{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JBLSIQ5ZGLCRC3R7MD6ROICVIR","short_pith_number":"pith:JBLSIQ5Z","canonical_record":{"source":{"id":"1405.0123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-01T10:12:44Z","cross_cats_sorted":[],"title_canon_sha256":"8a1b0905adcf3dbb40e57e3a158e497dc7f260e5222c2492d6d5c0a267ba2d89","abstract_canon_sha256":"f5c79f7e724b6dabc0b273db452e93e301b105552bd2ccd7e9ec1fa826f7453e"},"schema_version":"1.0"},"canonical_sha256":"48572443b932c5116e3f60fd17205544417a0f8c748995ef3e84636505edda32","source":{"kind":"arxiv","id":"1405.0123","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0123","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0123v1","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0123","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"pith_short_12","alias_value":"JBLSIQ5ZGLCR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JBLSIQ5ZGLCRC3R7","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JBLSIQ5Z","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JBLSIQ5ZGLCRC3R7MD6ROICVIR","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-01T10:12:44Z","cross_cats_sorted":[],"title_canon_sha256":"8a1b0905adcf3dbb40e57e3a158e497dc7f260e5222c2492d6d5c0a267ba2d89","abstract_canon_sha256":"f5c79f7e724b6dabc0b273db452e93e301b105552bd2ccd7e9ec1fa826f7453e"},"schema_version":"1.0"},"canonical_sha256":"48572443b932c5116e3f60fd17205544417a0f8c748995ef3e84636505edda32","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:41.842372Z","signature_b64":"0IyWuVJ5LtXHgqMkSLSGg3G6eEWWcQG8wBgxDn7T2etrOEp74A36aiRBXYSdtQ6AASKq9jQ4s4iI3s+p64nDBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48572443b932c5116e3f60fd17205544417a0f8c748995ef3e84636505edda32","last_reissued_at":"2026-05-18T01:04:41.841920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:41.841920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0123","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":"2026-05-18T01:04:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lc2L3kLmZ2vHKJp3KedLUZbkT8YkhfOy5wj4oDhE+0Gzj9ulQQSsgnyplDksneJJ/20sq+szLSblBftJtEdzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:07:50.727334Z"},"content_sha256":"64044def373a4ee4222315c81bbfd422d05c5cc6930180cdc86006cca4300ca0","schema_version":"1.0","event_id":"sha256:64044def373a4ee4222315c81bbfd422d05c5cc6930180cdc86006cca4300ca0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JBLSIQ5ZGLCRC3R7MD6ROICVIR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the notion of 'retractable modules' in the context of algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Christian Lomp","submitted_at":"2014-05-01T10:12:44Z","abstract_excerpt":"This is a survey on the usage of the module theoretic notion of a \"retractable module\" in the study of algebras with actions. We explain how classical results can be interpreted using module theory and end the paper with some open questions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0123","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":"2026-05-18T01:04:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QmhJcgrH0gOLINSe9gSe1cGx5iwJFor5L4oIymCk4pGvOSZW4tEiwNlsVvfrVyDEM4JvfjIjNbXhD0y4MLNDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:07:50.727686Z"},"content_sha256":"277d2bcb4ec11d17723c291590fb6fd827020f70f0407231f3a0cab36428edb7","schema_version":"1.0","event_id":"sha256:277d2bcb4ec11d17723c291590fb6fd827020f70f0407231f3a0cab36428edb7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JBLSIQ5ZGLCRC3R7MD6ROICVIR/bundle.json","state_url":"https://pith.science/pith/JBLSIQ5ZGLCRC3R7MD6ROICVIR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JBLSIQ5ZGLCRC3R7MD6ROICVIR/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":"2026-06-01T12:07:50Z","links":{"resolver":"https://pith.science/pith/JBLSIQ5ZGLCRC3R7MD6ROICVIR","bundle":"https://pith.science/pith/JBLSIQ5ZGLCRC3R7MD6ROICVIR/bundle.json","state":"https://pith.science/pith/JBLSIQ5ZGLCRC3R7MD6ROICVIR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JBLSIQ5ZGLCRC3R7MD6ROICVIR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JBLSIQ5ZGLCRC3R7MD6ROICVIR","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":"f5c79f7e724b6dabc0b273db452e93e301b105552bd2ccd7e9ec1fa826f7453e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-01T10:12:44Z","title_canon_sha256":"8a1b0905adcf3dbb40e57e3a158e497dc7f260e5222c2492d6d5c0a267ba2d89"},"schema_version":"1.0","source":{"id":"1405.0123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0123","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0123v1","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0123","created_at":"2026-05-18T01:04:41Z"},{"alias_kind":"pith_short_12","alias_value":"JBLSIQ5ZGLCR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JBLSIQ5ZGLCRC3R7","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JBLSIQ5Z","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:277d2bcb4ec11d17723c291590fb6fd827020f70f0407231f3a0cab36428edb7","target":"graph","created_at":"2026-05-18T01:04:41Z","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":"This is a survey on the usage of the module theoretic notion of a \"retractable module\" in the study of algebras with actions. We explain how classical results can be interpreted using module theory and end the paper with some open questions.","authors_text":"Christian Lomp","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-01T10:12:44Z","title":"On the notion of 'retractable modules' in the context of algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0123","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":"sha256:64044def373a4ee4222315c81bbfd422d05c5cc6930180cdc86006cca4300ca0","target":"record","created_at":"2026-05-18T01:04:41Z","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":"f5c79f7e724b6dabc0b273db452e93e301b105552bd2ccd7e9ec1fa826f7453e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-01T10:12:44Z","title_canon_sha256":"8a1b0905adcf3dbb40e57e3a158e497dc7f260e5222c2492d6d5c0a267ba2d89"},"schema_version":"1.0","source":{"id":"1405.0123","kind":"arxiv","version":1}},"canonical_sha256":"48572443b932c5116e3f60fd17205544417a0f8c748995ef3e84636505edda32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48572443b932c5116e3f60fd17205544417a0f8c748995ef3e84636505edda32","first_computed_at":"2026-05-18T01:04:41.841920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:41.841920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0IyWuVJ5LtXHgqMkSLSGg3G6eEWWcQG8wBgxDn7T2etrOEp74A36aiRBXYSdtQ6AASKq9jQ4s4iI3s+p64nDBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:41.842372Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64044def373a4ee4222315c81bbfd422d05c5cc6930180cdc86006cca4300ca0","sha256:277d2bcb4ec11d17723c291590fb6fd827020f70f0407231f3a0cab36428edb7"],"state_sha256":"62c5466a5cb53a7b5786e17bb1b34d9a779f6f4774e4bd87e2d85226347677e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8uWOS0mSipUK4pmmUsxRu5pRCWYOjJeoNEZSNeA63gzVhp3Yhc2KQ0Sb8T4zVS887etcgyEv82RyjdY954IKDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:07:50.729652Z","bundle_sha256":"cd04607a4c2a4a5a80bb8ee7422f31ea0961594aabb5d6f19ca49c461f9dffe9"}}