{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:3K3DNQSOQ4AOY5APYWPIMQYNCM","short_pith_number":"pith:3K3DNQSO","canonical_record":{"source":{"id":"math/0009167","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2000-09-18T14:53:37Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"ad02d9b53348825fe8dad2c5db9236457ac78067ac5cbae713f685ff0a0c89d6","abstract_canon_sha256":"c65c93ffa61e985be36450ddc9fd0c9b5dbc8be909e7649bc3b8fdc5a4e6c936"},"schema_version":"1.0"},"canonical_sha256":"dab636c24e8700ec740fc59e86430d133204af9d93b874809bf8fcb78326df6e","source":{"kind":"arxiv","id":"math/0009167","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0009167","created_at":"2026-07-04T14:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"math/0009167v2","created_at":"2026-07-04T14:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0009167","created_at":"2026-07-04T14:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"3K3DNQSOQ4AO","created_at":"2026-07-04T14:34:42Z"},{"alias_kind":"pith_short_16","alias_value":"3K3DNQSOQ4AOY5AP","created_at":"2026-07-04T14:34:42Z"},{"alias_kind":"pith_short_8","alias_value":"3K3DNQSO","created_at":"2026-07-04T14:34:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:3K3DNQSOQ4AOY5APYWPIMQYNCM","target":"record","payload":{"canonical_record":{"source":{"id":"math/0009167","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2000-09-18T14:53:37Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"ad02d9b53348825fe8dad2c5db9236457ac78067ac5cbae713f685ff0a0c89d6","abstract_canon_sha256":"c65c93ffa61e985be36450ddc9fd0c9b5dbc8be909e7649bc3b8fdc5a4e6c936"},"schema_version":"1.0"},"canonical_sha256":"dab636c24e8700ec740fc59e86430d133204af9d93b874809bf8fcb78326df6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:34:42.368118Z","signature_b64":"rST0aiMzNuisNMnAcOFgn4t0DBt4vaQqpzHNCK73mmqT86aEF/xW4iVOzPA7N9VXJwFUkVw8vDhdOjrpzVcQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dab636c24e8700ec740fc59e86430d133204af9d93b874809bf8fcb78326df6e","last_reissued_at":"2026-07-04T14:34:42.367720Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:34:42.367720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0009167","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":"2026-07-04T14:34:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HPZ9rjt/jabZ5semwyOYwqp5UcncveJhrEdNlc5bCb7O0MFpFSgOQwm+/UFF01y7YY1ZTEcRaQ//P16SCGPxDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:08:26.295152Z"},"content_sha256":"bc44f24c1ff2e19cbbbfe897de484f040aac1b3a3eec92176035f58745a62ae8","schema_version":"1.0","event_id":"sha256:bc44f24c1ff2e19cbbbfe897de484f040aac1b3a3eec92176035f58745a62ae8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:3K3DNQSOQ4AOY5APYWPIMQYNCM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generators for the cohomology ring of Hilbert schemes of points on surfaces","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AG","authors_text":"Wei-ping Li, Weiqiang Wang, Zhenbo Qin","submitted_at":"2000-09-18T14:53:37Z","abstract_excerpt":"Using the methods developed in [LQW], math.AG/0009132, we obtain a second set of generators for the cohomology ring of the Hilbert scheme of points on an arbitrary smooth projective surface over the field of complex numbers. These generators have clear and simple geometric as well as algebraic descriptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0009167","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0009167/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:34:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X3WEXluDC6IaxeluVaf9Tvx9O593ertf8BJt4jT0+9rW31fOkCaE1lBgI2uYTZZwhamXNTqujMuly8oqP477DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:08:26.295649Z"},"content_sha256":"7d72cefe93d923f5deae3400fe98688e5a6958bf9875808ae58a95670ca3cd29","schema_version":"1.0","event_id":"sha256:7d72cefe93d923f5deae3400fe98688e5a6958bf9875808ae58a95670ca3cd29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3K3DNQSOQ4AOY5APYWPIMQYNCM/bundle.json","state_url":"https://pith.science/pith