{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:V4FOCDB2UOUSLVR5AR6BV2SB5N","short_pith_number":"pith:V4FOCDB2","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"},"canonical_sha256":"af0ae10c3aa3a925d63d047c1aea41eb7912f7ffc0dbc88441181c94cf4fedc7","source":{"kind":"arxiv","id":"1312.7388","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7388","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7388v1","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7388","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"pith_short_12","alias_value":"V4FOCDB2UOUS","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V4FOCDB2UOUSLVR5","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V4FOCDB2","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:V4FOCDB2UOUSLVR5AR6BV2SB5N","target":"record","payload":{"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"},"canonical_sha256":"af0ae10c3aa3a925d63d047c1aea41eb7912f7ffc0dbc88441181c94cf4fedc7","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"},"source_kind":"arxiv","source_id":"1312.7388","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"osCMR4UMNdWC+oE1oH/6fbG21mtVRui/KTMwB7Lxj7Nc3d9mlWsCRx2eiPiAXC25j6HwXujaOZbHyXhYXrV0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:56:17.002549Z"},"content_sha256":"8207cba83ea910656f6617059b87ea8e3d0c3b4b7511f84ae950de22658ee925","schema_version":"1.0","event_id":"sha256:8207cba83ea910656f6617059b87ea8e3d0c3b4b7511f84ae950de22658ee925"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:V4FOCDB2UOUSLVR5AR6BV2SB5N","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oBkwcwlYCwN3K/vyb8+npdWT4pWV0cy4m5f6HdNBKOP4smY4pKo0tzAEELMNvFfBxypR1EetFaIRwlY2oIT0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:56:17.003180Z"},"content_sha256":"e5dd41a23bf8503073da1d98a9cb6654afc18287aa852f68aa1e9097d1ba93a4","schema_version":"1.0","event_id":"sha256:e5dd41a23bf8503073da1d98a9cb6654afc18287aa852f68aa1e9097d1ba93a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N/bundle.json","state_url":"https://pith.science/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T21:56:17Z","links":{"resolver":"https://pith.science/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N","bundle":"https://pith.science/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N/bundle.json","state":"https://pith.science/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4FOCDB2UOUSLVR5AR6BV2SB5N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:V4FOCDB2UOUSLVR5AR6BV2SB5N","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4d8bdf4dc02c483729646f0480659372f11c3f5c5b8d014ea13a0c72fddc0ac3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2013-12-28T04:02:29Z","title_canon_sha256":"9e7a013166bf71497c7e1d1e50a740b42e6d797350ee716b3f7345bfc5250a90"},"schema_version":"1.0","source":{"id":"1312.7388","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7388","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7388v1","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7388","created_at":"2026-05-18T03:03:43Z"},{"alias_kind":"pith_short_12","alias_value":"V4FOCDB2UOUS","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V4FOCDB2UOUSLVR5","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V4FOCDB2","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:e5dd41a23bf8503073da1d98a9cb6654afc18287aa852f68aa1e9097d1ba93a4","target":"graph","created_at":"2026-05-18T03:03:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 ","authors_text":"Doan The Hieu, Tran Le Nam","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2013-12-28T04:02:29Z","title":"The classification of constant weighted curvature curves in the plane with a log-linear density"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7388","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8207cba83ea910656f6617059b87ea8e3d0c3b4b7511f84ae950de22658ee925","target":"record","created_at":"2026-05-18T03:03:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4d8bdf4dc02c483729646f0480659372f11c3f5c5b8d014ea13a0c72fddc0ac3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2013-12-28T04:02:29Z","title_canon_sha256":"9e7a013166bf71497c7e1d1e50a740b42e6d797350ee716b3f7345bfc5250a90"},"schema_version":"1.0","source":{"id":"1312.7388","kind":"arxiv","version":1}},"canonical_sha256":"af0ae10c3aa3a925d63d047c1aea41eb7912f7ffc0dbc88441181c94cf4fedc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af0ae10c3aa3a925d63d047c1aea41eb7912f7ffc0dbc88441181c94cf4fedc7","first_computed_at":"2026-05-18T03:03:43.642474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:43.642474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IBHUk/aH1hr5MOOck0N0uZ5rdb0SXSlyJlR5vxOCX1j0vivJ5Z/muDIzgdtOnjLYKQP50/tZpcTK2jIqh4ztAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:43.642997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7388","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8207cba83ea910656f6617059b87ea8e3d0c3b4b7511f84ae950de22658ee925","sha256:e5dd41a23bf8503073da1d98a9cb6654afc18287aa852f68aa1e9097d1ba93a4"],"state_sha256":"128487882e94a29d9942304b36957df45356049a1ba9551ef388361336bdd8f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OoSG58SScTsi8UyWKYmEXeXBM/jHOOcHSObHfct39/iysTl8Ed7tHqJDuVn5gkSHtGf9FH1ov8jrVbgKnrh5Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T21:56:17.010712Z","bundle_sha256":"18de3c193834d986c360d70d5eb8d8e90ed43a5496fd74c356650da1db0146ba"}}