{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:34FZSGDSO24QVKLFZJ2WRZVSFO","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":"b23da22e76427f046b7f6d34b46ea21840f89b36b2a86da10e61401970d5e4fa","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-03-28T13:34:45Z","title_canon_sha256":"d575818b41e29205bb07ed88e9733dc24c8bccca92b9e9617bb3d1b10b36fd9f"},"schema_version":"1.0","source":{"id":"0803.4113","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.4113","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"arxiv_version","alias_value":"0803.4113v3","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.4113","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"pith_short_12","alias_value":"34FZSGDSO24Q","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"34FZSGDSO24QVKLF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"34FZSGDS","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:72b454fd2cb43659a9582d19e594f99ecd1f527d75c1eb1c1108c43f3bfc357e","target":"graph","created_at":"2026-05-18T04:33:36Z","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":"A recent paper by the first and third authors together with Sabourin raised the question of what the possible Hilbert functions are for fat point subschemes of the form $2p_1+...+2p_r$, for all possible choices of $r$ distinct points in the projective plane. We study this problem for $r$ points in the plane over an algebraically closed field $k$ of arbitrary characteristic in case either $r \\le 8$ or the points lie on a (possibly reducible) conic. In either case, it follows from work of the second author that there are only finitely many configuration types of points, where our notion of confi","authors_text":"A.V. Geramita, B. Harbourne, J. Migliore","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-03-28T13:34:45Z","title":"Classifying Hilbert functions of fat point subschemes in $\\mathbb P^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.4113","kind":"arxiv","version":3},"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":"sha256:656f7973a501f26e5be17373c97706527efcf3a156b24619238f3f05cedb48fe","target":"record","created_at":"2026-05-18T04:33:36Z","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":"b23da22e76427f046b7f6d34b46ea21840f89b36b2a86da10e61401970d5e4fa","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-03-28T13:34:45Z","title_canon_sha256":"d575818b41e29205bb07ed88e9733dc24c8bccca92b9e9617bb3d1b10b36fd9f"},"schema_version":"1.0","source":{"id":"0803.4113","kind":"arxiv","version":3}},"canonical_sha256":"df0b99187276b90aa965ca7568e6b22b895391908fde3455702583c36ed7db0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df0b99187276b90aa965ca7568e6b22b895391908fde3455702583c36ed7db0a","first_computed_at":"2026-05-18T04:33:36.750156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:36.750156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xl7oSfd6rk4JGqjh9U+afrP3w35SODengeQKcKg9dmU7uxzt9Jyu+CvTv+KA6rogbAxf6NCNRjdP3kZub82ZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:36.750731Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.4113","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:656f7973a501f26e5be17373c97706527efcf3a156b24619238f3f05cedb48fe","sha256:72b454fd2cb43659a9582d19e594f99ecd1f527d75c1eb1c1108c43f3bfc357e"],"state_sha256":"cd52c0db9b1d8c9a03b52174f7992fd994664624ad1f423e5d9644ed8a59fb62"}