{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MJCVX6WZLUDGNRVVAMKQKAXWTY","short_pith_number":"pith:MJCVX6WZ","canonical_record":{"source":{"id":"2607.00517","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-01T07:04:04Z","cross_cats_sorted":[],"title_canon_sha256":"f51fbb2ccf36dadf97ac0a5507000a5661e2e9daaf6672fec175eb7a27ecc064","abstract_canon_sha256":"8fd98750e0340176986a2019acfa67591fbfd3f246dca39cc259b0dfc99d49b2"},"schema_version":"1.0"},"canonical_sha256":"62455bfad95d0666c6b503150502f69e0135bb328b7c9670a3575df8517fd77e","source":{"kind":"arxiv","id":"2607.00517","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00517","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00517v1","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00517","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"MJCVX6WZLUDG","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"MJCVX6WZLUDGNRVV","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"MJCVX6WZ","created_at":"2026-07-02T01:17:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MJCVX6WZLUDGNRVVAMKQKAXWTY","target":"record","payload":{"canonical_record":{"source":{"id":"2607.00517","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-01T07:04:04Z","cross_cats_sorted":[],"title_canon_sha256":"f51fbb2ccf36dadf97ac0a5507000a5661e2e9daaf6672fec175eb7a27ecc064","abstract_canon_sha256":"8fd98750e0340176986a2019acfa67591fbfd3f246dca39cc259b0dfc99d49b2"},"schema_version":"1.0"},"canonical_sha256":"62455bfad95d0666c6b503150502f69e0135bb328b7c9670a3575df8517fd77e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:17:46.446845Z","signature_b64":"TWRVq+RESZEczcB7zoaasEaafSfj0z/9aWPdKHN7+4GaNH9QHOKlsawisI/PG40zPVD3zyIz6yQECyfeQJlDDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62455bfad95d0666c6b503150502f69e0135bb328b7c9670a3575df8517fd77e","last_reissued_at":"2026-07-02T01:17:46.446468Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:17:46.446468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.00517","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":"2026-07-02T01:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eVye141AFzXBlXBi/4ekML2HQGErBUeHpMV5HHNZdJia1BTwKKLN16mQZVV9MfIt122Lcb0oDdMHefS4d0jpCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T21:11:58.771230Z"},"content_sha256":"d5e29fbe46e8f3783f9af0a041e3b4ee665a03091e815083a2f23f0eb572d694","schema_version":"1.0","event_id":"sha256:d5e29fbe46e8f3783f9af0a041e3b4ee665a03091e815083a2f23f0eb572d694"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MJCVX6WZLUDGNRVVAMKQKAXWTY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Minimax Approach to Relative Periodic Orbits in Symmetric Three-Degree-of-Freedom Hamiltonian Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mitsuru Shibayama, Shu Sakaguchi","submitted_at":"2026-07-01T07:04:04Z","abstract_excerpt":"We study three-degree-of-freedom Hamiltonian systems that are invariant under rotations about the $z$-axis and under reflection across the $xy$-plane. Fixing the angular momentum, such systems reduce to Hamiltonian systems with two degrees of freedom. We focus on the range of energy values for which the corresponding Hill regions are compact. First, under suitable assumptions on the topology of these compact Hill regions, we prove the existence of periodic solutions on each prescribed energy surface of the reduced system by means of a variational minimax method. These periodic solutions are ob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00517","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/2607.00517/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":"2026-07-02T01:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VByvjfAdoUcl9qT6hqGaFzwjeoZym8yvsj7o+dz75cKdKyTS/gkVIq5IJAo0iYEuxv8yiuHLdHM6OQKFF1SxAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T21:11:58.771633Z"},"content_sha256":"9f9bded9ee3adfc8697704579388a60de2b1f0fe505a04d09913fc8bf8fcf114","schema_version":"1.0","event_id":"sha256:9f9bded9ee3adfc8697704579388a60de2b1f0fe505a04d09913fc8bf8fcf114"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MJCVX6WZLUDGNRVVAMKQKAXWTY/bundle.json","state_url":"https://pith.science/pith