{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:3VPH2I64NB42JBQIPT3EUIFAG3","short_pith_number":"pith:3VPH2I64","canonical_record":{"source":{"id":"1901.07921","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-01-23T14:42:49Z","cross_cats_sorted":[],"title_canon_sha256":"dcc241d55555dc48d17fc95ab5f0e1620a5d28b439b5579e5430a4b9dab7c926","abstract_canon_sha256":"71cb54e3d770705e9a8dd38720911c5a08bd16ec3193f324c60a728ee7c7a6dd"},"schema_version":"1.0"},"canonical_sha256":"dd5e7d23dc6879a486087cf64a20a036f122bcb22de15cd0c09ebd997013e59a","source":{"kind":"arxiv","id":"1901.07921","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07921","created_at":"2026-07-05T00:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07921v2","created_at":"2026-07-05T00:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07921","created_at":"2026-07-05T00:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"3VPH2I64NB42","created_at":"2026-07-05T00:48:58Z"},{"alias_kind":"pith_short_16","alias_value":"3VPH2I64NB42JBQI","created_at":"2026-07-05T00:48:58Z"},{"alias_kind":"pith_short_8","alias_value":"3VPH2I64","created_at":"2026-07-05T00:48:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:3VPH2I64NB42JBQIPT3EUIFAG3","target":"record","payload":{"canonical_record":{"source":{"id":"1901.07921","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-01-23T14:42:49Z","cross_cats_sorted":[],"title_canon_sha256":"dcc241d55555dc48d17fc95ab5f0e1620a5d28b439b5579e5430a4b9dab7c926","abstract_canon_sha256":"71cb54e3d770705e9a8dd38720911c5a08bd16ec3193f324c60a728ee7c7a6dd"},"schema_version":"1.0"},"canonical_sha256":"dd5e7d23dc6879a486087cf64a20a036f122bcb22de15cd0c09ebd997013e59a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:48:58.494534Z","signature_b64":"FGl3uJKibK8hy08QcQWx0XmcdfaPBU7Aory0UuNZacf9aJ3II8QRnMylQ7mtSHA8kNNosDS6zTE0+FEI1Na0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd5e7d23dc6879a486087cf64a20a036f122bcb22de15cd0c09ebd997013e59a","last_reissued_at":"2026-07-05T00:48:58.494153Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:48:58.494153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.07921","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":"2026-07-05T00:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cqTo6lGe2IuTtKC7UVZsV+ipP3CPPQ2t46XMhZOH/skg2Rtb8zmB+Nh/wf7X+3rRNjaVYjoZPYFaHf2Tv5HFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T07:48:51.471766Z"},"content_sha256":"4866851e7a0726e9794d2f47ef6ae777662183037cbf36ede9f5e1a0c26c16e0","schema_version":"1.0","event_id":"sha256:4866851e7a0726e9794d2f47ef6ae777662183037cbf36ede9f5e1a0c26c16e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:3VPH2I64NB42JBQIPT3EUIFAG3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enveloping Classes over Commutative Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Giovanna Le Gros, Silvana Bazzoni","submitted_at":"2019-01-23T14:42:49Z","abstract_excerpt":"Given a $1$-tilting cotorsion pair over a commutative ring, we characterise the rings over which the $1$-tilting class is an enveloping class. To do so, we consider the faithful finitely generated Gabriel topology $\\mathcal{G}$ associated to the $1$-tilting class $\\mathcal{T}$ over a commutative ring as illustrated by Hrbek. We prove that a $1$-tilting class $\\mathcal{T}$ is enveloping if and only if $ \\mathcal{G}$ is a perfect Gabriel topology (that is, it arises from a perfect localisation) and $R/J$ is a perfect ring for each $J \\in \\mathcal{G}$, or equivalently $\\mathcal{G}$ is a perfect G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07921","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1901.07921/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZX/6Ea73yZxdcBpX5mGJOnDyVZKiUy0B9NADup2Rbe3toEX4qNlYtqMUAePuulg5se+lvhjQlqlIfMvtQ0itCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T07:48:51.472341Z"},"content_sha256":"6196f28aee2a2f6a524130b4b1b4ab8d656d1faea725a49da3385dce94505aef","schema_version":"1.0","event_id":"sha256:6196f28aee2a2f6a524130b4b1b4ab8d656d1faea725a49da3385dce94505aef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3VPH2I64NB42JBQIPT3EUIFAG3/bundle.json","state_url":"https://pith.science/pith/3VPH2I64NB42JBQIPT