/3K3DNQSOQ4AOY5APYWPIMQYNCM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3K3DNQSOQ4AOY5APYWPIMQYNCM/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":"2026-08-04T05:08:26Z","links":{"resolver":"https://pith.science/pith/3K3DNQSOQ4AOY5APYWPIMQYNCM","bundle":"https://pith.science/pith/3K3DNQSOQ4AOY5APYWPIMQYNCM/bundle.json","state":"https://pith.science/pith/3K3DNQSOQ4AOY5APYWPIMQYNCM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3K3DNQSOQ4AOY5APYWPIMQYNCM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:3K3DNQSOQ4AOY5APYWPIMQYNCM","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":"c65c93ffa61e985be36450ddc9fd0c9b5dbc8be909e7649bc3b8fdc5a4e6c936","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.AG","submitted_at":"2000-09-18T14:53:37Z","title_canon_sha256":"ad02d9b53348825fe8dad2c5db9236457ac78067ac5cbae713f685ff0a0c89d6"},"schema_version":"1.0","source":{"id":"math/0009167","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0009167","created_at":"2026-07-04T14:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"math/0009167v2","created_at":"2026-07-04T14:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0009167","created_at":"2026-07-04T14:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"3K3DNQSOQ4AO","created_at":"2026-07-04T14:34:42Z"},{"alias_kind":"pith_short_16","alias_value":"3K3DNQSOQ4AOY5AP","created_at":"2026-07-04T14:34:42Z"},{"alias_kind":"pith_short_8","alias_value":"3K3DNQSO","created_at":"2026-07-04T14:34:42Z"}],"graph_snapshots":[{"event_id":"sha256:7d72cefe93d923f5deae3400fe98688e5a6958bf9875808ae58a95670ca3cd29","target":"graph","created_at":"2026-07-04T14:34:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0009167/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using the methods developed in [LQW], math.AG/0009132, we obtain a second set of generators for the cohomology ring of the Hilbert scheme of points on an arbitrary smooth projective surface over the field of complex numbers. These generators have clear and simple geometric as well as algebraic descriptions.","authors_text":"Wei-ping Li, Weiqiang Wang, Zhenbo Qin","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2000-09-18T14:53:37Z","title":"Generators for the cohomology ring of Hilbert schemes of points on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0009167","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:bc44f24c1ff2e19cbbbfe897de484f040aac1b3a3eec92176035f58745a62ae8","target":"record","created_at":"2026-07-04T14:34:42Z","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":"c65c93ffa61e985be36450ddc9fd0c9b5dbc8be909e7649bc3b8fdc5a4e6c936","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.AG","submitted_at":"2000-09-18T14:53:37Z","title_canon_sha256":"ad02d9b53348825fe8dad2c5db9236457ac78067ac5cbae713f685ff0a0c89d6"},"schema_version":"1.0","source":{"id":"math/0009167","kind":"arxiv","version":2}},"canonical_sha256":"dab636c24e8700ec740fc59e86430d133204af9d93b874809bf8fcb78326df6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dab636c24e8700ec740fc59e86430d133204af9d93b874809bf8fcb78326df6e","first_computed_at":"2026-07-04T14:34:42.367720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:34:42.367720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rST0aiMzNuisNMnAcOFgn4t0DBt4vaQqpzHNCK73mmqT86aEF/xW4iVOzPA7N9VXJwFUkVw8vDhdOjrpzVcQBA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:34:42.368118Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0009167","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc44f24c1ff2e19cbbbfe897de484f040aac1b3a3eec92176035f58745a62ae8","sha256:7d72cefe93d923f5deae3400fe98688e5a6958bf9875808ae58a95670ca3cd29"],"state_sha256":"12c6e2c960e63b4562f86e1fb7038b6af232c8aaf74eb6a76d68928f566e1a52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"USmG9snjLR/n+rhffU4wXikEgWcfbXEBuDAadIwJ+rjQKLigRp3uzcu48wHTMCjHvYFf4u0Xf+yZE0p1lRfjAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T05:08:26.316634Z","bundle_sha256":"4f7be01a0d4a76fea6b3e6b7899b9667b88aeafa3be7c04842eedbe5cbe0e218"}}