{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4A3R56OIBZAJQ53BT4E3EQ7DMH","short_pith_number":"pith:4A3R56OI","canonical_record":{"source":{"id":"1802.04786","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-13T18:43:47Z","cross_cats_sorted":[],"title_canon_sha256":"d008797b0b27da7de11dcbe8e1de447a44a07d3f30d05faabc85507ae9a88132","abstract_canon_sha256":"5b095070aebc60ff76257da72d1eaf798d7566d78c15c9a9d176c13b20c9e0f8"},"schema_version":"1.0"},"canonical_sha256":"e0371ef9c80e409877619f09b243e361c110741f95c15b97b31a1f4b8e46eae1","source":{"kind":"arxiv","id":"1802.04786","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04786","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04786v2","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04786","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"4A3R56OIBZAJ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4A3R56OIBZAJQ53B","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4A3R56OI","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4A3R56OIBZAJQ53BT4E3EQ7DMH","target":"record","payload":{"canonical_record":{"source":{"id":"1802.04786","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-13T18:43:47Z","cross_cats_sorted":[],"title_canon_sha256":"d008797b0b27da7de11dcbe8e1de447a44a07d3f30d05faabc85507ae9a88132","abstract_canon_sha256":"5b095070aebc60ff76257da72d1eaf798d7566d78c15c9a9d176c13b20c9e0f8"},"schema_version":"1.0"},"canonical_sha256":"e0371ef9c80e409877619f09b243e361c110741f95c15b97b31a1f4b8e46eae1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:45.609750Z","signature_b64":"a//8501E2OK0DR6WkZbwc/AUscK/Z0N10q+J4fWn5h9pTxxtUBwEKnOdtyr81dtfZYWEEOIqZ7zeeRtgACQuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0371ef9c80e409877619f09b243e361c110741f95c15b97b31a1f4b8e46eae1","last_reissued_at":"2026-05-18T00:21:45.609164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:45.609164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.04786","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hugvxsxupeoVQyk67qsgkrB/c82NHjgDHN782pCKRTSD20nN75ySvVS9B7EwBvgrCMXrmvGIKAA4kgQRTKSEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:54:02.121871Z"},"content_sha256":"127a6e01d687042dc0490d1c650a27e9c9cee177c05c7eebc630f1de9643f225","schema_version":"1.0","event_id":"sha256:127a6e01d687042dc0490d1c650a27e9c9cee177c05c7eebc630f1de9643f225"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4A3R56OIBZAJQ53BT4E3EQ7DMH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal Cohen-Macaulay modules over certain Segre products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Linquan Ma","submitted_at":"2018-02-13T18:43:47Z","abstract_excerpt":"We prove some results on the non-existence of rank one maximal Cohen-Macaulay modules over certain Segre product rings. As an application we show that over these Segre product rings there do not exist maximal Cohen-Macaulay modules with multiplicity less than or equal to the parameter degree of the ring, which disproves a conjecture of Schoutens."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04786","kind":"arxiv","version":2},"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":"2026-05-18T00:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9LG2nrGtfSCT2umdBsPfjTY+ixUqaB9yz7BKicL7g6Hzi+KfRHqR/WZUBSJ5GL+rTT9/AnjdAf2ATKEx4LufDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:54:02.122217Z"},"content_sha256":"0408da8fd5cecb1d5315f27b2eb8698b58085fc493da7d375871514839cc9937","schema_version":"1.0","event_id":"sha256:0408da8fd5cecb1d5315f27b2eb8698b58085fc493da7d375871514839cc9937"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4A3R56OIBZAJQ53BT4E3EQ7DMH/bundle.json","state_url":"https://pith.science/pith/4A3R56OIBZAJQ53BT4E3EQ7DMH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4A3R56OIBZAJQ53BT4E3EQ7DMH/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":"2026-06-22T11:54:02Z","links":{"resolver":"https://pith.science/pith/4A3R56OIBZAJQ53BT4E3EQ7DMH","bundle":"https://pith.science/pith/4A3R56OIBZAJQ53BT4E3EQ7DMH/bundle.json","state":"https://pith.science/pith/4A3R56OIBZAJQ53BT4E3EQ7DMH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4A3R56OIBZAJQ53BT4E3EQ7DMH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4A3R56OIBZAJQ53BT4E3EQ7DMH","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":"5b095070aebc60ff76257da72d1eaf798d7566d78c15c9a9d176c13b20c9e0f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-13T18:43:47Z","title_canon_sha256":"d008797b0b27da7de11dcbe8e1de447a44a07d3f30d05faabc85507ae9a88132"},"schema_version":"1.0","source":{"id":"1802.04786","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04786","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04786v2","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04786","created_at":"2026-05-18T00:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"4A3R56OIBZAJ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4A3R56OIBZAJQ53B","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4A3R56OI","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:0408da8fd5cecb1d5315f27b2eb8698b58085fc493da7d375871514839cc9937","target":"graph","created_at":"2026-05-18T00:21:45Z","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":"We prove some results on the non-existence of rank one maximal Cohen-Macaulay modules over certain Segre product rings. As an application we show that over these Segre product rings there do not exist maximal Cohen-Macaulay modules with multiplicity less than or equal to the parameter degree of the ring, which disproves a conjecture of Schoutens.","authors_text":"Linquan Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-13T18:43:47Z","title":"Maximal Cohen-Macaulay modules over certain Segre products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04786","kind":"arxiv","version":2},"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":"sha256:127a6e01d687042dc0490d1c650a27e9c9cee177c05c7eebc630f1de9643f225","target":"record","created_at":"2026-05-18T00:21:45Z","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":"5b095070aebc60ff76257da72d1eaf798d7566d78c15c9a9d176c13b20c9e0f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-13T18:43:47Z","title_canon_sha256":"d008797b0b27da7de11dcbe8e1de447a44a07d3f30d05faabc85507ae9a88132"},"schema_version":"1.0","source":{"id":"1802.04786","kind":"arxiv","version":2}},"canonical_sha256":"e0371ef9c80e409877619f09b243e361c110741f95c15b97b31a1f4b8e46eae1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0371ef9c80e409877619f09b243e361c110741f95c15b97b31a1f4b8e46eae1","first_computed_at":"2026-05-18T00:21:45.609164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:45.609164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a//8501E2OK0DR6WkZbwc/AUscK/Z0N10q+J4fWn5h9pTxxtUBwEKnOdtyr81dtfZYWEEOIqZ7zeeRtgACQuBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:45.609750Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04786","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:127a6e01d687042dc0490d1c650a27e9c9cee177c05c7eebc630f1de9643f225","sha256:0408da8fd5cecb1d5315f27b2eb8698b58085fc493da7d375871514839cc9937"],"state_sha256":"120d6fde85db5af1afecfb2269f0a0dce7e04c272865237f940cd9afc3e5a5a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"URqDvGZv3hKO3VFOi/ZvEkXqBdSJXW63p7zOhkGio+XwyRikPbn/K9/3ZlCNNvhBRhHVH7IMuR5eecWdM5AmBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:54:02.124281Z","bundle_sha256":"9156bbeffafb2024424631f0fae60bb41a86a3c3b086c0eb0113fb349c1b9069"}}