{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:H3BMH6QLF54VVHL3EPACNRWACQ","short_pith_number":"pith:H3BMH6QL","schema_version":"1.0","canonical_sha256":"3ec2c3fa0b2f795a9d7b23c026c6c0143d836bd002ea1ddccd9d0258910845f4","source":{"kind":"arxiv","id":"nlin/0102004","version":2},"attestation_state":"computed","paper":{"title":"Pattern and wavenumber selection in ferrofluids","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Andreas Engel, Ren\\'e Friedrichs","submitted_at":"2001-02-02T21:59:22Z","abstract_excerpt":"The formation of patterns of peaks on the free surface of a ferrofluid subject to a magnetic field normal to the undisturbed interface is investigated theoretically. The relative stability of ridge, square, and hexagon planforms is studied using a perturbative energy minimization procedure. Extending previous studies the finite depth of the fluid layer is taken into account. Moreover, adding the wavenumber modulus $k$ to the set of variational parameters also the wavenumber selection problem is addressed. The results are compared with previous investigations and recent experimental findings."},"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":"nlin/0102004","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nlin.PS","submitted_at":"2001-02-02T21:59:22Z","cross_cats_sorted":[],"title_canon_sha256":"298e359a882fa0154a6bd8de852861f3f0c12daf52264340ef10dcdbf7b8bd46","abstract_canon_sha256":"5a0a3ec1621c02681b8ac476075eae152e26cb7bb8633dbcef40490439425b9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:07.749109Z","signature_b64":"GM+7e8/5sX1MvMiCNZZcCFR7eQM6q/aC1P8XfuADfBOlUWBmpF9LZ9tZnbhdouYRotdpJ1LjpQT3dOk8vELqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ec2c3fa0b2f795a9d7b23c026c6c0143d836bd002ea1ddccd9d0258910845f4","last_reissued_at":"2026-05-18T01:09:07.748625Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:07.748625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pattern and wavenumber selection in ferrofluids","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Andreas Engel, Ren\\'e Friedrichs","submitted_at":"2001-02-02T21:59:22Z","abstract_excerpt":"The formation of patterns of peaks on the free surface of a ferrofluid subject to a magnetic field normal to the undisturbed interface is investigated theoretically. The relative stability of ridge, square, and hexagon planforms is studied using a perturbative energy minimization procedure. Extending previous studies the finite depth of the fluid layer is taken into account. Moreover, adding the wavenumber modulus $k$ to the set of variational parameters also the wavenumber selection problem is addressed. The results are compared with previous investigations and recent experimental findings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0102004","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"nlin/0102004","created_at":"2026-05-18T01:09:07.748704+00:00"},{"alias_kind":"arxiv_version","alias_value":"nlin/0102004v2","created_at":"2026-05-18T01:09:07.748704+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0102004","created_at":"2026-05-18T01:09:07.748704+00:00"},{"alias_kind":"pith_short_12","alias_value":"H3BMH6QLF54V","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_16","alias_value":"H3BMH6QLF54VVHL3","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_8","alias_value":"H3BMH6QL","created_at":"2026-05-18T12:25:50.254431+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/H3BMH6QLF54VVHL3EPACNRWACQ","json":"https://pith.science/pith/H3BMH6QLF54VVHL3EPACNRWACQ.json","graph_json":"https://pith.science/api/pith-number/H3BMH6QLF54VVHL3EPACNRWACQ/graph.json","events_json":"https://pith.science/api/pith-number/H3BMH6QLF54VVHL3EPACNRWACQ/events.json","paper":"https://pith.science/paper/H3BMH6QL"},"agent_actions":{"view_html":"https://pith.science/pith/H3BMH6QLF54VVHL3EPACNRWACQ","download_json":"https://pith.science/pith/H3BMH6QLF54VVHL3EPACNRWACQ.json","view_paper":"https://pith.science/paper/H3BMH6QL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=nlin/0102004&json=true","fetch_graph":"https://pith.science/api/pith-number/H3BMH6QLF54VVHL3EPACNRWACQ/graph.json","fetch_events":"https://pith.science/api/pith-number/H3BMH6QLF54VVHL3EPACNRWACQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H3BMH6QLF54VVHL3EPACNRWACQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H3BMH6QLF54VVHL3EPACNRWACQ/action/storage_attestation","attest_author":"https://pith.science/pith/H3BMH6QLF54VVHL3EPACNRWACQ/action/author_attestation","sign_citation":"https://pith.science/pith/H3BMH6QLF54VVHL3EPACNRWACQ/action/citation_signature","submit_replication":"https://pith.science/pith/H3BMH6QLF54VVHL3EPACNRWACQ/action/replication_record"}},"created_at":"2026-05-18T01:09:07.748704+00:00","updated_at":"2026-05-18T01:09:07.748704+00:00"}