{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2G456DYGNUU3RYIMRV3REN7CPY","short_pith_number":"pith:2G456DYG","canonical_record":{"source":{"id":"1206.5640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-25T10:42:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c14a6cf9d358d1e2f8feb173cde849a152e1c5a47e75e9b6bb2354d446e20080","abstract_canon_sha256":"d4dad6449ec43ec515ad842ab5880f8365f5f015692bf431552cb1dfc5359936"},"schema_version":"1.0"},"canonical_sha256":"d1b9df0f066d29b8e10c8d771237e27e2c8b801c784844e1403eac6b3c2d7546","source":{"kind":"arxiv","id":"1206.5640","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5640","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5640v2","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5640","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"pith_short_12","alias_value":"2G456DYGNUU3","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2G456DYGNUU3RYIM","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2G456DYG","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2G456DYGNUU3RYIMRV3REN7CPY","target":"record","payload":{"canonical_record":{"source":{"id":"1206.5640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-25T10:42:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c14a6cf9d358d1e2f8feb173cde849a152e1c5a47e75e9b6bb2354d446e20080","abstract_canon_sha256":"d4dad6449ec43ec515ad842ab5880f8365f5f015692bf431552cb1dfc5359936"},"schema_version":"1.0"},"canonical_sha256":"d1b9df0f066d29b8e10c8d771237e27e2c8b801c784844e1403eac6b3c2d7546","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:47.930167Z","signature_b64":"mO8GLGXGWmxt7BNoe5AOpEm/75YhBXrm+rLZFONxWXwH+is21HehXZHTre1ixoAXeyVisf7YMiPkocAy1IYrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1b9df0f066d29b8e10c8d771237e27e2c8b801c784844e1403eac6b3c2d7546","last_reissued_at":"2026-05-18T02:30:47.929701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:47.929701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.5640","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":"2026-05-18T02:30:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b3Il9s8s2SPDltrJ7Ilt28r/xl/ga/wWnmPs9iaj96uPSgD8NhqGouoAyWLsH2lRJ2RD8dwdlkmrh36im/hMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:38:01.404911Z"},"content_sha256":"6038e1c2a50b4280c3df4388cda10d679d2d981d48f75e42049a7cc6ab588484","schema_version":"1.0","event_id":"sha256:6038e1c2a50b4280c3df4388cda10d679d2d981d48f75e42049a7cc6ab588484"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2G456DYGNUU3RYIMRV3REN7CPY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"A. Buryak, B. L. Feigin","submitted_at":"2012-06-25T10:42:08Z","abstract_excerpt":"In this paper we prove that the generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes of points in the plane has a beautiful decomposition into an infinite product. We also compute the generating series of the numbers of quasihomogeneous components in a moduli space of sheaves on the projective plane. The answer is given in terms of characters of the affine Lie algebra $\\hat{sl}_m$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5640","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":"2026-05-18T02:30:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PRS+KKL6w1VCKfPIwdUELhA6k6xbraFNWDWmD2kHRjw3YkgoTanShSNNNYy+GvmbfzYN3cUV2SdOgP/WzU8cDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T12:38:01.405605Z"},"content_sha256":"9477841de98808fddb50db9e14c621b223050c81eb7199bf998f750d3fd64b8f","schema_version":"1.0","event_id":"sha256:9477841de98808fddb50db9e14c621b223050c81eb7199bf998f750d3fd64b8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2G456DYGNUU3RYIMRV3REN7CPY/bundle.json","state_url":"https://pith.science/pith/2G456DYGNUU3RYIMRV3REN7CPY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2G456DYGNUU3RYIMRV3REN7CPY/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":"2026-06-06T12:38:01Z","links":{"resolver":"https://pith.science/pith/2G456DYGNUU3RYIMRV3REN7CPY","bundle":"https://pith.science/pith/2G456DYGNUU3RYIMRV3REN7CPY/bundle.json","state":"https://pith.science/pith/2G456DYGNUU3RYIMRV3REN7CPY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2G456DYGNUU3RYIMRV3REN7CPY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2G456DYGNUU3RYIMRV3REN7CPY","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":"d4dad6449ec43ec515ad842ab5880f8365f5f015692bf431552cb1dfc5359936","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-25T10:42:08Z","title_canon_sha256":"c14a6cf9d358d1e2f8feb173cde849a152e1c5a47e75e9b6bb2354d446e20080"},"schema_version":"1.0","source":{"id":"1206.5640","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5640","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5640v2","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5640","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"pith_short_12","alias_value":"2G456DYGNUU3","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2G456DYGNUU3RYIM","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2G456DYG","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:9477841de98808fddb50db9e14c621b223050c81eb7199bf998f750d3fd64b8f","target":"graph","created_at":"2026-05-18T02:30:47Z","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":"In this paper we prove that the generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes of points in the plane has a beautiful decomposition into an infinite product. We also compute the generating series of the numbers of quasihomogeneous components in a moduli space of sheaves on the projective plane. The answer is given in terms of characters of the affine Lie algebra $\\hat{sl}_m$.","authors_text":"A. Buryak, B. L. Feigin","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-25T10:42:08Z","title":"Generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5640","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":"sha256:6038e1c2a50b4280c3df4388cda10d679d2d981d48f75e42049a7cc6ab588484","target":"record","created_at":"2026-05-18T02:30:47Z","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":"d4dad6449ec43ec515ad842ab5880f8365f5f015692bf431552cb1dfc5359936","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-25T10:42:08Z","title_canon_sha256":"c14a6cf9d358d1e2f8feb173cde849a152e1c5a47e75e9b6bb2354d446e20080"},"schema_version":"1.0","source":{"id":"1206.5640","kind":"arxiv","version":2}},"canonical_sha256":"d1b9df0f066d29b8e10c8d771237e27e2c8b801c784844e1403eac6b3c2d7546","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1b9df0f066d29b8e10c8d771237e27e2c8b801c784844e1403eac6b3c2d7546","first_computed_at":"2026-05-18T02:30:47.929701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:47.929701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mO8GLGXGWmxt7BNoe5AOpEm/75YhBXrm+rLZFONxWXwH+is21HehXZHTre1ixoAXeyVisf7YMiPkocAy1IYrBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:47.930167Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5640","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6038e1c2a50b4280c3df4388cda10d679d2d981d48f75e42049a7cc6ab588484","sha256:9477841de98808fddb50db9e14c621b223050c81eb7199bf998f750d3fd64b8f"],"state_sha256":"59eed386adab4ea5db800e0a057bebff81d0ad0fc80753bb8a5f54f0d4e9dccf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HA4vIE+/N0pi/1dsbeOMR7HU2E4GqawF721nBzGrcAVhjGtkEdHZIrfrr1pOxNcUnYngTe5f9d3OqPNhyrjCDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T12:38:01.409242Z","bundle_sha256":"72307baef5753e8e4d4ff5c6c608f127f210149fd2842a6b2b96ddf0170e38c2"}}