{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:R57ZM6SWWVWLN3IJYP632CN2PZ","short_pith_number":"pith:R57ZM6SW","canonical_record":{"source":{"id":"0810.1372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-10-08T07:26:08Z","cross_cats_sorted":[],"title_canon_sha256":"a183d50b60737b6e62779414df58e5b986fd695a06e6b0bb0e2d96a955b2e880","abstract_canon_sha256":"a8fa130431cfecd6e2602bfe14bffe425ea07559f05db26296937afeee25bf61"},"schema_version":"1.0"},"canonical_sha256":"8f7f967a56b56cb6ed09c3fdbd09ba7e57ce8ee8746cd19e35907f72301ae717","source":{"kind":"arxiv","id":"0810.1372","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.1372","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"arxiv_version","alias_value":"0810.1372v1","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.1372","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"pith_short_12","alias_value":"R57ZM6SWWVWL","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"R57ZM6SWWVWLN3IJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"R57ZM6SW","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:R57ZM6SWWVWLN3IJYP632CN2PZ","target":"record","payload":{"canonical_record":{"source":{"id":"0810.1372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-10-08T07:26:08Z","cross_cats_sorted":[],"title_canon_sha256":"a183d50b60737b6e62779414df58e5b986fd695a06e6b0bb0e2d96a955b2e880","abstract_canon_sha256":"a8fa130431cfecd6e2602bfe14bffe425ea07559f05db26296937afeee25bf61"},"schema_version":"1.0"},"canonical_sha256":"8f7f967a56b56cb6ed09c3fdbd09ba7e57ce8ee8746cd19e35907f72301ae717","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:11.801134Z","signature_b64":"BLg0QOFYNlmzfrFDtG7Q4cYo0BFGJhFROIvqB5BD7Gh15NX04WKk0ss8hKdwabeefYNbQJrXiZk/Dw7CfIegBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f7f967a56b56cb6ed09c3fdbd09ba7e57ce8ee8746cd19e35907f72301ae717","last_reissued_at":"2026-05-18T04:23:11.800671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:11.800671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.1372","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:23:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I1MD3b4xgxL8n01ndhRktzj8qzpAff8B5MMYJ8tlsTMgRWaEg+nvbMfN88SYJYDLHQ4GcDfMVHqdnNZa2/hLCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T09:54:32.992861Z"},"content_sha256":"74365765938ed8f80de6e2c995b8d7652d5c2d2fdc7c972dedb679051c5ec808","schema_version":"1.0","event_id":"sha256:74365765938ed8f80de6e2c995b8d7652d5c2d2fdc7c972dedb679051c5ec808"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:R57ZM6SWWVWLN3IJYP632CN2PZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Postulation of general quartuple fat point schemes in P^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Edoardo Ballico, Maria Chiara Brambilla","submitted_at":"2008-10-08T07:26:08Z","abstract_excerpt":"We study the postulation of a general union $Y$ of double, triple, and quartuple points of $\\mathbb{P}^3$. We prove that $Y$ has the expected postulation in degree $d\\ge 41$, using the Horace differential lemma. We also discuss the cases of low degree with the aid of computer algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1372","kind":"arxiv","version":1},"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":"2026-05-18T04:23:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E/OfNCsRkrXm7vsa1WUQGDX0rLYBt5EPsofyIxG7A+9i7EmxS+JACO2G6Qwxb7+tYNc6UqdtAo6UmCxQy72YAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T09:54:32.993200Z"},"content_sha256":"b133873049a43e4e1ee0670d841a6c21c30f49b6edcb536a9b88eed8cbfeb658","schema_version":"1.0","event_id":"sha256:b133873049a43e4e1ee0670d841a6c21c30f49b6edcb536a9b88eed8cbfeb658"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R57ZM6SWWVWLN3IJYP632CN2PZ/bundle.json","state_url":"https://pith.science/pith/R57ZM6SWWVWLN3IJYP632CN2PZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R57ZM6SWWVWLN3IJYP632CN2PZ/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":"2026-06-20T09:54:32Z","links":{"resolver":"https://pith.science/pith/R57ZM6SWWVWLN3IJYP632CN2PZ","bundle":"https://pith.science/pith/R57ZM6SWWVWLN3IJYP632CN2PZ/bundle.json","state":"https://pith.science/pith/R57ZM6SWWVWLN3IJYP632CN2PZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R57ZM6SWWVWLN3IJYP632CN2PZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:R57ZM6SWWVWLN3IJYP632CN2PZ","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":"a8fa130431cfecd6e2602bfe14bffe425ea07559f05db26296937afeee25bf61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-10-08T07:26:08Z","title_canon_sha256":"a183d50b60737b6e62779414df58e5b986fd695a06e6b0bb0e2d96a955b2e880"},"schema_version":"1.0","source":{"id":"0810.1372","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.1372","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"arxiv_version","alias_value":"0810.1372v1","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.1372","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"pith_short_12","alias_value":"R57ZM6SWWVWL","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"R57ZM6SWWVWLN3IJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"R57ZM6SW","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:b133873049a43e4e1ee0670d841a6c21c30f49b6edcb536a9b88eed8cbfeb658","target":"graph","created_at":"2026-05-18T04:23:11Z","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":"We study the postulation of a general union $Y$ of double, triple, and quartuple points of $\\mathbb{P}^3$. We prove that $Y$ has the expected postulation in degree $d\\ge 41$, using the Horace differential lemma. We also discuss the cases of low degree with the aid of computer algebra.","authors_text":"Edoardo Ballico, Maria Chiara Brambilla","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-10-08T07:26:08Z","title":"Postulation of general quartuple fat point schemes in P^3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1372","kind":"arxiv","version":1},"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":"sha256:74365765938ed8f80de6e2c995b8d7652d5c2d2fdc7c972dedb679051c5ec808","target":"record","created_at":"2026-05-18T04:23:11Z","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":"a8fa130431cfecd6e2602bfe14bffe425ea07559f05db26296937afeee25bf61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-10-08T07:26:08Z","title_canon_sha256":"a183d50b60737b6e62779414df58e5b986fd695a06e6b0bb0e2d96a955b2e880"},"schema_version":"1.0","source":{"id":"0810.1372","kind":"arxiv","version":1}},"canonical_sha256":"8f7f967a56b56cb6ed09c3fdbd09ba7e57ce8ee8746cd19e35907f72301ae717","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f7f967a56b56cb6ed09c3fdbd09ba7e57ce8ee8746cd19e35907f72301ae717","first_computed_at":"2026-05-18T04:23:11.800671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:11.800671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BLg0QOFYNlmzfrFDtG7Q4cYo0BFGJhFROIvqB5BD7Gh15NX04WKk0ss8hKdwabeefYNbQJrXiZk/Dw7CfIegBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:11.801134Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.1372","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74365765938ed8f80de6e2c995b8d7652d5c2d2fdc7c972dedb679051c5ec808","sha256:b133873049a43e4e1ee0670d841a6c21c30f49b6edcb536a9b88eed8cbfeb658"],"state_sha256":"919707bd2f8bcec8947a0be4459c66b5ca8e2d50c4bae3e3499687b7a48dad29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WGeBOXRC+8Gfu/q32s/ryzmnKFh8cM2FoOoTvKh8JEXXP5GQox22f6zk/wuzDI+1B8wfgNMKz8hNu5R1cX5wDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T09:54:32.995042Z","bundle_sha256":"365ac311f3d8a04ff7025bef133e166f3ffd08e1086870ff881bc9ebb346fd9e"}}