{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:EAF6W6I2F44UFG6P3XO3OKD7FJ","short_pith_number":"pith:EAF6W6I2","schema_version":"1.0","canonical_sha256":"200beb791a2f39429bcfddddb7287f2a6176499c8c70175ec3f1890aaac6dd71","source":{"kind":"arxiv","id":"2509.07458","version":1},"attestation_state":"computed","paper":{"title":"Unveiling Biological Models Through Turing Patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.bio-ph","q-bio.BM","q-bio.CB"],"primary_cat":"math.AP","authors_text":"Catharine W. K. Lo, Hongyu Liu, Yuhan Li","submitted_at":"2025-09-09T07:26:36Z","abstract_excerpt":"Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as boundary measurements, neglecting the rich information embedded in the patterns themselves. Here we introduce a new research direction that directly leverages physical observables from nature--the amplitude of Turing patterns--to achieve complete parameter identification. We present a framework that uses the spatial amplitude profile of a single pattern to simul"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2509.07458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-09-09T07:26:36Z","cross_cats_sorted":["physics.bio-ph","q-bio.BM","q-bio.CB"],"title_canon_sha256":"85e6f42dad2be8539ce10197c6e63091e9dcbf42097a737c9e2d3a9632c6d759","abstract_canon_sha256":"d8670307a859666f693d48ace271e66775d87ffab01774f8277018b01ee07dde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:07:21.734843Z","signature_b64":"3MnK1qkRjjT5SqD97IQHyObbVEqi84dGddiIPbhgLrMxDZhRVy+kTA+BYynHxQIqn4IIlvTFWj6ml8ZJU5naDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"200beb791a2f39429bcfddddb7287f2a6176499c8c70175ec3f1890aaac6dd71","last_reissued_at":"2026-07-05T12:07:21.734273Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:07:21.734273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unveiling Biological Models Through Turing Patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.bio-ph","q-bio.BM","q-bio.CB"],"primary_cat":"math.AP","authors_text":"Catharine W. K. Lo, Hongyu Liu, Yuhan Li","submitted_at":"2025-09-09T07:26:36Z","abstract_excerpt":"Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as boundary measurements, neglecting the rich information embedded in the patterns themselves. Here we introduce a new research direction that directly leverages physical observables from nature--the amplitude of Turing patterns--to achieve complete parameter identification. We present a framework that uses the spatial amplitude profile of a single pattern to simul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07458","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.07458/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2509.07458","created_at":"2026-07-05T12:07:21.734349+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.07458v1","created_at":"2026-07-05T12:07:21.734349+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07458","created_at":"2026-07-05T12:07:21.734349+00:00"},{"alias_kind":"pith_short_12","alias_value":"EAF6W6I2F44U","created_at":"2026-07-05T12:07:21.734349+00:00"},{"alias_kind":"pith_short_16","alias_value":"EAF6W6I2F44UFG6P","created_at":"2026-07-05T12:07:21.734349+00:00"},{"alias_kind":"pith_short_8","alias_value":"EAF6W6I2","created_at":"2026-07-05T12:07:21.734349+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.11554","citing_title":"Recovering the initial condition and physical coefficients in a nonlinear PDE model of cell invasion","ref_index":18,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EAF6W6I2F44UFG6P3XO3OKD7FJ","json":"https://pith.science/pith/EAF6W6I2F44UFG6P3XO3OKD7FJ.json","graph_json":"https://pith.science/api/pith-number/EAF6W6I2F44UFG6P3XO3OKD7FJ/graph.json","events_json":"https://pith.science/api/pith-number/EAF6W6I2F44UFG6P3XO3OKD7FJ/events.json","paper":"https://pith.science/paper/EAF6W6I2"},"agent_actions":{"view_html":"https://pith.science/pith/EAF6W6I2F44UFG6P3XO3OKD7FJ","download_json":"https://pith.science/pith/EAF6W6I2F44UFG6P3XO3OKD7FJ.json","view_paper":"https://pith.science/paper/EAF6W6I2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.07458&json=true","fetch_graph":"https://pith.science/api/pith-number/EAF6W6I2F44UFG6P3XO3OKD7FJ/graph.json","fetch_events":"https://pith.science/api/pith-number/EAF6W6I2F44UFG6P3XO3OKD7FJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EAF6W6I2F44UFG6P3XO3OKD7FJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EAF6W6I2F44UFG6P3XO3OKD7FJ/action/storage_attestation","attest_author":"https://pith.science/pith/EAF6W6I2F44UFG6P3XO3OKD7FJ/action/author_attestation","sign_citation":"https://pith.science/pith/EAF6W6I2F44UFG6P3XO3OKD7FJ/action/citation_signature","submit_replication":"https://pith.science/pith/EAF6W6I2F44UFG6P3XO3OKD7FJ/action/replication_record"}},"created_at":"2026-07-05T12:07:21.734349+00:00","updated_at":"2026-07-05T12:07:21.734349+00:00"}