{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IWFHVUVAOZXQO3FKRHEYLX4SNE","short_pith_number":"pith:IWFHVUVA","canonical_record":{"source":{"id":"1206.2558","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-06-12T15:00:51Z","cross_cats_sorted":[],"title_canon_sha256":"effe501e921fa7a5e63019811c2a5f3fcb8f8a247a5d112ad45e60915a993f90","abstract_canon_sha256":"5a569afa63e87700a9e981d059989b11ff4ac65431fbe0915a292e15eeeab0db"},"schema_version":"1.0"},"canonical_sha256":"458a7ad2a0766f076caa89c985df92691886cf8c2077af90ffbe97a178382b4c","source":{"kind":"arxiv","id":"1206.2558","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2558","created_at":"2026-05-18T03:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2558v2","created_at":"2026-05-18T03:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2558","created_at":"2026-05-18T03:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"IWFHVUVAOZXQ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IWFHVUVAOZXQO3FK","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IWFHVUVA","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IWFHVUVAOZXQO3FKRHEYLX4SNE","target":"record","payload":{"canonical_record":{"source":{"id":"1206.2558","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-06-12T15:00:51Z","cross_cats_sorted":[],"title_canon_sha256":"effe501e921fa7a5e63019811c2a5f3fcb8f8a247a5d112ad45e60915a993f90","abstract_canon_sha256":"5a569afa63e87700a9e981d059989b11ff4ac65431fbe0915a292e15eeeab0db"},"schema_version":"1.0"},"canonical_sha256":"458a7ad2a0766f076caa89c985df92691886cf8c2077af90ffbe97a178382b4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:13.837294Z","signature_b64":"7so2B5Vpy3a50SzrcpZEXnL/YN+V1TvE9rfIFonJ3fkq/zfiLpyXMI50pAM6yjB1jtrpcC8ZpoG8OehhUboWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"458a7ad2a0766f076caa89c985df92691886cf8c2077af90ffbe97a178382b4c","last_reissued_at":"2026-05-18T03:29:13.836624Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:13.836624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.2558","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":"2026-05-18T03:29:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hdp9bWkbfRQFC6X+6PM/05F3h7PaHlt/GtaboPVyO5I/4iJBQyKwiKhGfaudPHMK10njvQD//wWk9t0F/KPrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:05:16.416223Z"},"content_sha256":"07da0e810222e3a9799b47fd91dd2c578a0d3c8d930bad805cbaada6ba2385e5","schema_version":"1.0","event_id":"sha256:07da0e810222e3a9799b47fd91dd2c578a0d3c8d930bad805cbaada6ba2385e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IWFHVUVAOZXQO3FKRHEYLX4SNE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heegaard Floer homology and several families of Brieskorn spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eamonn Tweedy","submitted_at":"2012-06-12T15:00:51Z","abstract_excerpt":"Ozsv\\'ath and Szab\\'o gave a combinatorial description for the Heegaard Floer homology of boundaries of certain negative-definite plumbings. N\\'emethi constructed a remarkable algorithm for executing these computations for almost-rational plumbings, and his work gives a formula computing the invariants for the Brieskorn homology spheres -{\\Sigma} (p,q,pqn + 1). Here we give a formula for HF^{+}(-{\\Sigma}(p,q,pqn-1)), generalizing the one for the n=1 case given by Borodzik and N\\'emethi. We also compute HF^{+} for the families -{\\Sigma}(2,5,k) and -{\\Sigma}(2,7,k)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2558","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":"2026-05-18T03:29:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vRxdqGm/Kg3tmH/7D74JOetmWpie879a9/E8ekM0Rc1OHtKp6uy+box8/spGxxnx8bIUavypmo2ktrPNW/mTDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:05:16.416576Z"},"content_sha256":"bdce2461be7849a24c0308135a56fda63a42733cbd8a75bb2a58e9722e3bea7e","schema_version":"1.0","event_id":"sha256:bdce2461be7849a24c0308135a56fda63a42733cbd8a75bb2a58e9722e3bea7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IWFHVUVAOZXQO3FKRHEYLX4SNE/bundle.json","state_url":"https://pith.science/pith