{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:WGPPKH7YVKH6NKWOF5X2JDDP5X","short_pith_number":"pith:WGPPKH7Y","canonical_record":{"source":{"id":"1202.4412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-20T18:30:55Z","cross_cats_sorted":[],"title_canon_sha256":"26dfc9ee3af65012cd157fbb4d123a64c0e6a5b1d8a54c58cc2c9a8568869982","abstract_canon_sha256":"c0db9debcd6a819d319413b12e200a1de26df5167fa1033840874a8970e31b87"},"schema_version":"1.0"},"canonical_sha256":"b19ef51ff8aa8fe6aace2f6fa48c6fedd8cea47acc03df339b2e5220780f065d","source":{"kind":"arxiv","id":"1202.4412","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4412","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4412v2","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4412","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"WGPPKH7YVKH6","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WGPPKH7YVKH6NKWO","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WGPPKH7Y","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:WGPPKH7YVKH6NKWOF5X2JDDP5X","target":"record","payload":{"canonical_record":{"source":{"id":"1202.4412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-20T18:30:55Z","cross_cats_sorted":[],"title_canon_sha256":"26dfc9ee3af65012cd157fbb4d123a64c0e6a5b1d8a54c58cc2c9a8568869982","abstract_canon_sha256":"c0db9debcd6a819d319413b12e200a1de26df5167fa1033840874a8970e31b87"},"schema_version":"1.0"},"canonical_sha256":"b19ef51ff8aa8fe6aace2f6fa48c6fedd8cea47acc03df339b2e5220780f065d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:53.804799Z","signature_b64":"5GWfKN173d6vhrOq2npzZHjP2m+S3BXmvB9VkWoCGFdn6VsaKeDay6or7H0OFWjyrPhaF01tvG3siZaZ/sgPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b19ef51ff8aa8fe6aace2f6fa48c6fedd8cea47acc03df339b2e5220780f065d","last_reissued_at":"2026-05-18T02:57:53.804262Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:53.804262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.4412","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":"2026-05-18T02:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WGhF+EjzQwi5IAg+T+HF/WUtpGji5ia75oEX2uPaMvOV4YGkdNWthxqEvIaXpfKQdw2q3Lbg2Qr2NDuwik87Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:46:45.337105Z"},"content_sha256":"120f32784285d96ccd266c8e7e4a4b2f212ba67855a323e7174ce037bcbf1a27","schema_version":"1.0","event_id":"sha256:120f32784285d96ccd266c8e7e4a4b2f212ba67855a323e7174ce037bcbf1a27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:WGPPKH7YVKH6NKWOF5X2JDDP5X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heegaard Floer genus bounds for Dehn surgeries on knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Stanislav Jabuka","submitted_at":"2012-02-20T18:30:55Z","abstract_excerpt":"We provide a new obstruction for a rational homology 3-sphere to arise by Dehn surgery on a given knot in the 3-sphere. The obstruction takes the form of an inequality involving the genus of the knot, the surgery coefficient, and a count of L-structures on the 3-manifold, that is spin-c structures with the simplest possible associated Heegaard Floer group. Applications include an obstruction for two framed knots to yield the same 3-manifold, an obstruction that is particularly effective when working with families of framed knots. We introduce the rational and integral Dehn surgery genera for a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4412","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":"2026-05-18T02:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NqUGoyhSVVoCAoYaJgte/KK/VzjNdE5h3tZFnRpVmKdUj2sPLaWngCHnTpcOLokMDDXM4f8gRs5E586tnr+KDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:46:45.337808Z"},"content_sha256":"4c39258b3e686b1b44129d6c7ffff71182fc2c8e2f5c3b3cdf8a2a8b8fa9c715","schema_version":"1.0","event_id":"sha256:4c39258b3e686b1b44129d6c7ffff71182fc2c8e2f5c3b3cdf8a2a8b8fa9c715"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WGPPKH7YVKH6NKWOF5X2JDDP5X/bundle.json","state_url":"https://pith.science/pith