{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QL2CL4SKIOPMKWHOJOGTYBHUSW","short_pith_number":"pith:QL2CL4SK","canonical_record":{"source":{"id":"1411.6848","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2014-11-25T13:03:01Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"dd260ee0cda32bcd25fc305f04e0e561b041de90d4c71c646ebdca329e3867ce","abstract_canon_sha256":"f5b37a978a0e70d0ebac54548181ef712d6199abe72da6bf719ea74e6cd7d241"},"schema_version":"1.0"},"canonical_sha256":"82f425f24a439ec558ee4b8d3c04f495babbf763df138a8fc9d75fe5679a4f83","source":{"kind":"arxiv","id":"1411.6848","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6848","created_at":"2026-05-18T00:21:43Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6848v1","created_at":"2026-05-18T00:21:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6848","created_at":"2026-05-18T00:21:43Z"},{"alias_kind":"pith_short_12","alias_value":"QL2CL4SKIOPM","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QL2CL4SKIOPMKWHO","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QL2CL4SK","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QL2CL4SKIOPMKWHOJOGTYBHUSW","target":"record","payload":{"canonical_record":{"source":{"id":"1411.6848","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2014-11-25T13:03:01Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"dd260ee0cda32bcd25fc305f04e0e561b041de90d4c71c646ebdca329e3867ce","abstract_canon_sha256":"f5b37a978a0e70d0ebac54548181ef712d6199abe72da6bf719ea74e6cd7d241"},"schema_version":"1.0"},"canonical_sha256":"82f425f24a439ec558ee4b8d3c04f495babbf763df138a8fc9d75fe5679a4f83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:43.852212Z","signature_b64":"VRMlQSpovYCFms+BaQb5OjGOz2JFCT5/pBimWi9DeMKSThanUzlK4fml2D/3GrOhLyDUJn/LwJLxyMycvybsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82f425f24a439ec558ee4b8d3c04f495babbf763df138a8fc9d75fe5679a4f83","last_reissued_at":"2026-05-18T00:21:43.851607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:43.851607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.6848","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":"2026-05-18T00:21:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M5sv/7FVlRybD1nJtpTF4bpqf2M+VMLg/gSa3x/nalhnZbmwEVKOpgg1+j6hfsQkNRTYfMOwCIP39UyS9b2bCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:06:27.540202Z"},"content_sha256":"2da4312dd9dcedb9a3627c2b46eb975ec5051d49be8b550326377df62ccecc54","schema_version":"1.0","event_id":"sha256:2da4312dd9dcedb9a3627c2b46eb975ec5051d49be8b550326377df62ccecc54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QL2CL4SKIOPMKWHOJOGTYBHUSW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Magnetic Geodesics via the Heat Flow","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.DG","authors_text":"Florian Hanisch, Volker Branding","submitted_at":"2014-11-25T13:03:01Z","abstract_excerpt":"Magnetic geodesics describe the trajectory of a particle in a Riemannian manifold under the influence of an external magnetic field. In this article, we use the heat flow method to derive existence results for such curves. We first establish subconvergence of this flow to a magnetic geodesic under certain boundedness assumptions. It is then shown that these conditions are satisfied provided that either the magnetic field admits a global potential or the initial curve is sufficiently small. Finally, we discuss different examples which illustrate our results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6848","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":"2026-05-18T00:21:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e/240QOt4h5OV/YU4MWrpFNa+jdg1+ly1lNDHrACNQJqzbRKTBDEwOyQzfEnrVUxkN4rNFQ7dAwUc/2wqgnXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:06:27.540559Z"},"content_sha256":"1eafe46bff3b8aba8061af109eec2a846659c4e21e4c7803c28486b8e8ec4d17","schema_version":"1.0","event_id":"sha256:1eafe46bff3b8aba8061af109eec2a846659c4e21e4c7803c28486b8e8ec4d17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QL2CL4SKIOPMKWHOJOGTYBHUSW/bundle.json","state_url":"https://