{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:M3EAMOINHVUGLBXDKJM3ZW6PGY","short_pith_number":"pith:M3EAMOIN","canonical_record":{"source":{"id":"1901.03168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-10T14:09:03Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"28ee61c4b7c2e627aa9198af6d8a6963d6933bb7a566bd4f6eedbc1931cf9955","abstract_canon_sha256":"0e352a58a959e4ed6600e3c0c638d5fcace3ec2780e702f125c962511e9955b1"},"schema_version":"1.0"},"canonical_sha256":"66c806390d3d686586e35259bcdbcf360379f9a0cb26c53822cb58cff861d12e","source":{"kind":"arxiv","id":"1901.03168","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.03168","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"1901.03168v1","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.03168","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"M3EAMOINHVUG","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"M3EAMOINHVUGLBXD","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"M3EAMOIN","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:M3EAMOINHVUGLBXDKJM3ZW6PGY","target":"record","payload":{"canonical_record":{"source":{"id":"1901.03168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-10T14:09:03Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"28ee61c4b7c2e627aa9198af6d8a6963d6933bb7a566bd4f6eedbc1931cf9955","abstract_canon_sha256":"0e352a58a959e4ed6600e3c0c638d5fcace3ec2780e702f125c962511e9955b1"},"schema_version":"1.0"},"canonical_sha256":"66c806390d3d686586e35259bcdbcf360379f9a0cb26c53822cb58cff861d12e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:35.370884Z","signature_b64":"G4cBXWPU9ZmKEX/htkAOZf3BXPyBK0+bcNTcocDhibpirAHLVHlbWf0YHnsVDzcSKA1FAREN7EV83NfIo+rwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66c806390d3d686586e35259bcdbcf360379f9a0cb26c53822cb58cff861d12e","last_reissued_at":"2026-05-17T23:56:35.370351Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:35.370351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.03168","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":"2026-05-17T23:56:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ms8YxIeXSuZkXMQ0brIhqp5iBkNhtz3ECHbXD+A+ch3rJ3aNjE2ELChqz+sVEAoN2kTSNz9kwtlb5HRKyXkzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:44:42.815194Z"},"content_sha256":"f7761840cd72f943a8e61530d65d97b01a8e4b0ade0d039858b06fa6a44fa511","schema_version":"1.0","event_id":"sha256:f7761840cd72f943a8e61530d65d97b01a8e4b0ade0d039858b06fa6a44fa511"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:M3EAMOINHVUGLBXDKJM3ZW6PGY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tilting modules and tilting torsion pairs - filtrations induced by tilting modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Alberto Tonolo, Francesco Mattiello, Sergio Pavon","submitted_at":"2019-01-10T14:09:03Z","abstract_excerpt":"Tilting modules, generalising the notion of progenerator, furnish equivalences between pieces of module categories. This paper is dedicated to study how much these pieces say about the whole category. We will survey the existing results in the literature, introducing also some new insights."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03168","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":"2026-05-17T23:56:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PPI+na1ootflQL+s8U7QjbmDrgm+6bLUuYwscxKTQiEE2GgdwztYI+LqF3CeRMbAqvqqIU6nNHwc8mc49mFRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:44:42.815578Z"},"content_sha256":"b2795c842504a738216f1a30d3c152f10e66c4ffec23b6169173e6a6c7ce2757","schema_version":"1.0","event_id":"sha256:b2795c842504a738216f1a30d3c152f10e66c4ffec23b6169173e6a6c7ce2757"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M3EAMOINHVUGLBXDKJM3ZW6PGY/bundle.json","state_url":"https://pith.science/pith/M3EAMOINHVUGLBXDKJM3ZW6PGY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M3EAMOINHVUGLBXDKJM3ZW6PGY/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":"2026-06-05T08:44:42Z","links":{"resolver":"https://pith.science/pith/M3EAMOINHVUGLBXDKJM3ZW6PGY","bundle":"https://pith.science/pith/M3EAMOINHVUGLBXDKJM3ZW6PGY/bundle.json","state":"https://pith.science/pith/M3EAMOINHVUGLBXDKJM3ZW6PGY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M3EAMOINHVUGLBXDKJM3ZW6PGY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:M3EAMOINHVUGLBXDKJM3ZW6PGY","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":"0e352a58a959e4ed6600e3c0c638d5fcace3ec2780e702f125c962511e9955b1","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-10T14:09:03Z","title_canon_sha256":"28ee61c4b7c2e627aa9198af6d8a6963d6933bb7a566bd4f6eedbc1931cf9955"},"schema_version":"1.0","source":{"id":"1901.03168","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.03168","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"1901.03168v1","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.03168","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"M3EAMOINHVUG","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"M3EAMOINHVUGLBXD","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"M3EAMOIN","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:b2795c842504a738216f1a30d3c152f10e66c4ffec23b6169173e6a6c7ce2757","target":"graph","created_at":"2026-05-17T23:56:35Z","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":"Tilting modules, generalising the notion of progenerator, furnish equivalences between pieces of module categories. This paper is dedicated to study how much these pieces say about the whole category. We will survey the existing results in the literature, introducing also some new insights.","authors_text":"Alberto Tonolo, Francesco Mattiello, Sergio Pavon","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-10T14:09:03Z","title":"Tilting modules and tilting torsion pairs - filtrations induced by tilting modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03168","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:f7761840cd72f943a8e61530d65d97b01a8e4b0ade0d039858b06fa6a44fa511","target":"record","created_at":"2026-05-17T23:56:35Z","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":"0e352a58a959e4ed6600e3c0c638d5fcace3ec2780e702f125c962511e9955b1","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-10T14:09:03Z","title_canon_sha256":"28ee61c4b7c2e627aa9198af6d8a6963d6933bb7a566bd4f6eedbc1931cf9955"},"schema_version":"1.0","source":{"id":"1901.03168","kind":"arxiv","version":1}},"canonical_sha256":"66c806390d3d686586e35259bcdbcf360379f9a0cb26c53822cb58cff861d12e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66c806390d3d686586e35259bcdbcf360379f9a0cb26c53822cb58cff861d12e","first_computed_at":"2026-05-17T23:56:35.370351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:35.370351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G4cBXWPU9ZmKEX/htkAOZf3BXPyBK0+bcNTcocDhibpirAHLVHlbWf0YHnsVDzcSKA1FAREN7EV83NfIo+rwDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:35.370884Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.03168","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7761840cd72f943a8e61530d65d97b01a8e4b0ade0d039858b06fa6a44fa511","sha256:b2795c842504a738216f1a30d3c152f10e66c4ffec23b6169173e6a6c7ce2757"],"state_sha256":"b99e59a54de7f0eaec7b3fa19d32b23f06ca12b77702090943970d8cbc9a88b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"chOAmlcQRwebnsZhTQSeXXC0BSbLw6XydQHONl7tTdRSCcA27Yvy4lR6Qy6SokpBKQkrXdGi0FZoOxtfm0EGCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:44:42.818084Z","bundle_sha256":"47d9a6176d02c0c8a090ffc78fcd920045843f6489b0b864463ca6f6f33a484e"}}