/WGPPKH7YVKH6NKWOF5X2JDDP5X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WGPPKH7YVKH6NKWOF5X2JDDP5X/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":"2026-06-06T06:46:45Z","links":{"resolver":"https://pith.science/pith/WGPPKH7YVKH6NKWOF5X2JDDP5X","bundle":"https://pith.science/pith/WGPPKH7YVKH6NKWOF5X2JDDP5X/bundle.json","state":"https://pith.science/pith/WGPPKH7YVKH6NKWOF5X2JDDP5X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WGPPKH7YVKH6NKWOF5X2JDDP5X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WGPPKH7YVKH6NKWOF5X2JDDP5X","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":"c0db9debcd6a819d319413b12e200a1de26df5167fa1033840874a8970e31b87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-20T18:30:55Z","title_canon_sha256":"26dfc9ee3af65012cd157fbb4d123a64c0e6a5b1d8a54c58cc2c9a8568869982"},"schema_version":"1.0","source":{"id":"1202.4412","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4412","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4412v2","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4412","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"WGPPKH7YVKH6","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WGPPKH7YVKH6NKWO","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WGPPKH7Y","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:4c39258b3e686b1b44129d6c7ffff71182fc2c8e2f5c3b3cdf8a2a8b8fa9c715","target":"graph","created_at":"2026-05-18T02:57:53Z","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 provide a new obstruction for a rational homology 3-sphere to arise by Dehn surgery on a given knot in the 3-sphere. The obstruction takes the form of an inequality involving the genus of the knot, the surgery coefficient, and a count of L-structures on the 3-manifold, that is spin-c structures with the simplest possible associated Heegaard Floer group. Applications include an obstruction for two framed knots to yield the same 3-manifold, an obstruction that is particularly effective when working with families of framed knots. We introduce the rational and integral Dehn surgery genera for a","authors_text":"Stanislav Jabuka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-20T18:30:55Z","title":"Heegaard Floer genus bounds for Dehn surgeries on knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4412","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":"sha256:120f32784285d96ccd266c8e7e4a4b2f212ba67855a323e7174ce037bcbf1a27","target":"record","created_at":"2026-05-18T02:57:53Z","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":"c0db9debcd6a819d319413b12e200a1de26df5167fa1033840874a8970e31b87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-20T18:30:55Z","title_canon_sha256":"26dfc9ee3af65012cd157fbb4d123a64c0e6a5b1d8a54c58cc2c9a8568869982"},"schema_version":"1.0","source":{"id":"1202.4412","kind":"arxiv","version":2}},"canonical_sha256":"b19ef51ff8aa8fe6aace2f6fa48c6fedd8cea47acc03df339b2e5220780f065d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b19ef51ff8aa8fe6aace2f6fa48c6fedd8cea47acc03df339b2e5220780f065d","first_computed_at":"2026-05-18T02:57:53.804262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:53.804262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5GWfKN173d6vhrOq2npzZHjP2m+S3BXmvB9VkWoCGFdn6VsaKeDay6or7H0OFWjyrPhaF01tvG3siZaZ/sgPDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:53.804799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4412","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:120f32784285d96ccd266c8e7e4a4b2f212ba67855a323e7174ce037bcbf1a27","sha256:4c39258b3e686b1b44129d6c7ffff71182fc2c8e2f5c3b3cdf8a2a8b8fa9c715"],"state_sha256":"17820d18f75a1bef3ce550b031f97d811b162838a2b67a9e9f5fef632f2c94dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TJha1RP3a2PIHsPgyedUj0tfOdvTj0+KM0f5Mo2XZjA/4uK5i+2PvO9yjBDZUkVJtdC0QfrAd2CGTGnfpPoUCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T06:46:45.341652Z","bundle_sha256":"a3fca4d7539205a88fdfc9edde2e6b86427c497d4ed4b3261e17caadc840a999"}}