{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:I3MNTRPRXMDELTGDWCVKVUFMQR","short_pith_number":"pith:I3MNTRPR","canonical_record":{"source":{"id":"1907.11427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-07-26T08:32:50Z","cross_cats_sorted":[],"title_canon_sha256":"3fa488ba7e047a27a998b779a4427d3306e550db6fed0966a68a95f28e05eb41","abstract_canon_sha256":"062dfb0ab9953e0d12cfa9376fe742b2fe9e16aefd9e21a7b8688681736bc1d9"},"schema_version":"1.0"},"canonical_sha256":"46d8d9c5f1bb0645ccc3b0aaaad0ac846919bb55f3b44bab7d652b2ceb880122","source":{"kind":"arxiv","id":"1907.11427","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.11427","created_at":"2026-05-17T23:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1907.11427v1","created_at":"2026-05-17T23:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11427","created_at":"2026-05-17T23:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"I3MNTRPRXMDE","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"I3MNTRPRXMDELTGD","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"I3MNTRPR","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:I3MNTRPRXMDELTGDWCVKVUFMQR","target":"record","payload":{"canonical_record":{"source":{"id":"1907.11427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-07-26T08:32:50Z","cross_cats_sorted":[],"title_canon_sha256":"3fa488ba7e047a27a998b779a4427d3306e550db6fed0966a68a95f28e05eb41","abstract_canon_sha256":"062dfb0ab9953e0d12cfa9376fe742b2fe9e16aefd9e21a7b8688681736bc1d9"},"schema_version":"1.0"},"canonical_sha256":"46d8d9c5f1bb0645ccc3b0aaaad0ac846919bb55f3b44bab7d652b2ceb880122","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:29.113507Z","signature_b64":"yFjLNm8rKLPPB7/Wr0aaHdS+yuL+rdOqSJE5mbJjRHXrhtRdHt0zyOcLO6Z4jl1tsZSCZlYTD/ldNTUit1r4Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46d8d9c5f1bb0645ccc3b0aaaad0ac846919bb55f3b44bab7d652b2ceb880122","last_reissued_at":"2026-05-17T23:39:29.112829Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:29.112829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.11427","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":"2026-05-17T23:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FGMGsrHZr2MSLKxylRnNkkpt1MyRRtzZhaDiHjmBQZNJsOcuNrFHhYcj3a9etrC2oI1vhwEVUoLFJys6MJqjDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:26:08.278405Z"},"content_sha256":"c90cf356b85adb875d1a8ad974ad2944365617ef4329debe25ba321cc37bef4a","schema_version":"1.0","event_id":"sha256:c90cf356b85adb875d1a8ad974ad2944365617ef4329debe25ba321cc37bef4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:I3MNTRPRXMDELTGDWCVKVUFMQR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Castelnuovo-Mumford regularity and related invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ngo Viet Trung","submitted_at":"2019-07-26T08:32:50Z","abstract_excerpt":"These notes are an introduction to some basic aspects of the Castelnuovo-Mumford regularity and related topics such as weak regularity, a*-invariant and partial regularities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11427","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":"2026-05-17T23:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CB44x7XhNjwLq7Jwd2vSoNe6GxzWzodU7ng4E825gI01fh+fNOruE5RajyoJY0YIsIvNNBXOUuIMI75DvoeWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:26:08.279044Z"},"content_sha256":"5fca2a0bf5871d59387d55b48d346e45172c615f36dc56917d513c98b0f16c38","schema_version":"1.0","event_id":"sha256:5fca2a0bf5871d59387d55b48d346e45172c615f36dc56917d513c98b0f16c38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I3MNTRPRXMDELTGDWCVKVUFMQR/bundle.json","state_url":"https://pith.science/pith/I3MNTRPRXMDELTGDWCVKVUFMQR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I3MNTRPRXMDELTGDWCVKVUFMQR/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":"2026-05-27T19:26:08Z","links":{"resolver":"https://pith.science/pith/I3MNTRPRXMDELTGDWCVKVUFMQR","bundle":"https://pith.science/pith/I3MNTRPRXMDELTGDWCVKVUFMQR/bundle.json","state":"https://pith.science/pith/I3MNTRPRXMDELTGDWCVKVUFMQR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I3MNTRPRXMDELTGDWCVKVUFMQR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:I3MNTRPRXMDELTGDWCVKVUFMQR","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":"062dfb0ab9953e0d12cfa9376fe742b2fe9e16aefd9e21a7b8688681736bc1d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-07-26T08:32:50Z","title_canon_sha256":"3fa488ba7e047a27a998b779a4427d3306e550db6fed0966a68a95f28e05eb41"},"schema_version":"1.0","source":{"id":"1907.11427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.11427","created_at":"2026-05-17T23:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1907.11427v1","created_at":"2026-05-17T23:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11427","created_at":"2026-05-17T23:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"I3MNTRPRXMDE","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"I3MNTRPRXMDELTGD","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"I3MNTRPR","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:5fca2a0bf5871d59387d55b48d346e45172c615f36dc56917d513c98b0f16c38","target":"graph","created_at":"2026-05-17T23:39:29Z","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":"These notes are an introduction to some basic aspects of the Castelnuovo-Mumford regularity and related topics such as weak regularity, a*-invariant and partial regularities.","authors_text":"Ngo Viet Trung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-07-26T08:32:50Z","title":"Castelnuovo-Mumford regularity and related invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11427","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:c90cf356b85adb875d1a8ad974ad2944365617ef4329debe25ba321cc37bef4a","target":"record","created_at":"2026-05-17T23:39:29Z","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":"062dfb0ab9953e0d12cfa9376fe742b2fe9e16aefd9e21a7b8688681736bc1d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-07-26T08:32:50Z","title_canon_sha256":"3fa488ba7e047a27a998b779a4427d3306e550db6fed0966a68a95f28e05eb41"},"schema_version":"1.0","source":{"id":"1907.11427","kind":"arxiv","version":1}},"canonical_sha256":"46d8d9c5f1bb0645ccc3b0aaaad0ac846919bb55f3b44bab7d652b2ceb880122","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46d8d9c5f1bb0645ccc3b0aaaad0ac846919bb55f3b44bab7d652b2ceb880122","first_computed_at":"2026-05-17T23:39:29.112829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:29.112829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yFjLNm8rKLPPB7/Wr0aaHdS+yuL+rdOqSJE5mbJjRHXrhtRdHt0zyOcLO6Z4jl1tsZSCZlYTD/ldNTUit1r4Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:29.113507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.11427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c90cf356b85adb875d1a8ad974ad2944365617ef4329debe25ba321cc37bef4a","sha256:5fca2a0bf5871d59387d55b48d346e45172c615f36dc56917d513c98b0f16c38"],"state_sha256":"5246cb8942122122d97e8aeb41887479b1c70f74f99a338f27f3329da33a825a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OxW56tkrIrRTbAU6gpY8t2Z8V0c40bDUivyh2hNP/50LNSRs72LKAJAFTpw+YG+oDdPznPVCAeTJYYVtSSLcBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:26:08.282243Z","bundle_sha256":"47005db4c3afd715932907bf08ac79dd4c961a3c1bbb92374e497d5027c7a7e2"}}