{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FMUIT3RPOMI2Q4R6Y5G64N3F4O","short_pith_number":"pith:FMUIT3RP","canonical_record":{"source":{"id":"1410.4233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-15T21:25:02Z","cross_cats_sorted":[],"title_canon_sha256":"c2e2d7260ee063d79584ac82a25bfe38e86f801a6631148d77dd71674e2c677f","abstract_canon_sha256":"308e173133fd0483f2334d05bee17dc183049e260d8794476137eb6985213fce"},"schema_version":"1.0"},"canonical_sha256":"2b2889ee2f7311a8723ec74dee3765e392e2e2018034bda52999fc8d646f1f0d","source":{"kind":"arxiv","id":"1410.4233","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4233","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4233v1","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4233","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"pith_short_12","alias_value":"FMUIT3RPOMI2","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FMUIT3RPOMI2Q4R6","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FMUIT3RP","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FMUIT3RPOMI2Q4R6Y5G64N3F4O","target":"record","payload":{"canonical_record":{"source":{"id":"1410.4233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-15T21:25:02Z","cross_cats_sorted":[],"title_canon_sha256":"c2e2d7260ee063d79584ac82a25bfe38e86f801a6631148d77dd71674e2c677f","abstract_canon_sha256":"308e173133fd0483f2334d05bee17dc183049e260d8794476137eb6985213fce"},"schema_version":"1.0"},"canonical_sha256":"2b2889ee2f7311a8723ec74dee3765e392e2e2018034bda52999fc8d646f1f0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:56.614243Z","signature_b64":"NHHU+nJ6dRLB32xrlscF9OkTqNVLpEHSc+aqfLPAtEmQ0NU0kGO4YhlKr3filP9dPx3+HDIXHU4DfBhXjDuBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b2889ee2f7311a8723ec74dee3765e392e2e2018034bda52999fc8d646f1f0d","last_reissued_at":"2026-05-18T02:39:56.613784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:56.613784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.4233","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":"2026-05-18T02:39:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RvcPC4gOR85cBNazaDjgs/skYfsgXehZpnXAXRqaM84pVwhuqYa9ubZm3WfFhf8l+agLiBp0Kkr87apdNbH/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:52:05.292607Z"},"content_sha256":"8898a3c888be2cb9c5c249e77a4e63d341b8e2a93b0ccdd6446f59ee2dd28b69","schema_version":"1.0","event_id":"sha256:8898a3c888be2cb9c5c249e77a4e63d341b8e2a93b0ccdd6446f59ee2dd28b69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FMUIT3RPOMI2Q4R6Y5G64N3F4O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds on the normal Hilbert coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alberto Corso, Claudia Polini, Maria Evelina Rossi","submitted_at":"2014-10-15T21:25:02Z","abstract_excerpt":"In this paper we consider extremal and almost extremal bounds on the normal Hilbert coefficients of ${\\mathfrak m}$-primary ideals of an analytically unramified Cohen-Macaulay ring $R$ of dimension $d>0$ and infinite residue field. In these circumstances we show that the associated graded ring of the normal filtration of the ideal is either Cohen-Macaulay or almost Cohen-Macaulay."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4233","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":"2026-05-18T02:39:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MmK8PkewugH4qXfu3l8HxkxNechHIWnHEuij711KHzlCBi0KZdhBHRUTpkgYceDKgAEnVWbNTlqTZy2wwp5ABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:52:05.293236Z"},"content_sha256":"d0bb1872d5221d301cd7d5858af596fd0b289a38797025490964a8649ed192c2","schema_version":"1.0","event_id":"sha256:d0bb1872d5221d301cd7d5858af596fd0b289a38797025490964a8649ed192c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMUIT3RPOMI2Q4R6Y5G64N3F4O/bundle.json","state_url":"https://pith.science/pith/FMUIT3RPOMI2Q4R6Y5G64N3F4O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMUIT3RPOMI2Q4R6Y5G64N3F4O/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":"2026-06-01T01:52:05Z","links":{"resolver":"https://pith.science/pith/FMUIT3RPOMI2Q4R6Y5G64N3F4O","bundle":"https://pith.science/pith/FMUIT3RPOMI2Q4R6Y5G64N3F4O/bundle.json","state":"https://pith.science/pith/FMUIT3RPOMI2Q4R6Y5G64N3F4O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMUIT3RPOMI2Q4R6Y5G64N3F4O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FMUIT3RPOMI2Q4R6Y5G64N3F4O","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":"308e173133fd0483f2334d05bee17dc183049e260d8794476137eb6985213fce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-15T21:25:02Z","title_canon_sha256":"c2e2d7260ee063d79584ac82a25bfe38e86f801a6631148d77dd71674e2c677f"},"schema_version":"1.0","source":{"id":"1410.4233","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4233","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4233v1","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4233","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"pith_short_12","alias_value":"FMUIT3RPOMI2","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FMUIT3RPOMI2Q4R6","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FMUIT3RP","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:d0bb1872d5221d301cd7d5858af596fd0b289a38797025490964a8649ed192c2","target":"graph","created_at":"2026-05-18T02:39:56Z","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 extremal and almost extremal bounds on the normal Hilbert coefficients of ${\\mathfrak m}$-primary ideals of an analytically unramified Cohen-Macaulay ring $R$ of dimension $d>0$ and infinite residue field. In these circumstances we show that the associated graded ring of the normal filtration of the ideal is either Cohen-Macaulay or almost Cohen-Macaulay.","authors_text":"Alberto Corso, Claudia Polini, Maria Evelina Rossi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-15T21:25:02Z","title":"Bounds on the normal Hilbert coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4233","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":"sha256:8898a3c888be2cb9c5c249e77a4e63d341b8e2a93b0ccdd6446f59ee2dd28b69","target":"record","created_at":"2026-05-18T02:39:56Z","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":"308e173133fd0483f2334d05bee17dc183049e260d8794476137eb6985213fce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-15T21:25:02Z","title_canon_sha256":"c2e2d7260ee063d79584ac82a25bfe38e86f801a6631148d77dd71674e2c677f"},"schema_version":"1.0","source":{"id":"1410.4233","kind":"arxiv","version":1}},"canonical_sha256":"2b2889ee2f7311a8723ec74dee3765e392e2e2018034bda52999fc8d646f1f0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b2889ee2f7311a8723ec74dee3765e392e2e2018034bda52999fc8d646f1f0d","first_computed_at":"2026-05-18T02:39:56.613784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:56.613784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NHHU+nJ6dRLB32xrlscF9OkTqNVLpEHSc+aqfLPAtEmQ0NU0kGO4YhlKr3filP9dPx3+HDIXHU4DfBhXjDuBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:56.614243Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.4233","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8898a3c888be2cb9c5c249e77a4e63d341b8e2a93b0ccdd6446f59ee2dd28b69","sha256:d0bb1872d5221d301cd7d5858af596fd0b289a38797025490964a8649ed192c2"],"state_sha256":"8751f9ffb0cb8a908c0f9ab8e6d31dfe53d438133b3970194cd42c17c6f75809"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lfaIxc4HcMXWZdPIosGxWeN2MuDbwkHb6yktRBSb6DMTNsYcxPzerzYWFgwzweyFssB2KpMVFafNAvRya8M6Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:52:05.296816Z","bundle_sha256":"2acdc2f3429f8cbbeb645108bff2dd56b67965c7c9bac73d8f960a4ca216182e"}}