{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:V4FOCDB2UOUSLVR5AR6BV2SB5N","short_pith_number":"pith:V4FOCDB2","schema_version":"1.0","canonical_sha256":"af0ae10c3aa3a925d63d047c1aea41eb7912f7ffc0dbc88441181c94cf4fedc7","source":{"kind":"arxiv","id":"1312.7388","version":1},"attestation_state":"computed","paper":{"title":"The classification of constant weighted curvature curves in the plane with a log-linear density","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Doan The Hieu, Tran Le Nam","submitted_at":"2013-12-28T04:02:29Z","abstract_excerpt":"In this paper, we classify the class of constant weighted curvature curves in the plane with a log-linear density, or in other words, classify all traveling curved fronts with a constant forcing term in $\\Bbb R^2.$ The classification gives some interesting phenomena and consequences including: the family of curves converge to a round point when the weighted curvature of curves (or equivalently the forcing term of traveling curved fronts) goes to infinity, a simple proof for a main result in [13] as well as some well-known facts concerning to the isoperimetric problem in the plane with density "},"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":"1312.7388","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2013-12-28T04:02:29Z","cross_cats_sorted":[],"title_canon_sha256":"9e7a013166bf71497c7e1d1e50a740b42e6d797350ee716b3f7345bfc5250a90","abstract_canon_sha256":"4d8bdf4dc02c483729646f0480659372f11c3f5c5b8d014ea13a0c72fddc0ac3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:43.642997Z","signature_b64":"IBHUk/aH1hr5MOOck0N0uZ5rdb0SXSlyJlR5vxOCX1j0vivJ5Z/muDIzgdtOnjLYKQP50/tZpcTK2jIqh4ztAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af0ae10c3aa3a925d63d047c1aea41eb7912f7ffc0dbc88441181c94cf4fedc7","last_reissued_at":"2026-05-18T03:03:43.642474Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:43.642474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The classification of constant weighted curvature curves in the plane with a log-linear density","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Doan The Hieu, Tran Le Nam","submitted_at":"2013-12-28T04:02:29Z","abstract_excerpt":"In this paper, we classify the class of constant weighted curvature curves in the plane with a log-linear density, or in other words, classify all traveling curved fronts with a constant forcing term in $\\Bbb R^2.$ The classification gives some interesting phenomena and consequences including: the family of curves converge to a round point when the weighted curvature of curves (or equivalently the forcing term of traveling curved fronts) goes to infinity, a simple proof for a main result in [13] as well as some well-known facts concerning to the isoperimetric problem in the plane with density "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7388","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":""},"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":"1312.7388","created_at":"2026-05-18T03:03:43.642557+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.7388v1","created_at":"2026-05-18T03:03:43.642557+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7388","created_at":"2026-05-18T03:03:43.642557+00:00"},{"alias_kind":"pith_short_12","alias_value":"V4FOCDB2UOUS","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"V4FOCDB2UOUSLVR5","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"V4FOCDB2","created_at":"2026-05-18T12:28:04.890932+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/V4FOCDB2UOUSLVR5AR6BV2SB5N","json":"https://pith.science/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N.json","graph_json":"https://pith.science/api/pith-number/V4FOCDB2UOUSLVR5AR6BV2SB5N/graph.json","events_json":"https://pith.science/api/pith-number/V4FOCDB2UOUSLVR5AR6BV2SB5N/events.json","paper":"https://pith.science/paper/V4FOCDB2"},"agent_actions":{"view_html":"https://pith.science/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N","download_json":"https://pith.science/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N.json","view_paper":"https://pith.science/paper/V4FOCDB2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.7388&json=true","fetch_graph":"https://pith.science/api/pith-number/V4FOCDB2UOUSLVR5AR6BV2SB5N/graph.json","fetch_events":"https://pith.science/api/pith-number/V4FOCDB2UOUSLVR5AR6BV2SB5N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N/action/storage_attestation","attest_author":"https://pith.science/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N/action/author_attestation","sign_citation":"https://pith.science/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N/action/citation_signature","submit_replication":"https://pith.science/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N/action/replication_record"}},"created_at":"2026-05-18T03:03:43.642557+00:00","updated_at":"2026-05-18T03:03:43.642557+00:00"}