{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GLKXVO22UI7G2PNCZXRIEC5S3K","short_pith_number":"pith:GLKXVO22","canonical_record":{"source":{"id":"1306.3773","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-06-17T08:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"f9e39cde684634b5e310d555e77ac7d9efb92f7741159eb452c33537e8534f8a","abstract_canon_sha256":"68b88289fe13588fcfc416d0db86b5f5981e439e087454ff4c5e3a61b05ca36f"},"schema_version":"1.0"},"canonical_sha256":"32d57abb5aa23e6d3da2cde2820bb2da98f69d0dc16c6c956ce39e2bc823c9fb","source":{"kind":"arxiv","id":"1306.3773","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3773","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3773v2","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3773","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"GLKXVO22UI7G","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GLKXVO22UI7G2PNC","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GLKXVO22","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GLKXVO22UI7G2PNCZXRIEC5S3K","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3773","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-06-17T08:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"f9e39cde684634b5e310d555e77ac7d9efb92f7741159eb452c33537e8534f8a","abstract_canon_sha256":"68b88289fe13588fcfc416d0db86b5f5981e439e087454ff4c5e3a61b05ca36f"},"schema_version":"1.0"},"canonical_sha256":"32d57abb5aa23e6d3da2cde2820bb2da98f69d0dc16c6c956ce39e2bc823c9fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:15.278556Z","signature_b64":"QmfJtNHnnHnGcPE5TASeMihMmhTSSUkXzzKYUxj5wbG815WrDQ+3XPxkWF3IKTg9luvm/K/lO4WXElyr4jbdDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32d57abb5aa23e6d3da2cde2820bb2da98f69d0dc16c6c956ce39e2bc823c9fb","last_reissued_at":"2026-05-18T01:18:15.277958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:15.277958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3773","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":"2026-05-18T01:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gwTeT7ADYCroOLabQM1TKyPcRm+bqvXFxNre8cp5GTc+fkg/cEcj/4je8BtQ35TMdBzlWYcuGDsmWrweZbmuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:08:18.822489Z"},"content_sha256":"15cfd0eee10652df67235bbdbfd95e5360cbb7272341f44368cb5d956a7e54d4","schema_version":"1.0","event_id":"sha256:15cfd0eee10652df67235bbdbfd95e5360cbb7272341f44368cb5d956a7e54d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GLKXVO22UI7G2PNCZXRIEC5S3K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on strong protomodularity, actions and quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Giuseppe Metere","submitted_at":"2013-06-17T08:48:48Z","abstract_excerpt":"In order to study the problems of extending an action along a quotient of the acted object and along a quotient of the acting object, we investigate some properties of the fibration of points. In fact, we obtain a characterization of protomodular categories among quasi-pointed regular ones, and, in the semi-abelian case, a characterization of strong protomodular categories. Eventually, we return to the initial questions by stating the results in terms of internal actions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3773","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":""},"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":"2026-05-18T01:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OJQ63pNLB+DNcJSzCVJ+zBLYmTM2kPFplaz4I9JQGrE2ruhVJnYQHiSVoapWcsDKz/fIFtw6iAwyosl2sf0sCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:08:18.823135Z"},"content_sha256":"33ba95e35798baca8902ea80f32ef6c70e48622097c299bc03cd343b58e2ca62","schema_version":"1.0","event_id":"sha256:33ba95e35798baca8902ea80f32ef6c70e48622097c299bc03cd343b58e2ca62"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GLKXVO22UI7G2PNCZXRIEC5S3K/bundle.json","state_url":"https://pith.science/pith/GLKXVO22UI7G2PNCZXRIEC5S3K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GLKXVO22UI7G2PNCZXRIEC5S3K/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":"2026-05-26T22:08:18Z","links":{"resolver":"https://pith.science/pith/GLKXVO22UI7G2PNCZXRIEC5S3K","bundle":"https://pith.science/pith/GLKXVO22UI7G2PNCZXRIEC5S3K/bundle.json","state":"https://pith.science/pith/GLKXVO22UI7G2PNCZXRIEC5S3K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GLKXVO22UI7G2PNCZXRIEC5S3K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GLKXVO22UI7G2PNCZXRIEC5S3K","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":"68b88289fe13588fcfc416d0db86b5f5981e439e087454ff4c5e3a61b05ca36f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-06-17T08:48:48Z","title_canon_sha256":"f9e39cde684634b5e310d555e77ac7d9efb92f7741159eb452c33537e8534f8a"},"schema_version":"1.0","source":{"id":"1306.3773","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3773","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3773v2","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3773","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"GLKXVO22UI7G","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GLKXVO22UI7G2PNC","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GLKXVO22","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:33ba95e35798baca8902ea80f32ef6c70e48622097c299bc03cd343b58e2ca62","target":"graph","created_at":"2026-05-18T01:18:15Z","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":"In order to study the problems of extending an action along a quotient of the acted object and along a quotient of the acting object, we investigate some properties of the fibration of points. In fact, we obtain a characterization of protomodular categories among quasi-pointed regular ones, and, in the semi-abelian case, a characterization of strong protomodular categories. Eventually, we return to the initial questions by stating the results in terms of internal actions.","authors_text":"Giuseppe Metere","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-06-17T08:48:48Z","title":"A note on strong protomodularity, actions and quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3773","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":"sha256:15cfd0eee10652df67235bbdbfd95e5360cbb7272341f44368cb5d956a7e54d4","target":"record","created_at":"2026-05-18T01:18:15Z","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":"68b88289fe13588fcfc416d0db86b5f5981e439e087454ff4c5e3a61b05ca36f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-06-17T08:48:48Z","title_canon_sha256":"f9e39cde684634b5e310d555e77ac7d9efb92f7741159eb452c33537e8534f8a"},"schema_version":"1.0","source":{"id":"1306.3773","kind":"arxiv","version":2}},"canonical_sha256":"32d57abb5aa23e6d3da2cde2820bb2da98f69d0dc16c6c956ce39e2bc823c9fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32d57abb5aa23e6d3da2cde2820bb2da98f69d0dc16c6c956ce39e2bc823c9fb","first_computed_at":"2026-05-18T01:18:15.277958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:15.277958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QmfJtNHnnHnGcPE5TASeMihMmhTSSUkXzzKYUxj5wbG815WrDQ+3XPxkWF3IKTg9luvm/K/lO4WXElyr4jbdDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:15.278556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3773","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15cfd0eee10652df67235bbdbfd95e5360cbb7272341f44368cb5d956a7e54d4","sha256:33ba95e35798baca8902ea80f32ef6c70e48622097c299bc03cd343b58e2ca62"],"state_sha256":"6fdba131c6fe0fa28d01455674504e64fb4ab9344e00ee6f356e05c08c5b0cee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CMoaFguEZN6wYaeuCqrwJyJ+9IMRFtp7XQ1nWReDU2iWkUBQ7f6eH6nNe+WA+R7IqvP0i2M+OAHtK0fcvzSuCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:08:18.826425Z","bundle_sha256":"3f6278e83a4301cf41f3f18b0a3c832a8924ecf5d77887fcff856b7afddb7bbb"}}