data were found only for molluscan shells: no digitised floret positions of sunflower capitula (the Swinton et al. 2016 citizen-science deposit gives parastichy counts and annotated photographs, not coordinates), no horn centre-line or outline data, and no foraminiferal chamber-position tables were located on Dryad, Zenodo or figshare; MorphoSource meshes require a login. The test therefore covers only the molluscan class, and its verdict is explicitly a test of that class with the caveat that a logarithmic fit for molluscs cannot establish the universal. 'Logarithmic spiral' is operationalized as exponential growth of linear whorl size with rotation angle: in a gastropod, the square root of aperture area at successive half whorls; in an ammonoid, conch diameter at successive half whorls (for a planispiral conch the diameter is the sum of two opposite radius vectors and grows exponentially if and only if the radius does). Both datasets were already downloaded for claim tests thompson1917-ch11-05 and thompson1917-ch11-15; those tests examined allometry of conch proportions and whorl-expansion and apical angles, not the comparison of spiral models made here. https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test http://www.w3.org/2000/01/rdf-schema#label Claim test of thompson1917-ch11-01: mixed, confidence 0.6 https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test http://www.w3.org/2000/01/rdf-schema#seeAlso https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/thompson-growth-form/thompson1917-ch11-01/result.json https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test 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/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/admissibleDatasets Planned datasets: dryad-p5hqbzknw-collins-2021-helicospiral-gastropods, dryad-c17p8-korn-walton-2018-ammonoid-ontogenetic-conch-parameters https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/assessmentType claim-test/0.1.0 https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/dataKind biological https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/disconfirmingObservation Pre-registered. The claim is refuted (for molluscan shells, and hence as a universal) if the logarithmic model is best in fewer than 50% of specimens in either group, or if the median RMSE ratio Archimedean / logarithmic is below 1.0 in either group. Intermediate results are 'mixed'. https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Dryad downloads are served behind a proof-of-work interstitial (Anubis); analysis.py completes it automatically and must download the 521 MB archive (only the 1.5 MB .tps inside is read). https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Gastropod series are short (median 8 half-whorl apertures spanning ~3-4 revolutions with a median expansion of 1.54 per revolution), which limits discrimination between exponential and linear growth; the median RMSE ratio of 1.39 reflects that limited leverage as well as genuine departures. https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Only the molluscan-shell class of Thompson's universal was tested; ruminant horns, foraminiferal shells and sunflower capitula (and the cordate-leaf exception) remain untested for lack of public coordinate data, so even a clean pass could not have established the universal claim. https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Tenagodus is a siliquariid whose coiling loosens and uncoils in adulthood, so its non-logarithmic fit is expected; removing it does not change the gastropod percentage materially (it contributes 2 of 145 specimens). https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/evidenceAgainst The Fermat (parabolic) spiral, which modern work (Vogel 1979) uses for sunflower capitula, is the worst of the three models for every mollusc group here (median RMSE ratio 3-25), i.e. molluscs are not sunflower-like; the sunflower class itself could not be tested. https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/evidenceAgainst Within molluscs the result is itself mixed: every one of 179 ammonoid species is fitted far better by the logarithmic spiral (median RMSE ratio 15 against Archimedean), but only 68% of gastropod specimens (14 of 21 species) are, and in the Struthiolariidae genus Pelicaria (36 specimens) and a handful of other species the whorl size grows closer to linearly than exponentially with angle over the digitised whorls. Collins et al. (2021) themselves report that struthiolariid coiling departs from constant-rate (logarithmic) growth. https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/expectedObservation Pre-registered. Only the molluscan-shell class can be tested with public data located (see interpretation). For every gastropod specimen in Collins et al. 2021 with >= 5 digitised successive half-whorl apertures, take the square root of aperture area as the linear whorl size at angles 0, pi, 2 pi, ...; for every ammonoid species in Korn & Walton 2018 with >= 5 half-whorl diameters, take conch diameter at