{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MEWXORBMXGHXNAR262WQDG2SCP","short_pith_number":"pith:MEWXORBM","canonical_record":{"source":{"id":"1907.10666","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-07-23T02:57:17Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"5b3efa8fb92fac4345d6e63cd0bc538fc1a0ea5113faf063523c8d7289c7108e","abstract_canon_sha256":"d77840e9e88e8fec73b94faabc066456c939defa0e8677cf196f2292ff78796e"},"schema_version":"1.0"},"canonical_sha256":"612d77442cb98f76823af6ad019b5213e5c7eca4646547145fe1606c867b154f","source":{"kind":"arxiv","id":"1907.10666","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.10666","created_at":"2026-05-17T23:39:34Z"},{"alias_kind":"arxiv_version","alias_value":"1907.10666v1","created_at":"2026-05-17T23:39:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.10666","created_at":"2026-05-17T23:39:34Z"},{"alias_kind":"pith_short_12","alias_value":"MEWXORBMXGHX","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MEWXORBMXGHXNAR2","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MEWXORBM","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MEWXORBMXGHXNAR262WQDG2SCP","target":"record","payload":{"canonical_record":{"source":{"id":"1907.10666","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-07-23T02:57:17Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"5b3efa8fb92fac4345d6e63cd0bc538fc1a0ea5113faf063523c8d7289c7108e","abstract_canon_sha256":"d77840e9e88e8fec73b94faabc066456c939defa0e8677cf196f2292ff78796e"},"schema_version":"1.0"},"canonical_sha256":"612d77442cb98f76823af6ad019b5213e5c7eca4646547145fe1606c867b154f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:34.856523Z","signature_b64":"z8+9jsxkd7t8r+2R0DW8gwRqK678nnDF8nzqVit5KJxfKy8TaT2Bto/vFUh3o9X8HaB3po9oLwFSkNBxmrfNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"612d77442cb98f76823af6ad019b5213e5c7eca4646547145fe1606c867b154f","last_reissued_at":"2026-05-17T23:39:34.855824Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:34.855824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.10666","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":"2026-05-17T23:39:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WmLwATl4JdY0P5KmoppYuRMaWn2nfEA9v3Uh8ce9EpwcsT14++Nrr02myleMKaa5EYXdCG7+5q67CwY8vg62Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:06:39.885534Z"},"content_sha256":"d53d46480c7ce7584bd0a45959e484d7cba1731b99e99ffc98c483affaf67b10","schema_version":"1.0","event_id":"sha256:d53d46480c7ce7584bd0a45959e484d7cba1731b99e99ffc98c483affaf67b10"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MEWXORBMXGHXNAR262WQDG2SCP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the colength of fractional ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Abramo Hefez, Edison Marcavillaca Ni\\~no de Guzm\\'an","submitted_at":"2019-07-23T02:57:17Z","abstract_excerpt":"The main result in this paper is to supply a recursive formula, on the number of minimal primes, for the colength of a fractional ideal in terms of the maximal points of the value set of the ideal itself. The fractional ideals are taken in the class of complete admissible rings, a more general class of rings than those of algebroid curves. For such rings with two or three minimal primes, a closed formula for that colength is provided, so improving results by Barucci, D'Anna and Fr\\\"oberg."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10666","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":"2026-05-17T23:39:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P7gdgZGGfThtYMbUqBq6lkwzNFlxNHP+p0heqif7eCpiAzgPvlNgib1wiwKbOAZg53i/8X5TJA55EsdNwPMnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:06:39.885883Z"},"content_sha256":"d8466b0bf06786dd044a9e4969c54f37d1c8b3a0d8a2b7107087acb0d70ac345","schema_version":"1.0","event_id":"sha256:d8466b0bf06786dd044a9e4969c54f37d1c8b3a0d8a2b7107087acb0d70ac345"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MEWXORBMXGHXNAR262WQDG2SCP/bundle.json","state_url":"https://pith.science