{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:CFYV4D36RAXFYFD7A5RPJOUUHA","short_pith_number":"pith:CFYV4D36","canonical_record":{"source":{"id":"1008.1852","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-08-11T08:01:22Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"74bedcf5da024ad3a54b8ceeca4ac13a8cd3420927e06e7f2320699260cb7d8d","abstract_canon_sha256":"88dff28d4579de0e19a52a3c25bb9719c303ef2a0c24c2bbad24f827888f262d"},"schema_version":"1.0"},"canonical_sha256":"11715e0f7e882e5c147f0762f4ba94383f4f6987fb32cd541f1c73a0d9838ee0","source":{"kind":"arxiv","id":"1008.1852","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1852","created_at":"2026-05-18T03:18:06Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1852v2","created_at":"2026-05-18T03:18:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1852","created_at":"2026-05-18T03:18:06Z"},{"alias_kind":"pith_short_12","alias_value":"CFYV4D36RAXF","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"CFYV4D36RAXFYFD7","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"CFYV4D36","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:CFYV4D36RAXFYFD7A5RPJOUUHA","target":"record","payload":{"canonical_record":{"source":{"id":"1008.1852","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-08-11T08:01:22Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"74bedcf5da024ad3a54b8ceeca4ac13a8cd3420927e06e7f2320699260cb7d8d","abstract_canon_sha256":"88dff28d4579de0e19a52a3c25bb9719c303ef2a0c24c2bbad24f827888f262d"},"schema_version":"1.0"},"canonical_sha256":"11715e0f7e882e5c147f0762f4ba94383f4f6987fb32cd541f1c73a0d9838ee0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:06.575962Z","signature_b64":"LkS2D2lSqUUmIcrcNt8vsTrcVXEoyRrGNENPtUQVU028HiynX9V7FblM+VRm6pM1aRE+7XP9d9Mmwgn8C3q8BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11715e0f7e882e5c147f0762f4ba94383f4f6987fb32cd541f1c73a0d9838ee0","last_reissued_at":"2026-05-18T03:18:06.575285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:06.575285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.1852","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":"2026-05-18T03:18:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3yCS64W4VpAhb1EQmQmoN33g3qaXQJRsKzohK3CYzIWHyKry2omg1uF2BAPP4FTaU8nnlpoVi87e2e1d0OCTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:51:04.033377Z"},"content_sha256":"0dd741d2718b3b19ca87ff48566688b6df4bf070bc89cef3e77b2cea1e9db22a","schema_version":"1.0","event_id":"sha256:0dd741d2718b3b19ca87ff48566688b6df4bf070bc89cef3e77b2cea1e9db22a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:CFYV4D36RAXFYFD7A5RPJOUUHA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Handle attaching in wrapped Floer homology and brake orbits in classical Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Kei Irie","submitted_at":"2010-08-11T08:01:22Z","abstract_excerpt":"The objective of this note is to prove an existence result for brake orbits in classical Hamiltonian systems (which was first proved by S.V.Bolotin) by using Floer theory. To this end, we compute an open string analogue of symplectic homology (so called wrapped Floer homology) of some domains in cotangent bundles, which appear naturally in the study of classical Hamiltonian systems. The main part of the computations is to show invariance of wrapped Floer homology under certain handle attaching to domains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1852","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":""},"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":"2026-05-18T03:18:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L3B7EChZ6nZrC1DUiuoH1aWSw6SMf/Ma4otESei+LLL31wprY9jXbu2oG0VA4rKDUlnxv37maMwUe4mHj/weDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:51:04.033715Z"},"content_sha256":"1234c2d718fb282e3e84c0ca98810dc3908dbc62aa27d82060422a0f460450fd","schema_version":"1.0","event_id":"sha256:1234c2d718fb282e3e84c0ca98810dc3908dbc62aa27d82060422a0f460450fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFYV4D36RAXFYFD7A5RPJOUUHA/bundle.json","state