{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:E4M32GGZELFYBBTCM7VJZI35HH","short_pith_number":"pith:E4M32GGZ","canonical_record":{"source":{"id":"1508.03798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-16T07:55:07Z","cross_cats_sorted":[],"title_canon_sha256":"ef0b2176a02283db3e96b9d4908cb41f612a7fd171e372746f2874ae9aba617f","abstract_canon_sha256":"761aaaf6e5031417eeb0bf989d51677c2ba0f58e3c14f3540ba2c97768975fa9"},"schema_version":"1.0"},"canonical_sha256":"2719bd18d922cb80866267ea9ca37d39d09a298594c65fe5c809a3fc92db247e","source":{"kind":"arxiv","id":"1508.03798","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03798","created_at":"2026-05-18T01:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03798v1","created_at":"2026-05-18T01:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03798","created_at":"2026-05-18T01:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"E4M32GGZELFY","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E4M32GGZELFYBBTC","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E4M32GGZ","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:E4M32GGZELFYBBTCM7VJZI35HH","target":"record","payload":{"canonical_record":{"source":{"id":"1508.03798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-16T07:55:07Z","cross_cats_sorted":[],"title_canon_sha256":"ef0b2176a02283db3e96b9d4908cb41f612a7fd171e372746f2874ae9aba617f","abstract_canon_sha256":"761aaaf6e5031417eeb0bf989d51677c2ba0f58e3c14f3540ba2c97768975fa9"},"schema_version":"1.0"},"canonical_sha256":"2719bd18d922cb80866267ea9ca37d39d09a298594c65fe5c809a3fc92db247e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:15.213635Z","signature_b64":"PM/rOVWlrAjxMeA/vSCWeE16QjT6LUXn9u8b90yAqFp5BS4ceGl54uzoJCIE7Uodz4Pmchx/mjQ5SPWmzEjnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2719bd18d922cb80866267ea9ca37d39d09a298594c65fe5c809a3fc92db247e","last_reissued_at":"2026-05-18T01:35:15.213121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:15.213121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.03798","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":"2026-05-18T01:35:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JpUQfukiix/0DjA5qeN7JZHeVm+GHEWzEYnTpTW1QmQCjOvYZRjLRIbG6H7me7AxY/DgqpPQ7I9sV88k7OGQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T08:43:31.810766Z"},"content_sha256":"07b72ab3268a45a69cfeb3b8af789601a68a0abf675ad4412fb4894ce00c0674","schema_version":"1.0","event_id":"sha256:07b72ab3268a45a69cfeb3b8af789601a68a0abf675ad4412fb4894ce00c0674"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:E4M32GGZELFYBBTCM7VJZI35HH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Criteria for a ring to have a left Noetherian left quotient ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"V. V. Bavula","submitted_at":"2015-08-16T07:55:07Z","abstract_excerpt":"Two criteria are given for a ring to have a left Noetherian left quotient ring (this was an open problem since 70's). It is proved that each such ring has only finitely many maximal left denominator sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03798","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":"2026-05-18T01:35:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kzrknpa6gBbkaSYM5rF49G2u3Y2OwEoDON7dqGV0XprcpwNbRqUXv7Oz+7BzuLMOOQmfwMERsQumvHRrCcchCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T08:43:31.811115Z"},"content_sha256":"1742780c10237b6aef06cfc46a7a4f70749f41134a10cb92658c39e40b4e5266","schema_version":"1.0","event_id":"sha256:1742780c10237b6aef06cfc46a7a4f70749f41134a10cb92658c39e40b4e5266"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E4M32GGZELFYBBTCM7VJZI35HH/bundle.json","state_url":"https://pith.science/pith/E4M32GGZELFYBBTCM7VJZI35HH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E4M32GGZELFYBBTCM7VJZI35HH/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":"2026-06-23T08:43:31Z","links":{"resolver":"https://pith.science/pith/E4M32GGZELFYBBTCM7VJZI35HH","bundle":"https://pith.science/pith/E4M32GGZELFYBBTCM7VJZI35HH/bundle.json","state":"https://pith.science/pith/E4M32GGZELFYBBTCM7VJZI35HH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E4M32GGZELFYBBTCM7VJZI35HH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:E4M32GGZELFYBBTCM7VJZI35HH","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":"761aaaf6e5031417eeb0bf989d51677c2ba0f58e3c14f3540ba2c97768975fa9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-16T07:55:07Z","title_canon_sha256":"ef0b2176a02283db3e96b9d4908cb41f612a7fd171e372746f2874ae9aba617f"},"schema_version":"1.0","source":{"id":"1508.03798","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03798","created_at":"2026-05-18T01:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03798v1","created_at":"2026-05-18T01:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03798","created_at":"2026-05-18T01:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"E4M32GGZELFY","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E4M32GGZELFYBBTC","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E4M32GGZ","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:1742780c10237b6aef06cfc46a7a4f70749f41134a10cb92658c39e40b4e5266","target":"graph","created_at":"2026-05-18T01:35:15Z","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":"Two criteria are given for a ring to have a left Noetherian left quotient ring (this was an open problem since 70's). It is proved that each such ring has only finitely many maximal left denominator sets.","authors_text":"V. V. Bavula","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-16T07:55:07Z","title":"Criteria for a ring to have a left Noetherian left quotient ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03798","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":"sha256:07b72ab3268a45a69cfeb3b8af789601a68a0abf675ad4412fb4894ce00c0674","target":"record","created_at":"2026-05-18T01:35:15Z","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":"761aaaf6e5031417eeb0bf989d51677c2ba0f58e3c14f3540ba2c97768975fa9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-16T07:55:07Z","title_canon_sha256":"ef0b2176a02283db3e96b9d4908cb41f612a7fd171e372746f2874ae9aba617f"},"schema_version":"1.0","source":{"id":"1508.03798","kind":"arxiv","version":1}},"canonical_sha256":"2719bd18d922cb80866267ea9ca37d39d09a298594c65fe5c809a3fc92db247e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2719bd18d922cb80866267ea9ca37d39d09a298594c65fe5c809a3fc92db247e","first_computed_at":"2026-05-18T01:35:15.213121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:15.213121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PM/rOVWlrAjxMeA/vSCWeE16QjT6LUXn9u8b90yAqFp5BS4ceGl54uzoJCIE7Uodz4Pmchx/mjQ5SPWmzEjnAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:15.213635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03798","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07b72ab3268a45a69cfeb3b8af789601a68a0abf675ad4412fb4894ce00c0674","sha256:1742780c10237b6aef06cfc46a7a4f70749f41134a10cb92658c39e40b4e5266"],"state_sha256":"bfee6ac79ca1a6f1a5785b754297507eb4e223f235df872055f8e4c9aca25493"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FJo5uBvM/+uHrqZvicraA6/CwagnoiogOLMiTy06v/oKucouiRVTqZ89zfj8RP5/lXVAfqzyuCttW2rtuTcmCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T08:43:31.813436Z","bundle_sha256":"4d0c40909904c5b915f2b7356baa4fd032dc73eab97f7909f927e50b509342e7"}}