/pith/MEWXORBMXGHXNAR262WQDG2SCP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MEWXORBMXGHXNAR262WQDG2SCP/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":"2026-06-10T18:06:39Z","links":{"resolver":"https://pith.science/pith/MEWXORBMXGHXNAR262WQDG2SCP","bundle":"https://pith.science/pith/MEWXORBMXGHXNAR262WQDG2SCP/bundle.json","state":"https://pith.science/pith/MEWXORBMXGHXNAR262WQDG2SCP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MEWXORBMXGHXNAR262WQDG2SCP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MEWXORBMXGHXNAR262WQDG2SCP","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":"d77840e9e88e8fec73b94faabc066456c939defa0e8677cf196f2292ff78796e","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-07-23T02:57:17Z","title_canon_sha256":"5b3efa8fb92fac4345d6e63cd0bc538fc1a0ea5113faf063523c8d7289c7108e"},"schema_version":"1.0","source":{"id":"1907.10666","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.10666","created_at":"2026-05-17T23:39:34Z"},{"alias_kind":"arxiv_version","alias_value":"1907.10666v1","created_at":"2026-05-17T23:39:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.10666","created_at":"2026-05-17T23:39:34Z"},{"alias_kind":"pith_short_12","alias_value":"MEWXORBMXGHX","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MEWXORBMXGHXNAR2","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MEWXORBM","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:d8466b0bf06786dd044a9e4969c54f37d1c8b3a0d8a2b7107087acb0d70ac345","target":"graph","created_at":"2026-05-17T23:39:34Z","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":"The main result in this paper is to supply a recursive formula, on the number of minimal primes, for the colength of a fractional ideal in terms of the maximal points of the value set of the ideal itself. The fractional ideals are taken in the class of complete admissible rings, a more general class of rings than those of algebroid curves. For such rings with two or three minimal primes, a closed formula for that colength is provided, so improving results by Barucci, D'Anna and Fr\\\"oberg.","authors_text":"Abramo Hefez, Edison Marcavillaca Ni\\~no de Guzm\\'an","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-07-23T02:57:17Z","title":"On the colength of fractional ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10666","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:d53d46480c7ce7584bd0a45959e484d7cba1731b99e99ffc98c483affaf67b10","target":"record","created_at":"2026-05-17T23:39:34Z","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":"d77840e9e88e8fec73b94faabc066456c939defa0e8677cf196f2292ff78796e","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-07-23T02:57:17Z","title_canon_sha256":"5b3efa8fb92fac4345d6e63cd0bc538fc1a0ea5113faf063523c8d7289c7108e"},"schema_version":"1.0","source":{"id":"1907.10666","kind":"arxiv","version":1}},"canonical_sha256":"612d77442cb98f76823af6ad019b5213e5c7eca4646547145fe1606c867b154f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"612d77442cb98f76823af6ad019b5213e5c7eca4646547145fe1606c867b154f","first_computed_at":"2026-05-17T23:39:34.855824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:34.855824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z8+9jsxkd7t8r+2R0DW8gwRqK678nnDF8nzqVit5KJxfKy8TaT2Bto/vFUh3o9X8HaB3po9oLwFSkNBxmrfNDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:34.856523Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.10666","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d53d46480c7ce7584bd0a45959e484d7cba1731b99e99ffc98c483affaf67b10","sha256:d8466b0bf06786dd044a9e4969c54f37d1c8b3a0d8a2b7107087acb0d70ac345"],"state_sha256":"25d29610573554bd5ef50f4bca134033ef4d57b01f0751a7802fa221d469bd7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xVE9Fyur+w+ZaoaV7SU01YElD5dUrAOkn2xVncxR2u/xa7p30mkH6T4W41fOfn8tyXLRwmJKBNka9dzamMpECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T18:06:39.888032Z","bundle_sha256":"de029989485e5bf15a25b4ef7df591a73a93182ec0bbc24bc865d1ac89664080"}}