{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EUNRS2WRXAGPMINLOGVTCICCOF","short_pith_number":"pith:EUNRS2WR","canonical_record":{"source":{"id":"1308.6796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-30T17:00:18Z","cross_cats_sorted":[],"title_canon_sha256":"ba772a6babbeed86a14290e2e0c6956ade328c35d357fdfc994e728eadb56ba1","abstract_canon_sha256":"88e3559a50e7daeb3a7f938b7ee010a7acec6196584c7ab59b6e110a9d8902c5"},"schema_version":"1.0"},"canonical_sha256":"251b196ad1b80cf621ab71ab312042715561268c5a98afec4cf40cf5629de7fa","source":{"kind":"arxiv","id":"1308.6796","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6796","created_at":"2026-05-18T03:14:30Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6796v1","created_at":"2026-05-18T03:14:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6796","created_at":"2026-05-18T03:14:30Z"},{"alias_kind":"pith_short_12","alias_value":"EUNRS2WRXAGP","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EUNRS2WRXAGPMINL","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EUNRS2WR","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EUNRS2WRXAGPMINLOGVTCICCOF","target":"record","payload":{"canonical_record":{"source":{"id":"1308.6796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-30T17:00:18Z","cross_cats_sorted":[],"title_canon_sha256":"ba772a6babbeed86a14290e2e0c6956ade328c35d357fdfc994e728eadb56ba1","abstract_canon_sha256":"88e3559a50e7daeb3a7f938b7ee010a7acec6196584c7ab59b6e110a9d8902c5"},"schema_version":"1.0"},"canonical_sha256":"251b196ad1b80cf621ab71ab312042715561268c5a98afec4cf40cf5629de7fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:30.883967Z","signature_b64":"0xsCMLJ+oO7dYbA/erqW6vtOBl6t01FzogeBZhyZRrze3a5QTeJBDrMg8UY5TwcIcGr74qqNy75w3Ea6ykofCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"251b196ad1b80cf621ab71ab312042715561268c5a98afec4cf40cf5629de7fa","last_reissued_at":"2026-05-18T03:14:30.883289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:30.883289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.6796","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":"2026-05-18T03:14:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r2+HHdKsOwpEx+OJ4x7whqQlvf+B2Nzl0fFYqEtjzAqNouxRF6kjKWOhrkU4MRODaN9buyM/zbWq755/7WNLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:46:24.065279Z"},"content_sha256":"4e6a43ad41c57b827466ecd0f77bba1ba8c9f4ecfcf5af3044adc74666728abd","schema_version":"1.0","event_id":"sha256:4e6a43ad41c57b827466ecd0f77bba1ba8c9f4ecfcf5af3044adc74666728abd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EUNRS2WRXAGPMINLOGVTCICCOF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reduced and non-reduced linear spaces: Lines and points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Anthony V. Geramita, Enrico Carlini, Maria Virginia Catalisano","submitted_at":"2013-08-30T17:00:18Z","abstract_excerpt":"In this paper we consider the problem of determining the Hilbert function of schemes X of the proiective space P^n which are the generic union of s lines and one m-multiple point. We completely solve this problem for any s and m when n > 3. When n=3 we find several defective such schemes and conjecture that they are the only ones. We verify this conjecture in several cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6796","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":"2026-05-18T03:14:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hgUqXnmluhoxWnupTGqXnmyrVp+kDfFOXXrOSAtLj8bgswDZQYfAcY5U6JZBvy3tDrwyLPtafoscEJZIZJPiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:46:24.066016Z"},"content_sha256":"85479583b56851f48a254773a81b6b6d6473bd382b20ad101611804f88ea1c65","schema_version":"1.0","event_id":"sha256:85479583b56851f48a254773a81b6b6d6473bd382b20ad101611804f88ea1c65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EUNRS2WRXAGPMINLOGVTCICCOF/bundle.json","state_url":"https://pith.science/pith/EUNRS2WRXAGPMINLOGVTCICCOF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EUNRS2WRXAGPMINLOGVTCICCOF/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":"2026-06-11T22:46:24Z","links":{"resolver":"https://pith.science/pith/EUNRS2WRXAGPMINLOGVTCICCOF","bundle":"https://pith.science/pith/EUNRS2WRXAGPMINLOGVTCICCOF/bundle.json","state":"https://pith.science/pith/EUNRS2WRXAGPMINLOGVTCICCOF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EUNRS2WRXAGPMINLOGVTCICCOF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EUNRS2WRXAGPMINLOGVTCICCOF","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":"88e3559a50e7daeb3a7f938b7ee010a7acec6196584c7ab59b6e110a9d8902c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-30T17:00:18Z","title_canon_sha256":"ba772a6babbeed86a14290e2e0c6956ade328c35d357fdfc994e728eadb56ba1"},"schema_version":"1.0","source":{"id":"1308.6796","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6796","created_at":"2026-05-18T03:14:30Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6796v1","created_at":"2026-05-18T03:14:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6796","created_at":"2026-05-18T03:14:30Z"},{"alias_kind":"pith_short_12","alias_value":"EUNRS2WRXAGP","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EUNRS2WRXAGPMINL","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EUNRS2WR","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:85479583b56851f48a254773a81b6b6d6473bd382b20ad101611804f88ea1c65","target":"graph","created_at":"2026-05-18T03:14:30Z","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 this paper we consider the problem of determining the Hilbert function of schemes X of the proiective space P^n which are the generic union of s lines and one m-multiple point. We completely solve this problem for any s and m when n > 3. When n=3 we find several defective such schemes and conjecture that they are the only ones. We verify this conjecture in several cases.","authors_text":"Anthony V. Geramita, Enrico Carlini, Maria Virginia Catalisano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-30T17:00:18Z","title":"Reduced and non-reduced linear spaces: Lines and points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6796","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":"sha256:4e6a43ad41c57b827466ecd0f77bba1ba8c9f4ecfcf5af3044adc74666728abd","target":"record","created_at":"2026-05-18T03:14:30Z","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":"88e3559a50e7daeb3a7f938b7ee010a7acec6196584c7ab59b6e110a9d8902c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-30T17:00:18Z","title_canon_sha256":"ba772a6babbeed86a14290e2e0c6956ade328c35d357fdfc994e728eadb56ba1"},"schema_version":"1.0","source":{"id":"1308.6796","kind":"arxiv","version":1}},"canonical_sha256":"251b196ad1b80cf621ab71ab312042715561268c5a98afec4cf40cf5629de7fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"251b196ad1b80cf621ab71ab312042715561268c5a98afec4cf40cf5629de7fa","first_computed_at":"2026-05-18T03:14:30.883289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:30.883289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0xsCMLJ+oO7dYbA/erqW6vtOBl6t01FzogeBZhyZRrze3a5QTeJBDrMg8UY5TwcIcGr74qqNy75w3Ea6ykofCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:30.883967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6796","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e6a43ad41c57b827466ecd0f77bba1ba8c9f4ecfcf5af3044adc74666728abd","sha256:85479583b56851f48a254773a81b6b6d6473bd382b20ad101611804f88ea1c65"],"state_sha256":"807a8e8dc8d237851bfc072e27f4fedc152aa61a6576e51be44afea5be8d19d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IWueUSv7D2rSlPrKNRyCEzT/5z5BpT+abBKko7waUMbGz4MwWDelOxC3qf/eGLt6artPHbKUMukJLIIq/C52CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:46:24.069921Z","bundle_sha256":"f9e371403e902d6e7708460f8b10c4110ff8af63290efa98c48fdeb26b9dd21c"}}