{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:CTRARI2NDFUTP3NAQMJE46LTRI","short_pith_number":"pith:CTRARI2N","canonical_record":{"source":{"id":"1012.5305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-23T21:17:11Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"76f37417290b61854f31d2fd875d982369e709ebbc76d128e0e041003aaf8fa2","abstract_canon_sha256":"134ae295c8a53603d2927a1c3da648fabe4811b8a52f57bb4366d82ea8b5c63a"},"schema_version":"1.0"},"canonical_sha256":"14e208a34d196937eda083124e79738a2d6dd3d48c5b7540485a3a0b814e8764","source":{"kind":"arxiv","id":"1012.5305","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5305","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5305v2","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5305","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"pith_short_12","alias_value":"CTRARI2NDFUT","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CTRARI2NDFUTP3NA","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CTRARI2N","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:CTRARI2NDFUTP3NAQMJE46LTRI","target":"record","payload":{"canonical_record":{"source":{"id":"1012.5305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-23T21:17:11Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"76f37417290b61854f31d2fd875d982369e709ebbc76d128e0e041003aaf8fa2","abstract_canon_sha256":"134ae295c8a53603d2927a1c3da648fabe4811b8a52f57bb4366d82ea8b5c63a"},"schema_version":"1.0"},"canonical_sha256":"14e208a34d196937eda083124e79738a2d6dd3d48c5b7540485a3a0b814e8764","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:46.315772Z","signature_b64":"4z/FgUlQXXMSMJh/NIoO2DBY62lwEGSI4AWWbOAyu27PoAnxd8jFDM5F9rsiHs0Kn9RerSLyiwJMQNu3FqKeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14e208a34d196937eda083124e79738a2d6dd3d48c5b7540485a3a0b814e8764","last_reissued_at":"2026-05-18T03:56:46.315222Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:46.315222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.5305","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":"2026-05-18T03:56:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F8VzkC9p2LJ31I0xjTY5XRtZY3gdXCqDRDBI75Az0rWMSj5h5v2KOo/9AQ9fLEbcPlXBwa970jm6WwHaUVpyAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:59:31.049897Z"},"content_sha256":"47d7babfea6f595c28cb8f62b1089665bdf83486426d602e13c73a6841ea6539","schema_version":"1.0","event_id":"sha256:47d7babfea6f595c28cb8f62b1089665bdf83486426d602e13c73a6841ea6539"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:CTRARI2NDFUTP3NAQMJE46LTRI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal Polynomials for Severi Degrees of Toric Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Federico Ardila, Florian Block","submitted_at":"2010-12-23T21:17:11Z","abstract_excerpt":"The Severi variety parameterizes plane curves of degree d with delta nodes. Its degree is called the Severi degree. For large enough d, the Severi degrees coincide with the Gromov-Witten invariants of P^2. Fomin and Mikhalkin (2009) proved the 1995 conjecture that, for fixed delta, Severi degrees are eventually polynomial in d.\n  In this paper, we study the Severi varieties corresponding to a large family of toric surfaces. We prove the analogous result that the Severi degrees are eventually polynomial as a function of the multidegree. More surprisingly, we show that the Severi degrees are als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5305","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":"2026-05-18T03:56:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CNnnxP0qAJXPmgp9JqQtpLsW9/JATdIoV5bCJltLqAQg/34rDdrPXM7ypjov+03g7HpuwaJDglMYEfN5OUq1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:59:31.050249Z"},"content_sha256":"9f11f52cd2e12305456fa1963b9b3e912cc0402bfc2882dd9537670d77df4dbd","schema_version":"1.0","event_id":"sha256:9f11f52cd2e12305456fa1963b9b3e912cc0402bfc2882dd9537670d77df4dbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CTRARI2NDFUTP3NAQMJE46LTRI/bundle.json","state_url":"https://pith.science/pith/CTRARI2NDFUTP3NAQMJE46LTRI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CTRARI2NDFUTP3NAQMJE46LTRI/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":"2026-06-23T17:59:31Z","links":{"resolver":"https://pith.science/pith/CTRARI2NDFUTP3NAQMJE46LTRI","bundle":"https://pith.science/pith/CTRARI2NDFUTP3NAQMJE46LTRI/bundle.json","state":"https://pith.science/pith/CTRARI2NDFUTP3NAQMJE46LTRI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CTRARI2NDFUTP3NAQMJE46LTRI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CTRARI2NDFUTP3NAQMJE46LTRI","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":"134ae295c8a53603d2927a1c3da648fabe4811b8a52f57bb4366d82ea8b5c63a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-23T21:17:11Z","title_canon_sha256":"76f37417290b61854f31d2fd875d982369e709ebbc76d128e0e041003aaf8fa2"},"schema_version":"1.0","source":{"id":"1012.5305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5305","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5305v2","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5305","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"pith_short_12","alias_value":"CTRARI2NDFUT","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CTRARI2NDFUTP3NA","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CTRARI2N","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:9f11f52cd2e12305456fa1963b9b3e912cc0402bfc2882dd9537670d77df4dbd","target":"graph","created_at":"2026-05-18T03:56:46Z","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":"The Severi variety parameterizes plane curves of degree d with delta nodes. Its degree is called the Severi degree. For large enough d, the Severi degrees coincide with the Gromov-Witten invariants of P^2. Fomin and Mikhalkin (2009) proved the 1995 conjecture that, for fixed delta, Severi degrees are eventually polynomial in d.\n  In this paper, we study the Severi varieties corresponding to a large family of toric surfaces. We prove the analogous result that the Severi degrees are eventually polynomial as a function of the multidegree. More surprisingly, we show that the Severi degrees are als","authors_text":"Federico Ardila, Florian Block","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-23T21:17:11Z","title":"Universal Polynomials for Severi Degrees of Toric Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5305","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":"sha256:47d7babfea6f595c28cb8f62b1089665bdf83486426d602e13c73a6841ea6539","target":"record","created_at":"2026-05-18T03:56:46Z","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":"134ae295c8a53603d2927a1c3da648fabe4811b8a52f57bb4366d82ea8b5c63a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-23T21:17:11Z","title_canon_sha256":"76f37417290b61854f31d2fd875d982369e709ebbc76d128e0e041003aaf8fa2"},"schema_version":"1.0","source":{"id":"1012.5305","kind":"arxiv","version":2}},"canonical_sha256":"14e208a34d196937eda083124e79738a2d6dd3d48c5b7540485a3a0b814e8764","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14e208a34d196937eda083124e79738a2d6dd3d48c5b7540485a3a0b814e8764","first_computed_at":"2026-05-18T03:56:46.315222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:46.315222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4z/FgUlQXXMSMJh/NIoO2DBY62lwEGSI4AWWbOAyu27PoAnxd8jFDM5F9rsiHs0Kn9RerSLyiwJMQNu3FqKeAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:46.315772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47d7babfea6f595c28cb8f62b1089665bdf83486426d602e13c73a6841ea6539","sha256:9f11f52cd2e12305456fa1963b9b3e912cc0402bfc2882dd9537670d77df4dbd"],"state_sha256":"82215d49dcdac1f9e985b2879ca7b934c23b0d732f6b9abcb13f2eeeeaab51e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qK5fcq/2Qqig8DjdAEovsmLygia/Kj7bXgKan+vEjTHy4V+HfyJ3PCdmVFyyryBY5nOYuP41b47We/POc9K5CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:59:31.052223Z","bundle_sha256":"b24ac341e6478cb52c48c383ee141d592065adc4469f9504596140d095ebb317"}}