pith.science/pith/QL2CL4SKIOPMKWHOJOGTYBHUSW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QL2CL4SKIOPMKWHOJOGTYBHUSW/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":"2026-06-23T14:06:27Z","links":{"resolver":"https://pith.science/pith/QL2CL4SKIOPMKWHOJOGTYBHUSW","bundle":"https://pith.science/pith/QL2CL4SKIOPMKWHOJOGTYBHUSW/bundle.json","state":"https://pith.science/pith/QL2CL4SKIOPMKWHOJOGTYBHUSW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QL2CL4SKIOPMKWHOJOGTYBHUSW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QL2CL4SKIOPMKWHOJOGTYBHUSW","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":"f5b37a978a0e70d0ebac54548181ef712d6199abe72da6bf719ea74e6cd7d241","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2014-11-25T13:03:01Z","title_canon_sha256":"dd260ee0cda32bcd25fc305f04e0e561b041de90d4c71c646ebdca329e3867ce"},"schema_version":"1.0","source":{"id":"1411.6848","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6848","created_at":"2026-05-18T00:21:43Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6848v1","created_at":"2026-05-18T00:21:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6848","created_at":"2026-05-18T00:21:43Z"},{"alias_kind":"pith_short_12","alias_value":"QL2CL4SKIOPM","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QL2CL4SKIOPMKWHO","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QL2CL4SK","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:1eafe46bff3b8aba8061af109eec2a846659c4e21e4c7803c28486b8e8ec4d17","target":"graph","created_at":"2026-05-18T00:21:43Z","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":"Magnetic geodesics describe the trajectory of a particle in a Riemannian manifold under the influence of an external magnetic field. In this article, we use the heat flow method to derive existence results for such curves. We first establish subconvergence of this flow to a magnetic geodesic under certain boundedness assumptions. It is then shown that these conditions are satisfied provided that either the magnetic field admits a global potential or the initial curve is sufficiently small. Finally, we discuss different examples which illustrate our results.","authors_text":"Florian Hanisch, Volker Branding","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2014-11-25T13:03:01Z","title":"Magnetic Geodesics via the Heat Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6848","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":"sha256:2da4312dd9dcedb9a3627c2b46eb975ec5051d49be8b550326377df62ccecc54","target":"record","created_at":"2026-05-18T00:21:43Z","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":"f5b37a978a0e70d0ebac54548181ef712d6199abe72da6bf719ea74e6cd7d241","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2014-11-25T13:03:01Z","title_canon_sha256":"dd260ee0cda32bcd25fc305f04e0e561b041de90d4c71c646ebdca329e3867ce"},"schema_version":"1.0","source":{"id":"1411.6848","kind":"arxiv","version":1}},"canonical_sha256":"82f425f24a439ec558ee4b8d3c04f495babbf763df138a8fc9d75fe5679a4f83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82f425f24a439ec558ee4b8d3c04f495babbf763df138a8fc9d75fe5679a4f83","first_computed_at":"2026-05-18T00:21:43.851607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:43.851607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VRMlQSpovYCFms+BaQb5OjGOz2JFCT5/pBimWi9DeMKSThanUzlK4fml2D/3GrOhLyDUJn/LwJLxyMycvybsBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:43.852212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6848","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2da4312dd9dcedb9a3627c2b46eb975ec5051d49be8b550326377df62ccecc54","sha256:1eafe46bff3b8aba8061af109eec2a846659c4e21e4c7803c28486b8e8ec4d17"],"state_sha256":"609993ca57369c40c87f2bf5b8cbd10993d82be78cd3c7222c597513df81c70c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b4OsAI7nhjPeEd9kZXzcDQ6xxO8HeQXDsGUX1s05gDv/6hKrrXqhIlk5N56odPOGG+0uLVmK/FoxoRvgqKllBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:06:27.542506Z","bundle_sha256":"7e4f79eb8d60d26ed953888d6a4120a3931dc4f6a8b8e39b204a3d00d9c11bd8"}}