each half whorl. Fit the three two-parameter models by least squares in the size domain and compare root-mean-square residuals. The claim (for molluscan shells) is supported if the logarithmic model has the lowest RMSE in >= 80% of gastropod specimens and in >= 80% of ammonoid species, and the median ratio RMSE(Archimedean) / RMSE(logarithmic) exceeds 1.5 in both groups. Because horns, foraminifera and sunflower capitula remain untested, the confidence attached to a supporting verdict is capped at 0.5. https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/failCriterion Pre-registered. The claim is refuted (for molluscan shells, and hence as a universal) if the logarithmic model is best in fewer than 50% of specimens in either group, or if the median RMSE ratio Archimedean / logarithmic is below 1.0 in either group. Intermediate results are 'mixed'. https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/hasConfidence 0.6 https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-1 https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/hasEvidence https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-2 https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/hasVerdict mixed https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/hypothesis If the permanent spiral forms of organisms (ruminant horns, molluscan and foraminiferal shells, sunflower capitula) are logarithmic spirals, then for any such structure the linear size of the growing edge (radius vector or whorl size) must increase exponentially with angle of rotation about the spiral's pole, r = a e^(b theta), and must do so better than the alternative simple spirals (Archimedean r = a + b theta, which grows linearly; Fermat / parabolic r = a sqrt(theta + theta0), which decelerates). https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/inferenceMethod For 145 gastropod specimens (>= 5 apertures) the series sqrt(aperture area in mm^2) versus angle (0, pi, 2pi, ...) and for 179 ammonoid species the series conch diameter versus whorl angle were each fitted by nonlinear least squares with a logarithmic spiral a e^(b theta), an Archimedean spiral a + b theta and a Fermat spiral a sqrt(theta + theta0); the model with the lowest RMSE was recorded per series and the median RMSE ratios Archimedean/logarithmic and Fermat/logarithmic computed per group. Pre-registered thresholds were then applied. https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/passCriterion Pre-registered. Only the molluscan-shell class can be tested with public data located (see interpretation). For every gastropod specimen in Collins et al. 2021 with >= 5 digitised successive half-whorl apertures, take the square root of aperture area as the linear whorl size at angles 0, pi, 2 pi, ...; for every ammonoid species in Korn & Walton 2018 with >= 5 half-whorl diameters, take conch diameter at each half whorl. Fit the three two-parameter models by least squares in the size domain and compare root-mean-square residuals. The claim (for molluscan shells) is supported if the logarithmic model has the lowest RMSE in >= 80% of gastropod specimens and in >= 80% of ammonoid species, and the median ratio RMSE(Archimedean) / RMSE(logarithmic) exceeds 1.5 in both groups. Because horns, foraminifera and sunflower capitula remain untested, the confidence attached to a supporting verdict is capped at 0.5. https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/ontology/preregistered false https://w3id.org/delphi/resource/claim/thompson1917-ch11-01 https://w3id.org/delphi/ontology/hasAssessment https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-1 http://purl.org/dc/terms/description sectioned_shells.tps inside the archive: aperture outlines (50 semilandmarks) every 180 degrees for 184 gastropod specimens of 29 species; 145 specimens (21 species) have >= 5 apertures https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-1 http://purl.org/dc/terms/license CC0 1.0 https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-1 http://www.w3.org/2000/01/rdf-schema#label Dataset: Data associated with: Going round the twist - An empirical analysis of shell coiling in helicospiral gastropods (Collins, Klapaukh, Crampton, Gazley, Schipper, Maksimenko, Hines 2021, Paleobiology) https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-1 http://www.w3.org/ns/prov#atLocation https://datadryad.org/downloads/file_stream/547236 https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-1 http://www.w3.org/ns/prov#wasDerivedFrom https://datadryad.org/dataset/doi:10.5061/dryad.p5hqbzknw https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-1 https://w3id.org/delphi/ontology/hasChecksum sha256:edab9e356820a43984bcf8130359ec29f7e6c00ca3995292fcd922ba2cb3a2a9 https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-2 http://purl.org/dc/terms/description 'dm' sheet: conch diameter at every half whorl (median 16 stages, ~0.5 to ~30 mm) for 179 planispiral ammonoid species https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-2 