{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:FSHL3AUP4IF5IV3ZZL332YY2TF","short_pith_number":"pith:FSHL3AUP","canonical_record":{"source":{"id":"math/0305242","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2003-05-16T16:33:22Z","cross_cats_sorted":["math.AG","math.SG"],"title_canon_sha256":"22fd13d84e11d4b9d07e49b6af759c642e69adbd256e64e1911b4e9d53527f61","abstract_canon_sha256":"04cdc7914c1e56c5c372373d324c1d756fbd9f19d2283f551328ca47d0a60d01"},"schema_version":"1.0"},"canonical_sha256":"2c8ebd828fe20bd45779caf7bd631a99453c55dc8b5aa6e455ec757bf294e69f","source":{"kind":"arxiv","id":"math/0305242","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0305242","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0305242v1","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0305242","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"FSHL3AUP4IF5","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"FSHL3AUP4IF5IV3Z","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"FSHL3AUP","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:FSHL3AUP4IF5IV3ZZL332YY2TF","target":"record","payload":{"canonical_record":{"source":{"id":"math/0305242","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2003-05-16T16:33:22Z","cross_cats_sorted":["math.AG","math.SG"],"title_canon_sha256":"22fd13d84e11d4b9d07e49b6af759c642e69adbd256e64e1911b4e9d53527f61","abstract_canon_sha256":"04cdc7914c1e56c5c372373d324c1d756fbd9f19d2283f551328ca47d0a60d01"},"schema_version":"1.0"},"canonical_sha256":"2c8ebd828fe20bd45779caf7bd631a99453c55dc8b5aa6e455ec757bf294e69f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:28.890088Z","signature_b64":"rfBx5sORvwCuDusmlY7gTAporeO7iYEzAN5fpeRPvfW+qfHuNUzubaH0kwn+5jhC0LZJd1IoDug4d421hhjUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c8ebd828fe20bd45779caf7bd631a99453c55dc8b5aa6e455ec757bf294e69f","last_reissued_at":"2026-05-18T01:05:28.889538Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:28.889538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0305242","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":"2026-05-18T01:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EjGhzNtjXezHE2k9JmUIr1Qvhq96Hzv6VPz79k9EQIWI4t8dmZPOLeaE/1zoJkKkNW81zJ6YzJcwMPmY8n2DBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T17:04:54.943784Z"},"content_sha256":"8a3464901bbb47430dcd08a48a053a0043ee46ae5dafe41b6abfe6bbdf8fc7a9","schema_version":"1.0","event_id":"sha256:8a3464901bbb47430dcd08a48a053a0043ee46ae5dafe41b6abfe6bbdf8fc7a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:FSHL3AUP4IF5IV3ZZL332YY2TF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Realization of finite Abelian groups by nets in P^2","license":"","headline":"","cross_cats":["math.AG","math.SG"],"primary_cat":"math.CO","authors_text":"Eugene), Sergey Yuzvinsky (Univ. of Oregon","submitted_at":"2003-05-16T16:33:22Z","abstract_excerpt":"In the paper, we study special configurations of lines and points in the complex projective plane, so called k-nets. We describe the role of these configurations in studies of cohomology on arrangement complements.\n Our most general result is the restriction on k - it can be only 3,4, or 5. The most interesting class of nets is formed by 3-nets that relate to finite geometries, latin squares, loops, etc.\n All known examples of 3-nets in P^2 realize finite Abelian groups.\n We study the problem what groups can be so realized. Our main result is that, except for groups with all invariant factors "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305242","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":"2026-05-18T01:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3WmYM6qlMhX1FHO7Fw/ePZqjOk9HMuWg2BGQR7/KTGO1OBLhhm2XOhWUXSA/xgKecVwNqfRwzUApCM+IjOsZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T17:04:54.944123Z"},"content_sha256":"ea78d46049ca4c6b26129512fa064d26222960c1a4461ec782a283d05f25d723","schema_version":"1.0","event_id":"sha256:ea78d46049ca4c6b26129512fa064d26222960c1a4461ec782a283d05f25d723"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FSHL3AUP4IF5IV3ZZL332YY2TF/bundle.json","state_url":"https://pith.science/pith/FSHL3AUP4IF5IV3ZZL332YY2TF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FSHL3AUP4IF5IV3ZZL332YY2TF/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":"2026-06-29T17:04:54Z","links":{"resolver":"https://pith.science/pith/FSHL3AUP4IF5IV3ZZL332YY2TF","bundle":"https://pith.science/pith/FSHL3AUP4IF5IV3ZZL332YY2TF/bundle.json","state":"https://pith.science/pith/FSHL3AUP4IF5IV3ZZL332YY2TF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FSHL3AUP4IF5IV3ZZL332YY2TF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:FSHL3AUP4IF5IV3ZZL332YY2TF","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":"04cdc7914c1e56c5c372373d324c1d756fbd9f19d2283f551328ca47d0a60d01","cross_cats_sorted":["math.AG","math.SG"],"license":"","primary_cat":"math.CO","submitted_at":"2003-05-16T16:33:22Z","title_canon_sha256":"22fd13d84e11d4b9d07e49b6af759c642e69adbd256e64e1911b4e9d53527f61"},"schema_version":"1.0","source":{"id":"math/0305242","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0305242","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0305242v1","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0305242","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"FSHL3AUP4IF5","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"FSHL3AUP4IF5IV3Z","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"FSHL3AUP","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:ea78d46049ca4c6b26129512fa064d26222960c1a4461ec782a283d05f25d723","target":"graph","created_at":"2026-05-18T01:05:28Z","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 the paper, we study special configurations of lines and points in the complex projective plane, so called k-nets. We describe the role of these configurations in studies of cohomology on arrangement complements.\n Our most general result is the restriction on k - it can be only 3,4, or 5. The most interesting class of nets is formed by 3-nets that relate to finite geometries, latin squares, loops, etc.\n All known examples of 3-nets in P^2 realize finite Abelian groups.\n We study the problem what groups can be so realized. Our main result is that, except for groups with all invariant factors ","authors_text":"Eugene), Sergey Yuzvinsky (Univ. of Oregon","cross_cats":["math.AG","math.SG"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2003-05-16T16:33:22Z","title":"Realization of finite Abelian groups by nets in P^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305242","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":"sha256:8a3464901bbb47430dcd08a48a053a0043ee46ae5dafe41b6abfe6bbdf8fc7a9","target":"record","created_at":"2026-05-18T01:05:28Z","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":"04cdc7914c1e56c5c372373d324c1d756fbd9f19d2283f551328ca47d0a60d01","cross_cats_sorted":["math.AG","math.SG"],"license":"","primary_cat":"math.CO","submitted_at":"2003-05-16T16:33:22Z","title_canon_sha256":"22fd13d84e11d4b9d07e49b6af759c642e69adbd256e64e1911b4e9d53527f61"},"schema_version":"1.0","source":{"id":"math/0305242","kind":"arxiv","version":1}},"canonical_sha256":"2c8ebd828fe20bd45779caf7bd631a99453c55dc8b5aa6e455ec757bf294e69f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c8ebd828fe20bd45779caf7bd631a99453c55dc8b5aa6e455ec757bf294e69f","first_computed_at":"2026-05-18T01:05:28.889538Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:28.889538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rfBx5sORvwCuDusmlY7gTAporeO7iYEzAN5fpeRPvfW+qfHuNUzubaH0kwn+5jhC0LZJd1IoDug4d421hhjUAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:28.890088Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0305242","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a3464901bbb47430dcd08a48a053a0043ee46ae5dafe41b6abfe6bbdf8fc7a9","sha256:ea78d46049ca4c6b26129512fa064d26222960c1a4461ec782a283d05f25d723"],"state_sha256":"be7158cf44e2bb8f7fd2c9bfd4bb9f91e9cb69c6ff7c0f9ee004fe1bbd687e6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QNKsDTy3tD0MDaaDxpQF1wTulSlHdEmvqGO9ZHhrIEQk+SAXhpjS26eTqwjmsIYFBBD1h1lqETtkwv/A3gYOCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T17:04:54.945985Z","bundle_sha256":"5cf4b58a6e77bb134ccaeaafe583749f75c5887a36dbee8fe82bb7ea31038dcc"}}