/IWFHVUVAOZXQO3FKRHEYLX4SNE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IWFHVUVAOZXQO3FKRHEYLX4SNE/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":"2026-06-27T01:05:16Z","links":{"resolver":"https://pith.science/pith/IWFHVUVAOZXQO3FKRHEYLX4SNE","bundle":"https://pith.science/pith/IWFHVUVAOZXQO3FKRHEYLX4SNE/bundle.json","state":"https://pith.science/pith/IWFHVUVAOZXQO3FKRHEYLX4SNE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IWFHVUVAOZXQO3FKRHEYLX4SNE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IWFHVUVAOZXQO3FKRHEYLX4SNE","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":"5a569afa63e87700a9e981d059989b11ff4ac65431fbe0915a292e15eeeab0db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-06-12T15:00:51Z","title_canon_sha256":"effe501e921fa7a5e63019811c2a5f3fcb8f8a247a5d112ad45e60915a993f90"},"schema_version":"1.0","source":{"id":"1206.2558","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2558","created_at":"2026-05-18T03:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2558v2","created_at":"2026-05-18T03:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2558","created_at":"2026-05-18T03:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"IWFHVUVAOZXQ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IWFHVUVAOZXQO3FK","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IWFHVUVA","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:bdce2461be7849a24c0308135a56fda63a42733cbd8a75bb2a58e9722e3bea7e","target":"graph","created_at":"2026-05-18T03:29:13Z","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":"Ozsv\\'ath and Szab\\'o gave a combinatorial description for the Heegaard Floer homology of boundaries of certain negative-definite plumbings. N\\'emethi constructed a remarkable algorithm for executing these computations for almost-rational plumbings, and his work gives a formula computing the invariants for the Brieskorn homology spheres -{\\Sigma} (p,q,pqn + 1). Here we give a formula for HF^{+}(-{\\Sigma}(p,q,pqn-1)), generalizing the one for the n=1 case given by Borodzik and N\\'emethi. We also compute HF^{+} for the families -{\\Sigma}(2,5,k) and -{\\Sigma}(2,7,k).","authors_text":"Eamonn Tweedy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-06-12T15:00:51Z","title":"Heegaard Floer homology and several families of Brieskorn spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2558","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":"sha256:07da0e810222e3a9799b47fd91dd2c578a0d3c8d930bad805cbaada6ba2385e5","target":"record","created_at":"2026-05-18T03:29:13Z","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":"5a569afa63e87700a9e981d059989b11ff4ac65431fbe0915a292e15eeeab0db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-06-12T15:00:51Z","title_canon_sha256":"effe501e921fa7a5e63019811c2a5f3fcb8f8a247a5d112ad45e60915a993f90"},"schema_version":"1.0","source":{"id":"1206.2558","kind":"arxiv","version":2}},"canonical_sha256":"458a7ad2a0766f076caa89c985df92691886cf8c2077af90ffbe97a178382b4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"458a7ad2a0766f076caa89c985df92691886cf8c2077af90ffbe97a178382b4c","first_computed_at":"2026-05-18T03:29:13.836624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:13.836624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7so2B5Vpy3a50SzrcpZEXnL/YN+V1TvE9rfIFonJ3fkq/zfiLpyXMI50pAM6yjB1jtrpcC8ZpoG8OehhUboWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:13.837294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.2558","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07da0e810222e3a9799b47fd91dd2c578a0d3c8d930bad805cbaada6ba2385e5","sha256:bdce2461be7849a24c0308135a56fda63a42733cbd8a75bb2a58e9722e3bea7e"],"state_sha256":"177fa1fc90d5b84461895db7407111808a40b135fe6253116cdf52e9ef10edb4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uOaFBSS2+ANNw6+RLiMlX/bK9jxJmSg49RF0fJHdm6B4SZ+Tb70TQUXQGKfZNlWiseujEKzN+D+RsTRG4xhlDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T01:05:16.418460Z","bundle_sha256":"9c32fca6272ebf37f6d0971236a9616db7a950db6c7b8a44fbb18d35c28001cf"}}