_url":"https://pith.science/pith/CFYV4D36RAXFYFD7A5RPJOUUHA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFYV4D36RAXFYFD7A5RPJOUUHA/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":"2026-06-27T15:51:04Z","links":{"resolver":"https://pith.science/pith/CFYV4D36RAXFYFD7A5RPJOUUHA","bundle":"https://pith.science/pith/CFYV4D36RAXFYFD7A5RPJOUUHA/bundle.json","state":"https://pith.science/pith/CFYV4D36RAXFYFD7A5RPJOUUHA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFYV4D36RAXFYFD7A5RPJOUUHA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CFYV4D36RAXFYFD7A5RPJOUUHA","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":"88dff28d4579de0e19a52a3c25bb9719c303ef2a0c24c2bbad24f827888f262d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-08-11T08:01:22Z","title_canon_sha256":"74bedcf5da024ad3a54b8ceeca4ac13a8cd3420927e06e7f2320699260cb7d8d"},"schema_version":"1.0","source":{"id":"1008.1852","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1852","created_at":"2026-05-18T03:18:06Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1852v2","created_at":"2026-05-18T03:18:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1852","created_at":"2026-05-18T03:18:06Z"},{"alias_kind":"pith_short_12","alias_value":"CFYV4D36RAXF","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"CFYV4D36RAXFYFD7","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"CFYV4D36","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:1234c2d718fb282e3e84c0ca98810dc3908dbc62aa27d82060422a0f460450fd","target":"graph","created_at":"2026-05-18T03:18:06Z","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":"The objective of this note is to prove an existence result for brake orbits in classical Hamiltonian systems (which was first proved by S.V.Bolotin) by using Floer theory. To this end, we compute an open string analogue of symplectic homology (so called wrapped Floer homology) of some domains in cotangent bundles, which appear naturally in the study of classical Hamiltonian systems. The main part of the computations is to show invariance of wrapped Floer homology under certain handle attaching to domains.","authors_text":"Kei Irie","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-08-11T08:01:22Z","title":"Handle attaching in wrapped Floer homology and brake orbits in classical Hamiltonian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1852","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":"sha256:0dd741d2718b3b19ca87ff48566688b6df4bf070bc89cef3e77b2cea1e9db22a","target":"record","created_at":"2026-05-18T03:18:06Z","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":"88dff28d4579de0e19a52a3c25bb9719c303ef2a0c24c2bbad24f827888f262d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-08-11T08:01:22Z","title_canon_sha256":"74bedcf5da024ad3a54b8ceeca4ac13a8cd3420927e06e7f2320699260cb7d8d"},"schema_version":"1.0","source":{"id":"1008.1852","kind":"arxiv","version":2}},"canonical_sha256":"11715e0f7e882e5c147f0762f4ba94383f4f6987fb32cd541f1c73a0d9838ee0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11715e0f7e882e5c147f0762f4ba94383f4f6987fb32cd541f1c73a0d9838ee0","first_computed_at":"2026-05-18T03:18:06.575285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:06.575285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LkS2D2lSqUUmIcrcNt8vsTrcVXEoyRrGNENPtUQVU028HiynX9V7FblM+VRm6pM1aRE+7XP9d9Mmwgn8C3q8BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:06.575962Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1852","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dd741d2718b3b19ca87ff48566688b6df4bf070bc89cef3e77b2cea1e9db22a","sha256:1234c2d718fb282e3e84c0ca98810dc3908dbc62aa27d82060422a0f460450fd"],"state_sha256":"4089bac556eb307ea0f5e7d6ed3c9c6f258b700ddd035527acc7dc7f24c525dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OhQNSssEkUTTVtlBTY45T2HKZsu3iJLxcDc3e4N5jChne/IfMYgFDeLmjYypCYJWpZpvgYbCj+ckZNcyakcLDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T15:51:04.035486Z","bundle_sha256":"4be24148b2a3d2a0edb6e5492260976e6f4f3770d0cc4211fa5eac29084ee6ed"}}