{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BUPRFNSXWA7OBFPJU3AWQ2XEKN","short_pith_number":"pith:BUPRFNSX","schema_version":"1.0","canonical_sha256":"0d1f12b657b03ee095e9a6c1686ae453744e9e82c6428cbad598d2b1e96229b2","source":{"kind":"arxiv","id":"1409.4848","version":3},"attestation_state":"computed","paper":{"title":"Virtual Poincar\\'e polynomial of the space of stable pairs supported on quintic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kiryong Chung","submitted_at":"2014-09-17T01:38:18Z","abstract_excerpt":"Let $\\mathbf{M}^{\\alpha}(d,\\chi)$ be the moduli space of $\\alpha$-stable pairs $(s,F)$ on the projective plane $\\mathbb{P}^2$ with Hilbert polynomial $\\chi(F(m))=dm+\\chi$. For sufficiently large $\\alpha$ (denoted by $\\infty$), it is well known that the moduli space is isomorphic to the relative Hilbert scheme of points over the universal degree $d$ plane curves. For the general $(d,\\chi)$, the relative Hilbert scheme does not have a bundle structure over the Hilbert scheme of points. In this paper, as the first non trivial such a case, we study the wall crossing of the $\\alpha$-stable pairs sp"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.4848","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-17T01:38:18Z","cross_cats_sorted":[],"title_canon_sha256":"cb8b1b137f1b084d8ccb1124bf49a74c777b1c1b58a6ada102658c5c0a7f6b30","abstract_canon_sha256":"33ddf3c1a62989bd12ef7c5c74b71d6c83f77d174990087e036ad3a672673d76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:58.431566Z","signature_b64":"ZfBQ5AW8Yie1dh8Bsj26IFuM3cpLZuhoAM0AfBI31qpe7povKfBF7skzlsCZJ7DHbSAOLg1QNCNu6w1vpfL/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d1f12b657b03ee095e9a6c1686ae453744e9e82c6428cbad598d2b1e96229b2","last_reissued_at":"2026-05-18T01:59:58.431002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:58.431002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Virtual Poincar\\'e polynomial of the space of stable pairs supported on quintic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kiryong Chung","submitted_at":"2014-09-17T01:38:18Z","abstract_excerpt":"Let $\\mathbf{M}^{\\alpha}(d,\\chi)$ be the moduli space of $\\alpha$-stable pairs $(s,F)$ on the projective plane $\\mathbb{P}^2$ with Hilbert polynomial $\\chi(F(m))=dm+\\chi$. For sufficiently large $\\alpha$ (denoted by $\\infty$), it is well known that the moduli space is isomorphic to the relative Hilbert scheme of points over the universal degree $d$ plane curves. For the general $(d,\\chi)$, the relative Hilbert scheme does not have a bundle structure over the Hilbert scheme of points. In this paper, as the first non trivial such a case, we study the wall crossing of the $\\alpha$-stable pairs sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4848","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1409.4848","created_at":"2026-05-18T01:59:58.431092+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.4848v3","created_at":"2026-05-18T01:59:58.431092+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4848","created_at":"2026-05-18T01:59:58.431092+00:00"},{"alias_kind":"pith_short_12","alias_value":"BUPRFNSXWA7O","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BUPRFNSXWA7OBFPJ","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BUPRFNSX","created_at":"2026-05-18T12:28:22.404517+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BUPRFNSXWA7OBFPJU3AWQ2XEKN","json":"https://pith.science/pith/BUPRFNSXWA7OBFPJU3AWQ2XEKN.json","graph_json":"https://pith.science/api/pith-number/BUPRFNSXWA7OBFPJU3AWQ2XEKN/graph.json","events_json":"https://pith.science/api/pith-number/BUPRFNSXWA7OBFPJU3AWQ2XEKN/events.json","paper":"https://pith.science/paper/BUPRFNSX"},"agent_actions":{"view_html":"https://pith.science/pith/BUPRFNSXWA7OBFPJU3AWQ2XEKN","download_json":"https://pith.science/pith/BUPRFNSXWA7OBFPJU3AWQ2XEKN.json","view_paper":"https://pith.science/paper/BUPRFNSX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.4848&json=true","fetch_graph":"https://pith.science/api/pith-number/BUPRFNSXWA7OBFPJU3AWQ2XEKN/graph.json","fetch_events":"https://pith.science/api/pith-number/BUPRFNSXWA7OBFPJU3AWQ2XEKN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BUPRFNSXWA7OBFPJU3AWQ2XEKN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BUPRFNSXWA7OBFPJU3AWQ2XEKN/action/storage_attestation","attest_author":"https://pith.science/pith/BUPRFNSXWA7OBFPJU3AWQ2XEKN/action/author_attestation","sign_citation":"https://pith.science/pith/BUPRFNSXWA7OBFPJU3AWQ2XEKN/action/citation_signature","submit_replication":"https://pith.science/pith/BUPRFNSXWA7OBFPJU3AWQ2XEKN/action/replication_record"}},"created_at":"2026-05-18T01:59:58.431092+00:00","updated_at":"2026-05-18T01:59:58.431092+00:00"}