{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:O34ZDSV5S5J7RBJDSXGYNT273T","short_pith_number":"pith:O34ZDSV5","schema_version":"1.0","canonical_sha256":"76f991cabd9753f8852395cd86cf5fdcf8faae58097e259b2d7fcb86e61d5e65","source":{"kind":"arxiv","id":"2502.06035","version":1},"attestation_state":"computed","paper":{"title":"Geometric flows and space-periodic solitons on the light-cone","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Yun Yang","submitted_at":"2025-02-09T21:18:23Z","abstract_excerpt":"This paper investigates curve flows on the light-cone in the 3-dimensional Minkowski space. We derive the Harnack inequality for the heat flow and present a detailed classification of space-periodic solitons for a third-order curvature flow. The nontrivial periodic solutions to this flow are expressed in terms of the Jacobi elliptic sine function. Additionally, the closed soliton solutions form a family of transcendental curves, denoted by $\\mathrm{x}_{p,q}$, which are characterized by a rotation index $p$ and close after $q$ periods of their curvature functions. The ratio $p/q$ satisfies $p/q"},"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":"2502.06035","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-02-09T21:18:23Z","cross_cats_sorted":[],"title_canon_sha256":"bc9cc548fcc165348604f64bd137b81c7a680ddb8e2c60d89b8980e4a466c319","abstract_canon_sha256":"47b690931df36f03c9eb4ae552a1d5f374bd830ca345996f5415e87fca901b3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:11:46.746142Z","signature_b64":"Rf6cmXcbMCQnbaTfUz05ynZM6tjA5iBLGQn7d0dsqKkNkz6RfH5ocPpKo3qLNafQCEFQv5jc3cw4s40rTjquBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76f991cabd9753f8852395cd86cf5fdcf8faae58097e259b2d7fcb86e61d5e65","last_reissued_at":"2026-07-05T10:11:46.745622Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:11:46.745622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric flows and space-periodic solitons on the light-cone","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Yun Yang","submitted_at":"2025-02-09T21:18:23Z","abstract_excerpt":"This paper investigates curve flows on the light-cone in the 3-dimensional Minkowski space. We derive the Harnack inequality for the heat flow and present a detailed classification of space-periodic solitons for a third-order curvature flow. The nontrivial periodic solutions to this flow are expressed in terms of the Jacobi elliptic sine function. Additionally, the closed soliton solutions form a family of transcendental curves, denoted by $\\mathrm{x}_{p,q}$, which are characterized by a rotation index $p$ and close after $q$ periods of their curvature functions. The ratio $p/q$ satisfies $p/q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06035","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/2502.06035/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":"2502.06035","created_at":"2026-07-05T10:11:46.745679+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.06035v1","created_at":"2026-07-05T10:11:46.745679+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06035","created_at":"2026-07-05T10:11:46.745679+00:00"},{"alias_kind":"pith_short_12","alias_value":"O34ZDSV5S5J7","created_at":"2026-07-05T10:11:46.745679+00:00"},{"alias_kind":"pith_short_16","alias_value":"O34ZDSV5S5J7RBJD","created_at":"2026-07-05T10:11:46.745679+00:00"},{"alias_kind":"pith_short_8","alias_value":"O34ZDSV5","created_at":"2026-07-05T10:11:46.745679+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/O34ZDSV5S5J7RBJDSXGYNT273T","json":"https://pith.science/pith/O34ZDSV5S5J7RBJDSXGYNT273T.json","graph_json":"https://pith.science/api/pith-number/O34ZDSV5S5J7RBJDSXGYNT273T/graph.json","events_json":"https://pith.science/api/pith-number/O34ZDSV5S5J7RBJDSXGYNT273T/events.json","paper":"https://pith.science/paper/O34ZDSV5"},"agent_actions":{"view_html":"https://pith.science/pith/O34ZDSV5S5J7RBJDSXGYNT273T","download_json":"https://pith.science/pith/O34ZDSV5S5J7RBJDSXGYNT273T.json","view_paper":"https://pith.science/paper/O34ZDSV5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.06035&json=true","fetch_graph":"https://pith.science/api/pith-number/O34ZDSV5S5J7RBJDSXGYNT273T/graph.json","fetch_events":"https://pith.science/api/pith-number/O34ZDSV5S5J7RBJDSXGYNT273T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O34ZDSV5S5J7RBJDSXGYNT273T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O34ZDSV5S5J7RBJDSXGYNT273T/action/storage_attestation","attest_author":"https://pith.science/pith/O34ZDSV5S5J7RBJDSXGYNT273T/action/author_attestation","sign_citation":"https://pith.science/pith/O34ZDSV5S5J7RBJDSXGYNT273T/action/citation_signature","submit_replication":"https://pith.science/pith/O34ZDSV5S5J7RBJDSXGYNT273T/action/replication_record"}},"created_at":"2026-07-05T10:11:46.745679+00:00","updated_at":"2026-07-05T10:11:46.745679+00:00"}