http://purl.org/dc/terms/license CC0 1.0 https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-2 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/EvidenceItem https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-2 http://www.w3.org/2000/01/rdf-schema#label Dataset: Data from: Iterative ontogenetic development of ammonoid conch shapes from the Devonian through to the Jurassic (Walton & Korn 2018, Palaeontology) https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-2 http://www.w3.org/ns/prov#atLocation https://datadryad.org/downloads/file_stream/34579 https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-2 http://www.w3.org/ns/prov#wasDerivedFrom https://datadryad.org/dataset/doi:10.5061/dryad.c17p8 https://w3id.org/delphi/resource/evidence/thompson1917-ch11-01--claim-test--dataset-2 https://w3id.org/delphi/ontology/hasChecksum sha256:fbe2012f1d420ef7b292141ae0ed0ea8d046c4c15303663565dc72e0727ebe40 https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/provenance https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#SoftwareAgent https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 http://www.w3.org/2000/01/rdf-schema#label delphisci claim tester (claude-fable-5.1; cursor/thompson-claim-tests-cf12) https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 http://www.w3.org/ns/prov#actedOnBehalfOf https://orcid.org/0009-0007-4948-9192 https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/delphi/ontology/usesModel https://w3id.org/delphi/resource/model/claude-fable-5-1 https://w3id.org/delphi/resource/model/claude-fable-5-1 http://purl.org/dc/terms/identifier claude-fable-5.1 https://w3id.org/delphi/resource/model/claude-fable-5-1 http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/delphi/ontology/LanguageModel https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/assertion http://www.w3.org/ns/prov#wasAttributedTo https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/assertion http://www.w3.org/ns/prov#wasDerivedFrom https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/thompson-growth-form/thompson1917-ch11-01/result.json https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/assertion http://www.w3.org/ns/prov#wasGeneratedBy https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/test https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/plan http://www.w3.org/ns/prov#hadPlan https://github.com/fractastical/delphisci/blob/bf2af6ee0a84e23ffa6414ad7a0a50a8c276506e/test-data/claim-tests/README.md https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/test http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.w3.org/ns/prov#Activity https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/test http://www.w3.org/ns/prov#qualifiedAssociation https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/plan https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/test http://www.w3.org/ns/prov#wasAssociatedWith https://w3id.org/delphi/resource/agent/delphisci-claim-tester-claude-fable-5-1 https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/pubinfo https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI http://purl.org/dc/terms/created 2026-11-08T16:24:31.904Z https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI http://purl.org/dc/terms/creator https://orcid.org/0009-0007-4948-9192 https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI http://purl.org/dc/terms/license https://creativecommons.org/licenses/by/4.0/ https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI http://purl.org/nanopub/x/hasNanopubType https://w3id.org/delphi/ontology/Assessment https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI http://purl.org/nanopub/x/introduces https://w3id.org/delphi/resource/assessment/thompson1917-ch11-01--claim-test https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI http://www.w3.org/2000/01/rdf-schema#label Claim test of thompson1917-ch11-01: mixed, confidence 0.6 https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI https://w3id.org/delphi/ontology/domain https://w3id.org/delphi/resource/domain/thompson-growth-form-1917 https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/sig http://purl.org/nanopub/x/hasAlgorithm RSA https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/sig http://purl.org/nanopub/x/hasPublicKey MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/sig http://purl.org/nanopub/x/hasSignature R8EuVoQAyjQihSg4IDNLrukibjRe/ih1t+U2zh3hLZqJQ07hcGm4tcvHg/XcUI0lVjYv85o2US+VWFUrI49xaV5K792CLg0ZcKQPEYVl3AQwC/dN2U4utnGjn7lUpwVP998nYEtRGx/Dcbrj7SzvRbo+4Wa0tzSI8TAbFUzv3cBnQpaXylKg48vTKdCG0YDqnscuqZvxY62gem9W99+yRVE6avsWRToodlhlWG1Gq9u/AEIP60TMAAkUlfEnndsq1lkvEqPX+tCgQ4059XpPf/4YENSwJRwr+2plLfjvMhIGFIhLSfwZ9es/t+XyzTFSpyxo/nVmD43u00ZM4vUOcw== https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/sig http://purl.org/nanopub/x/hasSignatureTarget https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI https://w3id.org/np/RAz2V-5k60PulCE151RvwYUTff5C4H3xEvVTsMnySLoYI/sig http://purl.org/nanopub/x/signedBy https://orcid.org/0009-0007-4948-9192