3EUIFAG3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3VPH2I64NB42JBQIPT3EUIFAG3/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":"2026-08-08T07:48:51Z","links":{"resolver":"https://pith.science/pith/3VPH2I64NB42JBQIPT3EUIFAG3","bundle":"https://pith.science/pith/3VPH2I64NB42JBQIPT3EUIFAG3/bundle.json","state":"https://pith.science/pith/3VPH2I64NB42JBQIPT3EUIFAG3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3VPH2I64NB42JBQIPT3EUIFAG3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3VPH2I64NB42JBQIPT3EUIFAG3","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":"71cb54e3d770705e9a8dd38720911c5a08bd16ec3193f324c60a728ee7c7a6dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-01-23T14:42:49Z","title_canon_sha256":"dcc241d55555dc48d17fc95ab5f0e1620a5d28b439b5579e5430a4b9dab7c926"},"schema_version":"1.0","source":{"id":"1901.07921","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07921","created_at":"2026-07-05T00:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07921v2","created_at":"2026-07-05T00:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07921","created_at":"2026-07-05T00:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"3VPH2I64NB42","created_at":"2026-07-05T00:48:58Z"},{"alias_kind":"pith_short_16","alias_value":"3VPH2I64NB42JBQI","created_at":"2026-07-05T00:48:58Z"},{"alias_kind":"pith_short_8","alias_value":"3VPH2I64","created_at":"2026-07-05T00:48:58Z"}],"graph_snapshots":[{"event_id":"sha256:6196f28aee2a2f6a524130b4b1b4ab8d656d1faea725a49da3385dce94505aef","target":"graph","created_at":"2026-07-05T00:48:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1901.07921/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a $1$-tilting cotorsion pair over a commutative ring, we characterise the rings over which the $1$-tilting class is an enveloping class. To do so, we consider the faithful finitely generated Gabriel topology $\\mathcal{G}$ associated to the $1$-tilting class $\\mathcal{T}$ over a commutative ring as illustrated by Hrbek. We prove that a $1$-tilting class $\\mathcal{T}$ is enveloping if and only if $ \\mathcal{G}$ is a perfect Gabriel topology (that is, it arises from a perfect localisation) and $R/J$ is a perfect ring for each $J \\in \\mathcal{G}$, or equivalently $\\mathcal{G}$ is a perfect G","authors_text":"Giovanna Le Gros, Silvana Bazzoni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-01-23T14:42:49Z","title":"Enveloping Classes over Commutative Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07921","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":"sha256:4866851e7a0726e9794d2f47ef6ae777662183037cbf36ede9f5e1a0c26c16e0","target":"record","created_at":"2026-07-05T00:48:58Z","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":"71cb54e3d770705e9a8dd38720911c5a08bd16ec3193f324c60a728ee7c7a6dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-01-23T14:42:49Z","title_canon_sha256":"dcc241d55555dc48d17fc95ab5f0e1620a5d28b439b5579e5430a4b9dab7c926"},"schema_version":"1.0","source":{"id":"1901.07921","kind":"arxiv","version":2}},"canonical_sha256":"dd5e7d23dc6879a486087cf64a20a036f122bcb22de15cd0c09ebd997013e59a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd5e7d23dc6879a486087cf64a20a036f122bcb22de15cd0c09ebd997013e59a","first_computed_at":"2026-07-05T00:48:58.494153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:48:58.494153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FGl3uJKibK8hy08QcQWx0XmcdfaPBU7Aory0UuNZacf9aJ3II8QRnMylQ7mtSHA8kNNosDS6zTE0+FEI1Na0Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:48:58.494534Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.07921","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4866851e7a0726e9794d2f47ef6ae777662183037cbf36ede9f5e1a0c26c16e0","sha256:6196f28aee2a2f6a524130b4b1b4ab8d656d1faea725a49da3385dce94505aef"],"state_sha256":"948b016bc123280e1e9426190ce090d03cc6819479ace57b39c5d6443d96e2d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m7tvKmSMunQn1QmRSlxRkowlazdZ0JyzU7fnGnfR//XrG2rJsWZ6fyzVyyIwJfgwlZaez4L0hzZoYL1/78WBDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T07:48:51.477031Z","bundle_sha256":"8ce572cf9fd83c83809653bfb86f10e598863dd59a2091c2be8c08c599f2b649"}}