{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:2GIG762RPTST6AXVHAAHQNTKQC","short_pith_number":"pith:2GIG762R","canonical_record":{"source":{"id":"1110.2244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-10-11T01:15:17Z","cross_cats_sorted":[],"title_canon_sha256":"e0053ea28aecf67647204bc62d7d799a327ab1605ba111e4bfa15b052637c522","abstract_canon_sha256":"8dc1b55519f5a63a61bb077b00fcda46a506f0beaad6b21ef47d689bde5126ec"},"schema_version":"1.0"},"canonical_sha256":"d1906ffb517ce53f02f5380078366a80b35b0bcacef405cb78d334d719b0e042","source":{"kind":"arxiv","id":"1110.2244","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2244","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2244v1","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2244","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"2GIG762RPTST","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2GIG762RPTST6AXV","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2GIG762R","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:2GIG762RPTST6AXVHAAHQNTKQC","target":"record","payload":{"canonical_record":{"source":{"id":"1110.2244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-10-11T01:15:17Z","cross_cats_sorted":[],"title_canon_sha256":"e0053ea28aecf67647204bc62d7d799a327ab1605ba111e4bfa15b052637c522","abstract_canon_sha256":"8dc1b55519f5a63a61bb077b00fcda46a506f0beaad6b21ef47d689bde5126ec"},"schema_version":"1.0"},"canonical_sha256":"d1906ffb517ce53f02f5380078366a80b35b0bcacef405cb78d334d719b0e042","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:17.250658Z","signature_b64":"Bm/dj7qKWLR90JAt8xfejNprW46uTDEo2FojcP15PqiskbB1e3XIj2CLPaaUityvFwSsm5TtDhl6DcE+pdpHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1906ffb517ce53f02f5380078366a80b35b0bcacef405cb78d334d719b0e042","last_reissued_at":"2026-05-18T04:11:17.250089Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:17.250089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.2244","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":"2026-05-18T04:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kTfflvUBQ8f0WFAMzFiSwGyHLQqQ1UPWc0wjctnONRC2be5sAjXVZVr7/aXWWzatiptJLqO3ngvljAXsqM3LAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:13:10.592867Z"},"content_sha256":"01e9914eebb6ac861490349cf4c4c6cf7c621d5c71a9a9723b23fed65c3af1a2","schema_version":"1.0","event_id":"sha256:01e9914eebb6ac861490349cf4c4c6cf7c621d5c71a9a9723b23fed65c3af1a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:2GIG762RPTST6AXVHAAHQNTKQC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hofer-Zehnder capacity of unit disk cotangent bundles and the loop product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Kei Irie","submitted_at":"2011-10-11T01:15:17Z","abstract_excerpt":"We prove the finiteness of the Hofer-Zehnder capacity of unit disk cotangent bundles of closed Riemannian manifolds, under some simple topological assumptions on the manifolds. The key ingredient of the proof is a computation of the pair-of-pants product on Floer homology of cotangent bundles. We reduce it to a simple computation of the loop product, making use of results of A.Abbondandolo- M.Schwarz."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2244","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":"2026-05-18T04:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rI5KRYn4R0sCw7P77tyLaOhU7o9PbUBn7QQbDqxikPd1w+2Bxu4O3uu58bf2U2Sci3MTByAxsv1yAN5iWhdlCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:13:10.593204Z"},"content_sha256":"b6f12af9598ac2d00e7959016221465f725a544c263405b15db74b0bec10f05c","schema_version":"1.0","event_id":"sha256:b6f12af9598ac2d00e7959016221465f725a544c263405b15db74b0bec10f05c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2GIG762RPTST6AXVHAAHQNTKQC/bundle.json","state_url":"https://pith.science/pith/2GIG762RPTST6AXVHAAHQNTKQC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2GIG762RPTST6AXVHAAHQNTKQC/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":"2026-06-27T16:13:10Z","links":{"resolver":"https://pith.science/pith/2GIG762RPTST6AXVHAAHQNTKQC","bundle":"https://pith.science/pith/2GIG762RPTST6AXVHAAHQNTKQC/bundle.json","state":"https://pith.science/pith/2GIG762RPTST6AXVHAAHQNTKQC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2GIG762RPTST6AXVHAAHQNTKQC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2GIG762RPTST6AXVHAAHQNTKQC","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":"8dc1b55519f5a63a61bb077b00fcda46a506f0beaad6b21ef47d689bde5126ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-10-11T01:15:17Z","title_canon_sha256":"e0053ea28aecf67647204bc62d7d799a327ab1605ba111e4bfa15b052637c522"},"schema_version":"1.0","source":{"id":"1110.2244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2244","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2244v1","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2244","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"2GIG762RPTST","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2GIG762RPTST6AXV","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2GIG762R","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:b6f12af9598ac2d00e7959016221465f725a544c263405b15db74b0bec10f05c","target":"graph","created_at":"2026-05-18T04:11:17Z","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":"We prove the finiteness of the Hofer-Zehnder capacity of unit disk cotangent bundles of closed Riemannian manifolds, under some simple topological assumptions on the manifolds. The key ingredient of the proof is a computation of the pair-of-pants product on Floer homology of cotangent bundles. We reduce it to a simple computation of the loop product, making use of results of A.Abbondandolo- M.Schwarz.","authors_text":"Kei Irie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-10-11T01:15:17Z","title":"Hofer-Zehnder capacity of unit disk cotangent bundles and the loop product"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2244","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":"sha256:01e9914eebb6ac861490349cf4c4c6cf7c621d5c71a9a9723b23fed65c3af1a2","target":"record","created_at":"2026-05-18T04:11:17Z","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":"8dc1b55519f5a63a61bb077b00fcda46a506f0beaad6b21ef47d689bde5126ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-10-11T01:15:17Z","title_canon_sha256":"e0053ea28aecf67647204bc62d7d799a327ab1605ba111e4bfa15b052637c522"},"schema_version":"1.0","source":{"id":"1110.2244","kind":"arxiv","version":1}},"canonical_sha256":"d1906ffb517ce53f02f5380078366a80b35b0bcacef405cb78d334d719b0e042","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1906ffb517ce53f02f5380078366a80b35b0bcacef405cb78d334d719b0e042","first_computed_at":"2026-05-18T04:11:17.250089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:17.250089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bm/dj7qKWLR90JAt8xfejNprW46uTDEo2FojcP15PqiskbB1e3XIj2CLPaaUityvFwSsm5TtDhl6DcE+pdpHCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:17.250658Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01e9914eebb6ac861490349cf4c4c6cf7c621d5c71a9a9723b23fed65c3af1a2","sha256:b6f12af9598ac2d00e7959016221465f725a544c263405b15db74b0bec10f05c"],"state_sha256":"095ba656cd6e0d4e1b81535f191459206b388b2ddb110e5c8220b7f7feb039de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"264JfGdar/3rr+xfIzncckPZgb7ZsQWdctj5Fpuvoie7GWPCBuuURgmgpY+QONgQD0J14Ffm+4h12xFAglVEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:13:10.595023Z","bundle_sha256":"5f155487c35e8d1e23d19acedf79b2489ad4fa00c86bf38e35653ba683d6b065"}}