{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FXGSMOPPVV2J3JELLPTHII2RZF","short_pith_number":"pith:FXGSMOPP","canonical_record":{"source":{"id":"1708.01330","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-08-03T23:22:30Z","cross_cats_sorted":[],"title_canon_sha256":"ff7e82b5b6603069515197985d1d838f613debfa33b45e8ac64e686eca203623","abstract_canon_sha256":"e10659a4a745bee735a5135a45f8ba0c41042c1c4ed48eb6b5f51349c3f3581e"},"schema_version":"1.0"},"canonical_sha256":"2dcd2639efad749da48b5be6742351c94baca231082d109fb8789ddbd4700768","source":{"kind":"arxiv","id":"1708.01330","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01330","created_at":"2026-05-18T00:38:37Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01330v1","created_at":"2026-05-18T00:38:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01330","created_at":"2026-05-18T00:38:37Z"},{"alias_kind":"pith_short_12","alias_value":"FXGSMOPPVV2J","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FXGSMOPPVV2J3JEL","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FXGSMOPP","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FXGSMOPPVV2J3JELLPTHII2RZF","target":"record","payload":{"canonical_record":{"source":{"id":"1708.01330","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-08-03T23:22:30Z","cross_cats_sorted":[],"title_canon_sha256":"ff7e82b5b6603069515197985d1d838f613debfa33b45e8ac64e686eca203623","abstract_canon_sha256":"e10659a4a745bee735a5135a45f8ba0c41042c1c4ed48eb6b5f51349c3f3581e"},"schema_version":"1.0"},"canonical_sha256":"2dcd2639efad749da48b5be6742351c94baca231082d109fb8789ddbd4700768","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:37.659467Z","signature_b64":"qtgIMjIJGEE+8ohVeO/73WHEt6jjMcnfIZloP/16Zkp1EWXuSUQkKse9R1Br1TFU+dtYANJv2Jo3j7tNc1RKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2dcd2639efad749da48b5be6742351c94baca231082d109fb8789ddbd4700768","last_reissued_at":"2026-05-18T00:38:37.658868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:37.658868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.01330","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":"2026-05-18T00:38:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b9N6xSZtrH37zW8t/I28XBdV1I4G+iYwo5qgGi6MTz/ru2YN9xBltcp5aOy2maclLihtzO+u9/OmF+wY8Ej3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:15:56.438735Z"},"content_sha256":"7f82e863bb4d2417dc32b8598c32f2c310460f35eeec2aa22dcc16afc5c9b1f3","schema_version":"1.0","event_id":"sha256:7f82e863bb4d2417dc32b8598c32f2c310460f35eeec2aa22dcc16afc5c9b1f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FXGSMOPPVV2J3JELLPTHII2RZF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Description of Partial actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Eduardo Marcos, Wagner Cortes","submitted_at":"2017-08-03T23:22:30Z","abstract_excerpt":"In this paper, we study partial actions of groups on $R$-algebras, where $R$ is a commutative ring. We describe the partial actions of groups on the indecomposable algebras with enveloping actions. Then we work on algebras that can be decomposed as product of indecomposable algebras and we give a description of the partial actions of groups on these algebras in terms of global actions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01330","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":"2026-05-18T00:38:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HnvK+DHcanKJtZ6hV9g3bFoUBLylz/xzdWJeyntLhSIm5AvbejDdfH+wNAmpvvTFj+ifdnOcwcns09+KNkU1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:15:56.439082Z"},"content_sha256":"d51c9a1bef3afc8f396ec13797c395dff45070e924af3897164742afe8df3266","schema_version":"1.0","event_id":"sha256:d51c9a1bef3afc8f396ec13797c395dff45070e924af3897164742afe8df3266"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FXGSMOPPVV2J3JELLPTHII2RZF/bundle.json","state_url":"https://pith.science/pith/FXGSMOPPVV2J3JELLPTHII2RZF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FXGSMOPPVV2J3JELLPTHII2RZF/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":"2026-06-02T01:15:56Z","links":{"resolver":"https://pith.science/pith/FXGSMOPPVV2J3JELLPTHII2RZF","bundle":"https://pith.science/pith/FXGSMOPPVV2J3JELLPTHII2RZF/bundle.json","state":"https://pith.science/pith/FXGSMOPPVV2J3JELLPTHII2RZF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FXGSMOPPVV2J3JELLPTHII2RZF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FXGSMOPPVV2J3JELLPTHII2RZF","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":"e10659a4a745bee735a5135a45f8ba0c41042c1c4ed48eb6b5f51349c3f3581e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-08-03T23:22:30Z","title_canon_sha256":"ff7e82b5b6603069515197985d1d838f613debfa33b45e8ac64e686eca203623"},"schema_version":"1.0","source":{"id":"1708.01330","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01330","created_at":"2026-05-18T00:38:37Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01330v1","created_at":"2026-05-18T00:38:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01330","created_at":"2026-05-18T00:38:37Z"},{"alias_kind":"pith_short_12","alias_value":"FXGSMOPPVV2J","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FXGSMOPPVV2J3JEL","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FXGSMOPP","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:d51c9a1bef3afc8f396ec13797c395dff45070e924af3897164742afe8df3266","target":"graph","created_at":"2026-05-18T00:38:37Z","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":"In this paper, we study partial actions of groups on $R$-algebras, where $R$ is a commutative ring. We describe the partial actions of groups on the indecomposable algebras with enveloping actions. Then we work on algebras that can be decomposed as product of indecomposable algebras and we give a description of the partial actions of groups on these algebras in terms of global actions.","authors_text":"Eduardo Marcos, Wagner Cortes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-08-03T23:22:30Z","title":"Description of Partial actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01330","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":"sha256:7f82e863bb4d2417dc32b8598c32f2c310460f35eeec2aa22dcc16afc5c9b1f3","target":"record","created_at":"2026-05-18T00:38:37Z","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":"e10659a4a745bee735a5135a45f8ba0c41042c1c4ed48eb6b5f51349c3f3581e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-08-03T23:22:30Z","title_canon_sha256":"ff7e82b5b6603069515197985d1d838f613debfa33b45e8ac64e686eca203623"},"schema_version":"1.0","source":{"id":"1708.01330","kind":"arxiv","version":1}},"canonical_sha256":"2dcd2639efad749da48b5be6742351c94baca231082d109fb8789ddbd4700768","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2dcd2639efad749da48b5be6742351c94baca231082d109fb8789ddbd4700768","first_computed_at":"2026-05-18T00:38:37.658868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:37.658868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qtgIMjIJGEE+8ohVeO/73WHEt6jjMcnfIZloP/16Zkp1EWXuSUQkKse9R1Br1TFU+dtYANJv2Jo3j7tNc1RKBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:37.659467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.01330","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f82e863bb4d2417dc32b8598c32f2c310460f35eeec2aa22dcc16afc5c9b1f3","sha256:d51c9a1bef3afc8f396ec13797c395dff45070e924af3897164742afe8df3266"],"state_sha256":"3540367c01999b1fa81f1b35f49a2e8b4e59f59b8fa08d18743f91e6411c277d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LG0hEw33LgsZElhiVCj69oWZkkT/v2Uf9ee+pv0dbcsFvKQLQ//GVBu7/Xz1LiJmXw8qKCIpic25rq8gTEsqDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:15:56.441285Z","bundle_sha256":"972fa77f2dcb9f9d9f97c73a8d97b94f926927f6ac25ebd77715587d0139d871"}}