{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3WYQMHDQ7RK4JGVNWDEDUQ65JT","short_pith_number":"pith:3WYQMHDQ","canonical_record":{"source":{"id":"1006.4383","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-06-22T21:37:15Z","cross_cats_sorted":["math.AG","math.DG"],"title_canon_sha256":"4fba056390ba63496beb9719c28c850d381ed582fdec497806cb27773ccc6b41","abstract_canon_sha256":"4d49dc865a7b59f9abd2db23a00450014a1ed022bfd5f6958c81cb08341b37c5"},"schema_version":"1.0"},"canonical_sha256":"ddb1061c70fc55c49aadb0c83a43dd4ce5d7671f3c46b2cb397d48ab9aa8b0b9","source":{"kind":"arxiv","id":"1006.4383","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.4383","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"arxiv_version","alias_value":"1006.4383v6","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4383","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"pith_short_12","alias_value":"3WYQMHDQ7RK4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3WYQMHDQ7RK4JGVN","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3WYQMHDQ","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3WYQMHDQ7RK4JGVNWDEDUQ65JT","target":"record","payload":{"canonical_record":{"source":{"id":"1006.4383","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-06-22T21:37:15Z","cross_cats_sorted":["math.AG","math.DG"],"title_canon_sha256":"4fba056390ba63496beb9719c28c850d381ed582fdec497806cb27773ccc6b41","abstract_canon_sha256":"4d49dc865a7b59f9abd2db23a00450014a1ed022bfd5f6958c81cb08341b37c5"},"schema_version":"1.0"},"canonical_sha256":"ddb1061c70fc55c49aadb0c83a43dd4ce5d7671f3c46b2cb397d48ab9aa8b0b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:50.847075Z","signature_b64":"yadwOL3VhXT9wBrv1Z4i/n7gYkc+HkO/h5Ntp9aasfJbxx0dqUfqujkxh3t4YSju8giTTBjFCU+j1kV+HHBpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddb1061c70fc55c49aadb0c83a43dd4ce5d7671f3c46b2cb397d48ab9aa8b0b9","last_reissued_at":"2026-05-18T02:41:50.846600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:50.846600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.4383","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aqc9kzujsmh8qE/9tqE3uTg9m5SfICl8FRlgZixhOrZVguUUqdwi2l3W7QS5bwUf2V9o9be+NYXfqBeSpqOMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:04:48.632272Z"},"content_sha256":"1b2402342fbdf530e3cec3f604f5c9f38e903bdc27a34eef0896d0e357619e66","schema_version":"1.0","event_id":"sha256:1b2402342fbdf530e3cec3f604f5c9f38e903bdc27a34eef0896d0e357619e66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3WYQMHDQ7RK4JGVNWDEDUQ65JT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gromov K-area and jumping curves in CP^n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.SG","authors_text":"Yasha Savelyev","submitted_at":"2010-06-22T21:37:15Z","abstract_excerpt":"We give here some extensions of Gromov's and Polterovich's theorems on $\\karea$ of $ \\mathbb{CP} ^{n}$, particularly in the symplectic and Hamiltonian context. Our main methods involve Gromov-Witten theory, and some connections with Bott periodicity, and loop groups. The argument is closely connected with study of jumping curves in $ \\mathbb{CP} ^{n}$, and as an upshot we prove a new symplectic geometric theorem on these jumping curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4383","kind":"arxiv","version":6},"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":"2026-05-18T02:41:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0J6+Dyb38YBtesZXuBK+dWAmGQH/Krq4kqdUzuvVVKBT8f7hrje3WoWuCEDHRnC7y73v3J1Nr+8Fw2zuchuAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:04:48.632630Z"},"content_sha256":"e948e1763058080457f37e9fd48eb3af5b7846b7501dce944c59e271742f56f0","schema_version":"1.0","event_id":"sha256:e948e1763058080457f37e9fd48eb3af5b7846b7501dce944c59e271742f56f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3WYQMHDQ7RK4JGVNWDEDUQ65JT/bundle.json","state_url":"https://pith.science/pith/3WYQMHDQ7RK4JGVNWDEDUQ65JT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3WYQMHDQ7RK4JGVNWDEDUQ65JT/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":"2026-06-11T10:04:48Z","links":{"resolver":"https://pith.science/pith/3WYQMHDQ7RK4JGVNWDEDUQ65JT","bundle":"https://pith.science/pith/3WYQMHDQ7RK4JGVNWDEDUQ65JT/bundle.json","state":"https://pith.science/pith/3WYQMHDQ7RK4JGVNWDEDUQ65JT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3WYQMHDQ7RK4JGVNWDEDUQ65JT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3WYQMHDQ7RK4JGVNWDEDUQ65JT","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":"4d49dc865a7b59f9abd2db23a00450014a1ed022bfd5f6958c81cb08341b37c5","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-06-22T21:37:15Z","title_canon_sha256":"4fba056390ba63496beb9719c28c850d381ed582fdec497806cb27773ccc6b41"},"schema_version":"1.0","source":{"id":"1006.4383","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.4383","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"arxiv_version","alias_value":"1006.4383v6","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4383","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"pith_short_12","alias_value":"3WYQMHDQ7RK4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3WYQMHDQ7RK4JGVN","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3WYQMHDQ","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:e948e1763058080457f37e9fd48eb3af5b7846b7501dce944c59e271742f56f0","target":"graph","created_at":"2026-05-18T02:41:50Z","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 give here some extensions of Gromov's and Polterovich's theorems on $\\karea$ of $ \\mathbb{CP} ^{n}$, particularly in the symplectic and Hamiltonian context. Our main methods involve Gromov-Witten theory, and some connections with Bott periodicity, and loop groups. The argument is closely connected with study of jumping curves in $ \\mathbb{CP} ^{n}$, and as an upshot we prove a new symplectic geometric theorem on these jumping curves.","authors_text":"Yasha Savelyev","cross_cats":["math.AG","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-06-22T21:37:15Z","title":"Gromov K-area and jumping curves in CP^n"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4383","kind":"arxiv","version":6},"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":"sha256:1b2402342fbdf530e3cec3f604f5c9f38e903bdc27a34eef0896d0e357619e66","target":"record","created_at":"2026-05-18T02:41:50Z","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":"4d49dc865a7b59f9abd2db23a00450014a1ed022bfd5f6958c81cb08341b37c5","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-06-22T21:37:15Z","title_canon_sha256":"4fba056390ba63496beb9719c28c850d381ed582fdec497806cb27773ccc6b41"},"schema_version":"1.0","source":{"id":"1006.4383","kind":"arxiv","version":6}},"canonical_sha256":"ddb1061c70fc55c49aadb0c83a43dd4ce5d7671f3c46b2cb397d48ab9aa8b0b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddb1061c70fc55c49aadb0c83a43dd4ce5d7671f3c46b2cb397d48ab9aa8b0b9","first_computed_at":"2026-05-18T02:41:50.846600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:50.846600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yadwOL3VhXT9wBrv1Z4i/n7gYkc+HkO/h5Ntp9aasfJbxx0dqUfqujkxh3t4YSju8giTTBjFCU+j1kV+HHBpCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:50.847075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.4383","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b2402342fbdf530e3cec3f604f5c9f38e903bdc27a34eef0896d0e357619e66","sha256:e948e1763058080457f37e9fd48eb3af5b7846b7501dce944c59e271742f56f0"],"state_sha256":"f31e35dcb9f5a937026326ea006dff9a81566268ae5c64c4a9e147b76ebbe4b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b4vzpdYlgeVBIZlJZVV6bjhQsd+ezGHDFE1kyQOgcbFDb+DzLiB3ES9j58J3SO9+Ah3c6lldagyxc/six0DlAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T10:04:48.634566Z","bundle_sha256":"baa8238bb42ccdbf600d577324af900ed455f2d4ae27ca567f064d3233d4fc46"}}