{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:Q4M5HSECI3VA47PDDD22SB5UFY","short_pith_number":"pith:Q4M5HSEC","schema_version":"1.0","canonical_sha256":"8719d3c88246ea0e7de318f5a907b42e253cb3354851a0283409f45e2d05fdc9","source":{"kind":"arxiv","id":"2605.25849","version":1},"attestation_state":"computed","paper":{"title":"Pattern Formation with Two Length Scales: Spatiotemporal Chaos","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Alastair M. Rucklidge, Cedric Beaume, Laura Pinkney","submitted_at":"2026-05-25T13:40:28Z","abstract_excerpt":"Three-wave interactions (or resonant triads) are the lowest-order nonlinear interaction in pattern formation and arise between waves with different orientations when the sum of two wavevectors equals a third one. When a pattern has only one length scale, stripe patterns are possible but three-wave interactions are responsible for the prevalence of hexagons close to onset. In problems with two length scales, there is a much wider range of possible three-wave interactions, leading to more complex structures such as superhexagons, stars, quasipatterns and even spatiotemporal chaos (STC). We inves"},"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":"2605.25849","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.PS","submitted_at":"2026-05-25T13:40:28Z","cross_cats_sorted":[],"title_canon_sha256":"473f14f408ccafd2a5e79307ba64c82706c9143e7acd82480f4461a881db898f","abstract_canon_sha256":"95ce04b5fb4e0bd3ccead55f2c2cba3026fe3d934f2304790ba7aa1e5e09595e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:05:15.162526Z","signature_b64":"WBhka++XnCWOrEWH54nOmF/d17Std68us4wkt5icUwuucFfGNCge4mYE/Ru4ari1NDthzpkM7C6JD/IUAkGGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8719d3c88246ea0e7de318f5a907b42e253cb3354851a0283409f45e2d05fdc9","last_reissued_at":"2026-05-26T02:05:15.161758Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:05:15.161758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pattern Formation with Two Length Scales: Spatiotemporal Chaos","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Alastair M. Rucklidge, Cedric Beaume, Laura Pinkney","submitted_at":"2026-05-25T13:40:28Z","abstract_excerpt":"Three-wave interactions (or resonant triads) are the lowest-order nonlinear interaction in pattern formation and arise between waves with different orientations when the sum of two wavevectors equals a third one. When a pattern has only one length scale, stripe patterns are possible but three-wave interactions are responsible for the prevalence of hexagons close to onset. In problems with two length scales, there is a much wider range of possible three-wave interactions, leading to more complex structures such as superhexagons, stars, quasipatterns and even spatiotemporal chaos (STC). We inves"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25849","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/2605.25849/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":"2605.25849","created_at":"2026-05-26T02:05:15.161879+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.25849v1","created_at":"2026-05-26T02:05:15.161879+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25849","created_at":"2026-05-26T02:05:15.161879+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q4M5HSECI3VA","created_at":"2026-05-26T02:05:15.161879+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q4M5HSECI3VA47PD","created_at":"2026-05-26T02:05:15.161879+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q4M5HSEC","created_at":"2026-05-26T02:05:15.161879+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Q4M5HSECI3VA47PDDD22SB5UFY","json":"https://pith.science/pith/Q4M5HSECI3VA47PDDD22SB5UFY.json","graph_json":"https://pith.science/api/pith-number/Q4M5HSECI3VA47PDDD22SB5UFY/graph.json","events_json":"https://pith.science/api/pith-number/Q4M5HSECI3VA47PDDD22SB5UFY/events.json","paper":"https://pith.science/paper/Q4M5HSEC"},"agent_actions":{"view_html":"https://pith.science/pith/Q4M5HSECI3VA47PDDD22SB5UFY","download_json":"https://pith.science/pith/Q4M5HSECI3VA47PDDD22SB5UFY.json","view_paper":"https://pith.science/paper/Q4M5HSEC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.25849&json=true","fetch_graph":"https://pith.science/api/pith-number/Q4M5HSECI3VA47PDDD22SB5UFY/graph.json","fetch_events":"https://pith.science/api/pith-number/Q4M5HSECI3VA47PDDD22SB5UFY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q4M5HSECI3VA47PDDD22SB5UFY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q4M5HSECI3VA47PDDD22SB5UFY/action/storage_attestation","attest_author":"https://pith.science/pith/Q4M5HSECI3VA47PDDD22SB5UFY/action/author_attestation","sign_citation":"https://pith.science/pith/Q4M5HSECI3VA47PDDD22SB5UFY/action/citation_signature","submit_replication":"https://pith.science/pith/Q4M5HSECI3VA47PDDD22SB5UFY/action/replication_record"}},"created_at":"2026-05-26T02:05:15.161879+00:00","updated_at":"2026-05-26T02:05:15.161879+00:00"}