{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7JEG42KNMQL6BATTYHBS7RT5LQ","short_pith_number":"pith:7JEG42KN","canonical_record":{"source":{"id":"1606.03429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-10T19:20:15Z","cross_cats_sorted":[],"title_canon_sha256":"e00911363156fc7ca1a5bbc24240f707a1ba1d5807929b3c9e0073259486f779","abstract_canon_sha256":"d74256cbf4df73b848d5802da44dd905663f2637ca62944ca2806b1b79c73388"},"schema_version":"1.0"},"canonical_sha256":"fa486e694d6417e08273c1c32fc67d5c168d14662ec8ff3e65ee1b572a0d96a2","source":{"kind":"arxiv","id":"1606.03429","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03429","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03429v1","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03429","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"7JEG42KNMQL6","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7JEG42KNMQL6BATT","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7JEG42KN","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7JEG42KNMQL6BATTYHBS7RT5LQ","target":"record","payload":{"canonical_record":{"source":{"id":"1606.03429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-10T19:20:15Z","cross_cats_sorted":[],"title_canon_sha256":"e00911363156fc7ca1a5bbc24240f707a1ba1d5807929b3c9e0073259486f779","abstract_canon_sha256":"d74256cbf4df73b848d5802da44dd905663f2637ca62944ca2806b1b79c73388"},"schema_version":"1.0"},"canonical_sha256":"fa486e694d6417e08273c1c32fc67d5c168d14662ec8ff3e65ee1b572a0d96a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:36.917761Z","signature_b64":"qpXzYoYyr8iPBfEmsf6v/yZ33AspBCTSpo7Mk6OsBs7gBFFKxn2oxaZ+9+XPbuDd/a5qwztC9ORb3+RAOI0DCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa486e694d6417e08273c1c32fc67d5c168d14662ec8ff3e65ee1b572a0d96a2","last_reissued_at":"2026-05-18T01:12:36.917271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:36.917271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.03429","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":"2026-05-18T01:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jWn5xKFRNTML4ztvGSCkpRgoh/NBZ/XupGpEzzNJB7Dx3eOkuLt+/vLyhSPK+JxCTowhSiC535S3cY6OLWAZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:52:52.977243Z"},"content_sha256":"6765316830be9418dd76a7ccf696a06f6264f28d54f76c5f4e83e13bd3295a44","schema_version":"1.0","event_id":"sha256:6765316830be9418dd76a7ccf696a06f6264f28d54f76c5f4e83e13bd3295a44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7JEG42KNMQL6BATTYHBS7RT5LQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gr\\\"obner coherent rings and modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrew Snowden, Rohit Nagpal","submitted_at":"2016-06-10T19:20:15Z","abstract_excerpt":"Let $R$ be a graded ring. We introduce a class of graded $R$-modules called Gr\\\"obner-coherent modules. Roughly, these are graded $R$-modules that are coherent as ungraded modules because they admit an adequate theory of Gr\\\"obner bases. The class of Gr\\\"obner-coherent modules is formally similar to the class of coherent modules: for instance, it is an abelian category closed under extension. However, Gr\\\"obner-coherent modules come with tools for effective computation that are not present for coherent modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03429","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":"2026-05-18T01:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hPsSUbVxTIbyqkVCHW32ReonmpPQJ4soNIXp4IePdDDV9pg2fViD0LbWgiWNx/cljUxfYMf8lwDO3qYaPUCSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:52:52.977599Z"},"content_sha256":"6c5d21e1a887a68ae83b90fac76ed6c01a1d35e66873f62607a0f355d556339d","schema_version":"1.0","event_id":"sha256:6c5d21e1a887a68ae83b90fac76ed6c01a1d35e66873f62607a0f355d556339d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7JEG42KNMQL6BATTYHBS7RT5LQ/bundle.json","state_url":"https://pith.science/pith/7JEG42KNMQL6BATTYHBS7RT5LQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7JEG42KNMQL6BATTYHBS7RT5LQ/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":"2026-07-03T13:52:52Z","links":{"resolver":"https://pith.science/pith/7JEG42KNMQL6BATTYHBS7RT5LQ","bundle":"https://pith.science/pith/7JEG42KNMQL6BATTYHBS7RT5LQ/bundle.json","state":"https://pith.science/pith/7JEG42KNMQL6BATTYHBS7RT5LQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7JEG42KNMQL6BATTYHBS7RT5LQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7JEG42KNMQL6BATTYHBS7RT5LQ","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":"d74256cbf4df73b848d5802da44dd905663f2637ca62944ca2806b1b79c73388","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-10T19:20:15Z","title_canon_sha256":"e00911363156fc7ca1a5bbc24240f707a1ba1d5807929b3c9e0073259486f779"},"schema_version":"1.0","source":{"id":"1606.03429","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03429","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03429v1","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03429","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"7JEG42KNMQL6","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7JEG42KNMQL6BATT","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7JEG42KN","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:6c5d21e1a887a68ae83b90fac76ed6c01a1d35e66873f62607a0f355d556339d","target":"graph","created_at":"2026-05-18T01:12:36Z","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":"Let $R$ be a graded ring. We introduce a class of graded $R$-modules called Gr\\\"obner-coherent modules. Roughly, these are graded $R$-modules that are coherent as ungraded modules because they admit an adequate theory of Gr\\\"obner bases. The class of Gr\\\"obner-coherent modules is formally similar to the class of coherent modules: for instance, it is an abelian category closed under extension. However, Gr\\\"obner-coherent modules come with tools for effective computation that are not present for coherent modules.","authors_text":"Andrew Snowden, Rohit Nagpal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-10T19:20:15Z","title":"Gr\\\"obner coherent rings and modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03429","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":"sha256:6765316830be9418dd76a7ccf696a06f6264f28d54f76c5f4e83e13bd3295a44","target":"record","created_at":"2026-05-18T01:12:36Z","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":"d74256cbf4df73b848d5802da44dd905663f2637ca62944ca2806b1b79c73388","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-06-10T19:20:15Z","title_canon_sha256":"e00911363156fc7ca1a5bbc24240f707a1ba1d5807929b3c9e0073259486f779"},"schema_version":"1.0","source":{"id":"1606.03429","kind":"arxiv","version":1}},"canonical_sha256":"fa486e694d6417e08273c1c32fc67d5c168d14662ec8ff3e65ee1b572a0d96a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa486e694d6417e08273c1c32fc67d5c168d14662ec8ff3e65ee1b572a0d96a2","first_computed_at":"2026-05-18T01:12:36.917271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:36.917271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qpXzYoYyr8iPBfEmsf6v/yZ33AspBCTSpo7Mk6OsBs7gBFFKxn2oxaZ+9+XPbuDd/a5qwztC9ORb3+RAOI0DCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:36.917761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03429","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6765316830be9418dd76a7ccf696a06f6264f28d54f76c5f4e83e13bd3295a44","sha256:6c5d21e1a887a68ae83b90fac76ed6c01a1d35e66873f62607a0f355d556339d"],"state_sha256":"0a33525c2067a4f57683e3edb85ac4f469fde05d9668f223d11d45482ab14a2f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Bx0ZuDA0jamTwodeU3bPwqtIS9rvGbuRH5+lrnuO5RI/h6vXbgOUjPovuKV5HA6aJowLFPVSbzvwMXGVi8ECg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T13:52:52.979473Z","bundle_sha256":"f3070b287a7c653be54a06ede6454b771c29dd0a5661318ab3d074701a6ed7bf"}}