/MJCVX6WZLUDGNRVVAMKQKAXWTY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MJCVX6WZLUDGNRVVAMKQKAXWTY/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":"2026-07-12T21:11:58Z","links":{"resolver":"https://pith.science/pith/MJCVX6WZLUDGNRVVAMKQKAXWTY","bundle":"https://pith.science/pith/MJCVX6WZLUDGNRVVAMKQKAXWTY/bundle.json","state":"https://pith.science/pith/MJCVX6WZLUDGNRVVAMKQKAXWTY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MJCVX6WZLUDGNRVVAMKQKAXWTY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MJCVX6WZLUDGNRVVAMKQKAXWTY","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":"8fd98750e0340176986a2019acfa67591fbfd3f246dca39cc259b0dfc99d49b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-01T07:04:04Z","title_canon_sha256":"f51fbb2ccf36dadf97ac0a5507000a5661e2e9daaf6672fec175eb7a27ecc064"},"schema_version":"1.0","source":{"id":"2607.00517","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00517","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00517v1","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00517","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"MJCVX6WZLUDG","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"MJCVX6WZLUDGNRVV","created_at":"2026-07-02T01:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"MJCVX6WZ","created_at":"2026-07-02T01:17:46Z"}],"graph_snapshots":[{"event_id":"sha256:9f9bded9ee3adfc8697704579388a60de2b1f0fe505a04d09913fc8bf8fcf114","target":"graph","created_at":"2026-07-02T01:17:46Z","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/2607.00517/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study three-degree-of-freedom Hamiltonian systems that are invariant under rotations about the $z$-axis and under reflection across the $xy$-plane. Fixing the angular momentum, such systems reduce to Hamiltonian systems with two degrees of freedom. We focus on the range of energy values for which the corresponding Hill regions are compact. First, under suitable assumptions on the topology of these compact Hill regions, we prove the existence of periodic solutions on each prescribed energy surface of the reduced system by means of a variational minimax method. These periodic solutions are ob","authors_text":"Mitsuru Shibayama, Shu Sakaguchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-01T07:04:04Z","title":"A Minimax Approach to Relative Periodic Orbits in Symmetric Three-Degree-of-Freedom Hamiltonian Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00517","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:d5e29fbe46e8f3783f9af0a041e3b4ee665a03091e815083a2f23f0eb572d694","target":"record","created_at":"2026-07-02T01:17:46Z","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":"8fd98750e0340176986a2019acfa67591fbfd3f246dca39cc259b0dfc99d49b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-01T07:04:04Z","title_canon_sha256":"f51fbb2ccf36dadf97ac0a5507000a5661e2e9daaf6672fec175eb7a27ecc064"},"schema_version":"1.0","source":{"id":"2607.00517","kind":"arxiv","version":1}},"canonical_sha256":"62455bfad95d0666c6b503150502f69e0135bb328b7c9670a3575df8517fd77e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62455bfad95d0666c6b503150502f69e0135bb328b7c9670a3575df8517fd77e","first_computed_at":"2026-07-02T01:17:46.446468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:17:46.446468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TWRVq+RESZEczcB7zoaasEaafSfj0z/9aWPdKHN7+4GaNH9QHOKlsawisI/PG40zPVD3zyIz6yQECyfeQJlDDA==","signature_status":"signed_v1","signed_at":"2026-07-02T01:17:46.446845Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00517","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5e29fbe46e8f3783f9af0a041e3b4ee665a03091e815083a2f23f0eb572d694","sha256:9f9bded9ee3adfc8697704579388a60de2b1f0fe505a04d09913fc8bf8fcf114"],"state_sha256":"a036cb0b3d3f4c2fddfe621119c87e133392bad6dde40e0307b8e6bf8e9579d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xQHA8RNtOU5Zg4GJZkk8xfkBWjUnKa6Ql6sDB97Fktcv4E/uwBAjnO/cVdN13Mg1RQacwCQSqCPCarDzxjE4Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-12T21:11:58.773833Z","bundle_sha256":"4b949a9daa288f8da8088b6e27e5e99afab5d39c802434389993b4e4fe66b7ea"}}