{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:AUJSTMJPIH5SVX7LSQDZTAY7BC","short_pith_number":"pith:AUJSTMJP","canonical_record":{"source":{"id":"2407.05515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-07T23:24:55Z","cross_cats_sorted":[],"title_canon_sha256":"90b5dba834d5ab50ff751a1e18a26b9e8d517d29f75a00c340bd3e5e601f2cd5","abstract_canon_sha256":"53d6e0ab8983f6436d1a3e0e9526a4dba3fbbf112af1e8ad50d8e6d2929dc6b9"},"schema_version":"1.0"},"canonical_sha256":"051329b12f41fb2adfeb940799831f089a090a624896553b58e16dfcb0ef4d05","source":{"kind":"arxiv","id":"2407.05515","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.05515","created_at":"2026-05-21T01:04:11Z"},{"alias_kind":"arxiv_version","alias_value":"2407.05515v2","created_at":"2026-05-21T01:04:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.05515","created_at":"2026-05-21T01:04:11Z"},{"alias_kind":"pith_short_12","alias_value":"AUJSTMJPIH5S","created_at":"2026-05-21T01:04:11Z"},{"alias_kind":"pith_short_16","alias_value":"AUJSTMJPIH5SVX7L","created_at":"2026-05-21T01:04:11Z"},{"alias_kind":"pith_short_8","alias_value":"AUJSTMJP","created_at":"2026-05-21T01:04:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:AUJSTMJPIH5SVX7LSQDZTAY7BC","target":"record","payload":{"canonical_record":{"source":{"id":"2407.05515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-07T23:24:55Z","cross_cats_sorted":[],"title_canon_sha256":"90b5dba834d5ab50ff751a1e18a26b9e8d517d29f75a00c340bd3e5e601f2cd5","abstract_canon_sha256":"53d6e0ab8983f6436d1a3e0e9526a4dba3fbbf112af1e8ad50d8e6d2929dc6b9"},"schema_version":"1.0"},"canonical_sha256":"051329b12f41fb2adfeb940799831f089a090a624896553b58e16dfcb0ef4d05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:11.715368Z","signature_b64":"GkuRa0Kk36Y9EsXC8/cZPz8EBYSNATeRaNqpZQY1OVkjDUOgCsH/M+N4cSaa2ftiHyYN5ZMfIA5A1cQjeWiLAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"051329b12f41fb2adfeb940799831f089a090a624896553b58e16dfcb0ef4d05","last_reissued_at":"2026-05-21T01:04:11.714768Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:11.714768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.05515","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:04:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oeO1dUWSrgQiIwCeZfRDPG858AS95557cnO50PcaUqlGeWqudk6gVUPYIfDzoRTWDBbK4V2W+3LEwRamqhe6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:55:37.688704Z"},"content_sha256":"886dd1bcee2d6f2f08ca1051fe1b7eab63bf5ae3f580416968029887a326d501","schema_version":"1.0","event_id":"sha256:886dd1bcee2d6f2f08ca1051fe1b7eab63bf5ae3f580416968029887a326d501"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:AUJSTMJPIH5SVX7LSQDZTAY7BC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Closed Magnetic geodesics on Heisenberg nilmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gabriela P. Ovando, Mauro Subils","submitted_at":"2024-07-07T23:24:55Z","abstract_excerpt":"In this work we study the existence of closed magnetic geodesics on three-dimensional Heisenberg nilmanifolds for every left-invariant Lorentz force. Our first objective is to establish the existence of closed contractible magnetic geodesics on $H_3$. Once the invariant magnetic field is induced to a compact quotient $M=\\Lambda \\backslash H_3$, we study magnetic geodesics on $M$. Firstly, we determine conditions on a lattice $\\Lambda \\subset H_3$ to ensure that a given magnetic geodesic projects to a closed curve on $M$. In particular, we prove that for {\\it any} energy level below the Ma\\~n\\'"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.05515","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.05515/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:04:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/29WVmoEmedBRwOzEA6vI18DK1l1IVLCxbsErUaU5IY3vHcttaC1KSzPiM+VW5E157NmNUbNqJc8Wmf96GPzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:55:37.689118Z"},"content_sha256":"8abdb06849202922d16e81375d041e1967449e658e8078bbea9cd742c5a255a5","schema_version":"1.0","event_id":"sha256:8abdb06849202922d16e81375d041e1967449e658e8078bbea9cd742c5a255a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AUJSTMJPIH5SVX7LSQDZTAY7BC/bundle.json","state_url":"https://pith.science/pith/AUJSTMJPIH5SVX7LSQDZTAY7BC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AUJSTMJPIH5SVX7LSQDZTAY7BC/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":"2026-06-09T09:55:37Z","links":{"resolver":"https://pith.science/pith/AUJSTMJPIH5SVX7LSQDZTAY7BC","bundle":"https://pith.science/pith/AUJSTMJPIH5SVX7LSQDZTAY7BC/bundle.json","state":"https://pith.science/pith/AUJSTMJPIH5SVX7LSQDZTAY7BC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AUJSTMJPIH5SVX7LSQDZTAY7BC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AUJSTMJPIH5SVX7LSQDZTAY7BC","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":"53d6e0ab8983f6436d1a3e0e9526a4dba3fbbf112af1e8ad50d8e6d2929dc6b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-07T23:24:55Z","title_canon_sha256":"90b5dba834d5ab50ff751a1e18a26b9e8d517d29f75a00c340bd3e5e601f2cd5"},"schema_version":"1.0","source":{"id":"2407.05515","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.05515","created_at":"2026-05-21T01:04:11Z"},{"alias_kind":"arxiv_version","alias_value":"2407.05515v2","created_at":"2026-05-21T01:04:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.05515","created_at":"2026-05-21T01:04:11Z"},{"alias_kind":"pith_short_12","alias_value":"AUJSTMJPIH5S","created_at":"2026-05-21T01:04:11Z"},{"alias_kind":"pith_short_16","alias_value":"AUJSTMJPIH5SVX7L","created_at":"2026-05-21T01:04:11Z"},{"alias_kind":"pith_short_8","alias_value":"AUJSTMJP","created_at":"2026-05-21T01:04:11Z"}],"graph_snapshots":[{"event_id":"sha256:8abdb06849202922d16e81375d041e1967449e658e8078bbea9cd742c5a255a5","target":"graph","created_at":"2026-05-21T01:04:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2407.05515/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we study the existence of closed magnetic geodesics on three-dimensional Heisenberg nilmanifolds for every left-invariant Lorentz force. Our first objective is to establish the existence of closed contractible magnetic geodesics on $H_3$. Once the invariant magnetic field is induced to a compact quotient $M=\\Lambda \\backslash H_3$, we study magnetic geodesics on $M$. Firstly, we determine conditions on a lattice $\\Lambda \\subset H_3$ to ensure that a given magnetic geodesic projects to a closed curve on $M$. In particular, we prove that for {\\it any} energy level below the Ma\\~n\\'","authors_text":"Gabriela P. Ovando, Mauro Subils","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-07T23:24:55Z","title":"Closed Magnetic geodesics on Heisenberg nilmanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.05515","kind":"arxiv","version":2},"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":"sha256:886dd1bcee2d6f2f08ca1051fe1b7eab63bf5ae3f580416968029887a326d501","target":"record","created_at":"2026-05-21T01:04:11Z","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":"53d6e0ab8983f6436d1a3e0e9526a4dba3fbbf112af1e8ad50d8e6d2929dc6b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-07T23:24:55Z","title_canon_sha256":"90b5dba834d5ab50ff751a1e18a26b9e8d517d29f75a00c340bd3e5e601f2cd5"},"schema_version":"1.0","source":{"id":"2407.05515","kind":"arxiv","version":2}},"canonical_sha256":"051329b12f41fb2adfeb940799831f089a090a624896553b58e16dfcb0ef4d05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"051329b12f41fb2adfeb940799831f089a090a624896553b58e16dfcb0ef4d05","first_computed_at":"2026-05-21T01:04:11.714768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:11.714768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GkuRa0Kk36Y9EsXC8/cZPz8EBYSNATeRaNqpZQY1OVkjDUOgCsH/M+N4cSaa2ftiHyYN5ZMfIA5A1cQjeWiLAg==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:11.715368Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.05515","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:886dd1bcee2d6f2f08ca1051fe1b7eab63bf5ae3f580416968029887a326d501","sha256:8abdb06849202922d16e81375d041e1967449e658e8078bbea9cd742c5a255a5"],"state_sha256":"0122ef0aee7a1edc8f7c79fdd93e83f40725e2d905303302cd0a91577d330a11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LHJf/yucoNLH36FsNd+nrjBA651jlY1F1VD6MWSFY0bbvgqPb/4VaO34jwF72sgJF3PHPScJKkWYe0jHbhNFDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:55:37.691097Z","bundle_sha256":"c47ff0b85ddedfefbd36e659fcb3779463bb66374771f88a3efc6b20fb7db879"}}