{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6CTXZOFDZ5PTA5UIHBXZFUEKLU","short_pith_number":"pith:6CTXZOFD","canonical_record":{"source":{"id":"1205.1773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-08T19:04:12Z","cross_cats_sorted":[],"title_canon_sha256":"e28876f81e55a2d9495e736651f7f24778ab47b11f23ccbc9e3091a3da47e305","abstract_canon_sha256":"698e121a60b6e232aca991ac37ec2c0bba99e1c692eaec060efd36f0c6b95809"},"schema_version":"1.0"},"canonical_sha256":"f0a77cb8a3cf5f307688386f92d08a5d0eb65868223bd1746d4bedc86a0bc13a","source":{"kind":"arxiv","id":"1205.1773","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1773","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1773v1","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1773","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"6CTXZOFDZ5PT","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6CTXZOFDZ5PTA5UI","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6CTXZOFD","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6CTXZOFDZ5PTA5UIHBXZFUEKLU","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-08T19:04:12Z","cross_cats_sorted":[],"title_canon_sha256":"e28876f81e55a2d9495e736651f7f24778ab47b11f23ccbc9e3091a3da47e305","abstract_canon_sha256":"698e121a60b6e232aca991ac37ec2c0bba99e1c692eaec060efd36f0c6b95809"},"schema_version":"1.0"},"canonical_sha256":"f0a77cb8a3cf5f307688386f92d08a5d0eb65868223bd1746d4bedc86a0bc13a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:09.007621Z","signature_b64":"OY/ZMXJGgAhCvBlxbHMIUa/mui/rI82bgbIEoeR6bfuvnOghnAX1GRakR8EHCaVJ59LiJ2v7Zptk5zDzc4S4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0a77cb8a3cf5f307688386f92d08a5d0eb65868223bd1746d4bedc86a0bc13a","last_reissued_at":"2026-05-18T03:56:09.006790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:09.006790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1773","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":"2026-05-18T03:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ifL3pdpJXBABPZVO1LznXnmhxKQYnVDSDbvOO0TlT93BnrzKA4DL49aYmKFe6axa/nMkYp+8bz1ChNF6tEmdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:27:28.169055Z"},"content_sha256":"8f0de97e5073366c630e3e055cb27db1b2377d2aeeef217115b26f293b0a9b81","schema_version":"1.0","event_id":"sha256:8f0de97e5073366c630e3e055cb27db1b2377d2aeeef217115b26f293b0a9b81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6CTXZOFDZ5PTA5UIHBXZFUEKLU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New methods for determining speciality of linear systems based at fat points in P^n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Stepan Paul","submitted_at":"2012-05-08T19:04:12Z","abstract_excerpt":"In this paper we develop techniques for determining the dimension of linear systems of divisors based at a collection of general fat points in P^n by partitioning the monomial basis for the vector space of global sections of O(d). The methods we develop can be viewed as extensions of those developed by Dumnicki. We apply these techniques to produce new lower bounds on multi-point Seshadri constants of P^2 and to provide a new proof of a known result confirming the perfect-power cases of Iarrobino's analogue to Nagata's Conjecture in higher dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1773","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":"2026-05-18T03:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gencNAvC9Yf6EvkpHabKKcNFFW2KSWqpMGbvHR/ADsDn8zuQw7M+eQEF2lDDm4HloLd7eC0G4Ttuse/yowSlAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:27:28.169748Z"},"content_sha256":"b4fe9cc53ee1219a5449d99544364864bc3a92175d2c67e32dccde135991cfb1","schema_version":"1.0","event_id":"sha256:b4fe9cc53ee1219a5449d99544364864bc3a92175d2c67e32dccde135991cfb1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6CTXZOFDZ5PTA5UIHBXZFUEKLU/bundle.json","state_url":"https://pith.science/pith/6CTXZOFDZ5PTA5UIHBXZFUEKLU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6CTXZOFDZ5PTA5UIHBXZFUEKLU/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":"2026-06-08T15:27:28Z","links":{"resolver":"https://pith.science/pith/6CTXZOFDZ5PTA5UIHBXZFUEKLU","bundle":"https://pith.science/pith/6CTXZOFDZ5PTA5UIHBXZFUEKLU/bundle.json","state":"https://pith.science/pith/6CTXZOFDZ5PTA5UIHBXZFUEKLU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6CTXZOFDZ5PTA5UIHBXZFUEKLU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6CTXZOFDZ5PTA5UIHBXZFUEKLU","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":"698e121a60b6e232aca991ac37ec2c0bba99e1c692eaec060efd36f0c6b95809","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-08T19:04:12Z","title_canon_sha256":"e28876f81e55a2d9495e736651f7f24778ab47b11f23ccbc9e3091a3da47e305"},"schema_version":"1.0","source":{"id":"1205.1773","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1773","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1773v1","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1773","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"6CTXZOFDZ5PT","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6CTXZOFDZ5PTA5UI","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6CTXZOFD","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:b4fe9cc53ee1219a5449d99544364864bc3a92175d2c67e32dccde135991cfb1","target":"graph","created_at":"2026-05-18T03:56:09Z","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 develop techniques for determining the dimension of linear systems of divisors based at a collection of general fat points in P^n by partitioning the monomial basis for the vector space of global sections of O(d). The methods we develop can be viewed as extensions of those developed by Dumnicki. We apply these techniques to produce new lower bounds on multi-point Seshadri constants of P^2 and to provide a new proof of a known result confirming the perfect-power cases of Iarrobino's analogue to Nagata's Conjecture in higher dimension.","authors_text":"Stepan Paul","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-08T19:04:12Z","title":"New methods for determining speciality of linear systems based at fat points in P^n"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1773","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":"sha256:8f0de97e5073366c630e3e055cb27db1b2377d2aeeef217115b26f293b0a9b81","target":"record","created_at":"2026-05-18T03:56:09Z","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":"698e121a60b6e232aca991ac37ec2c0bba99e1c692eaec060efd36f0c6b95809","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-08T19:04:12Z","title_canon_sha256":"e28876f81e55a2d9495e736651f7f24778ab47b11f23ccbc9e3091a3da47e305"},"schema_version":"1.0","source":{"id":"1205.1773","kind":"arxiv","version":1}},"canonical_sha256":"f0a77cb8a3cf5f307688386f92d08a5d0eb65868223bd1746d4bedc86a0bc13a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0a77cb8a3cf5f307688386f92d08a5d0eb65868223bd1746d4bedc86a0bc13a","first_computed_at":"2026-05-18T03:56:09.006790Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:09.006790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OY/ZMXJGgAhCvBlxbHMIUa/mui/rI82bgbIEoeR6bfuvnOghnAX1GRakR8EHCaVJ59LiJ2v7Zptk5zDzc4S4Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:09.007621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1773","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f0de97e5073366c630e3e055cb27db1b2377d2aeeef217115b26f293b0a9b81","sha256:b4fe9cc53ee1219a5449d99544364864bc3a92175d2c67e32dccde135991cfb1"],"state_sha256":"cccaf468bca8da9145086cc87766cd2d79a365f4c5fdf7f700216a770e9da8d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l3vma6I8lEgSnfdWoaa5tXHZzEhCZGbaQ/3NqwbIaGjdVXTNYee96ybJslY1iP+ftRF+pc54QFyG90kL/MgdBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T15:27:28.173544Z","bundle_sha256":"1c6888f11d9d3fce439d69aa557638da76e294d45c9b2dbe5c003b66611870af"}}