{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:GY6555WP26IS73VCJFK2C3BFQR","short_pith_number":"pith:GY6555WP","canonical_record":{"source":{"id":"0901.3928","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-25T22:47:03Z","cross_cats_sorted":[],"title_canon_sha256":"92bd69df799e9872a84c4d66924559b79469e1aeacee5afc13ba8a9be8074193","abstract_canon_sha256":"9ffd21e6d2d52903f787aa1509f78da7e261456a7b797bde9dc1608bf476ccfc"},"schema_version":"1.0"},"canonical_sha256":"363ddef6cfd7912feea24955a16c25844cf32bef73bfd135245936d01b15b520","source":{"kind":"arxiv","id":"0901.3928","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.3928","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"arxiv_version","alias_value":"0901.3928v2","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.3928","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"pith_short_12","alias_value":"GY6555WP26IS","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"GY6555WP26IS73VC","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"GY6555WP","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:GY6555WP26IS73VCJFK2C3BFQR","target":"record","payload":{"canonical_record":{"source":{"id":"0901.3928","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-25T22:47:03Z","cross_cats_sorted":[],"title_canon_sha256":"92bd69df799e9872a84c4d66924559b79469e1aeacee5afc13ba8a9be8074193","abstract_canon_sha256":"9ffd21e6d2d52903f787aa1509f78da7e261456a7b797bde9dc1608bf476ccfc"},"schema_version":"1.0"},"canonical_sha256":"363ddef6cfd7912feea24955a16c25844cf32bef73bfd135245936d01b15b520","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:22.783450Z","signature_b64":"s80OCY99eSug3syDIS37k52tVLtpJvvbk4vp7nKMPddGCgonG1kQAglFyK8BpzwruDopRMuQ2oJ3GvFMhxjnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"363ddef6cfd7912feea24955a16c25844cf32bef73bfd135245936d01b15b520","last_reissued_at":"2026-05-18T03:19:22.782943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:22.782943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.3928","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":"2026-05-18T03:19:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"46rguVug6+6S6kbmoFb3kuMctKHMamWOjkeTGLATwp6FI6VE1AXcRFRfOKCg++kxbh4slo+PMMCuOJ2bjsBhDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:05:14.865274Z"},"content_sha256":"c2fa802234d380ed9ecafc7783a20497beb46762350bf33af31c97a1b07ff1fc","schema_version":"1.0","event_id":"sha256:c2fa802234d380ed9ecafc7783a20497beb46762350bf33af31c97a1b07ff1fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:GY6555WP26IS73VCJFK2C3BFQR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automorphisms of classical geometries in the sense of Klein","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alberto Navarro, Jose Navarro","submitted_at":"2009-01-25T22:47:03Z","abstract_excerpt":"In this note, we compute the group of automorphisms of Projective, Affine and Euclidean Geometries in the sense of Klein.\n  As an application, we give a simple construction of the outer automorphism of S_6."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.3928","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":"2026-05-18T03:19:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OB1zljXtHkU09dZp/nOj7t6JdWLWMthEaiaBp7VDPade3rafFJIBBylwU8nFkXmMKAZNf1CQ6F/TGwvjbvI2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:05:14.865955Z"},"content_sha256":"cec75f79d0cdd9eacd7143602d1bf874bfb3e7028fbdf1dc6b58c0624b2f3c57","schema_version":"1.0","event_id":"sha256:cec75f79d0cdd9eacd7143602d1bf874bfb3e7028fbdf1dc6b58c0624b2f3c57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GY6555WP26IS73VCJFK2C3BFQR/bundle.json","state_url":"https://pith.science/pith/GY6555WP26IS73VCJFK2C3BFQR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GY6555WP26IS73VCJFK2C3BFQR/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":"2026-05-25T16:05:14Z","links":{"resolver":"https://pith.science/pith/GY6555WP26IS73VCJFK2C3BFQR","bundle":"https://pith.science/pith/GY6555WP26IS73VCJFK2C3BFQR/bundle.json","state":"https://pith.science/pith/GY6555WP26IS73VCJFK2C3BFQR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GY6555WP26IS73VCJFK2C3BFQR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:GY6555WP26IS73VCJFK2C3BFQR","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":"9ffd21e6d2d52903f787aa1509f78da7e261456a7b797bde9dc1608bf476ccfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-25T22:47:03Z","title_canon_sha256":"92bd69df799e9872a84c4d66924559b79469e1aeacee5afc13ba8a9be8074193"},"schema_version":"1.0","source":{"id":"0901.3928","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.3928","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"arxiv_version","alias_value":"0901.3928v2","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.3928","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"pith_short_12","alias_value":"GY6555WP26IS","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"GY6555WP26IS73VC","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"GY6555WP","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:cec75f79d0cdd9eacd7143602d1bf874bfb3e7028fbdf1dc6b58c0624b2f3c57","target":"graph","created_at":"2026-05-18T03:19:22Z","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 note, we compute the group of automorphisms of Projective, Affine and Euclidean Geometries in the sense of Klein.\n  As an application, we give a simple construction of the outer automorphism of S_6.","authors_text":"Alberto Navarro, Jose Navarro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-25T22:47:03Z","title":"Automorphisms of classical geometries in the sense of Klein"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.3928","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:c2fa802234d380ed9ecafc7783a20497beb46762350bf33af31c97a1b07ff1fc","target":"record","created_at":"2026-05-18T03:19:22Z","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":"9ffd21e6d2d52903f787aa1509f78da7e261456a7b797bde9dc1608bf476ccfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-25T22:47:03Z","title_canon_sha256":"92bd69df799e9872a84c4d66924559b79469e1aeacee5afc13ba8a9be8074193"},"schema_version":"1.0","source":{"id":"0901.3928","kind":"arxiv","version":2}},"canonical_sha256":"363ddef6cfd7912feea24955a16c25844cf32bef73bfd135245936d01b15b520","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"363ddef6cfd7912feea24955a16c25844cf32bef73bfd135245936d01b15b520","first_computed_at":"2026-05-18T03:19:22.782943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:22.782943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s80OCY99eSug3syDIS37k52tVLtpJvvbk4vp7nKMPddGCgonG1kQAglFyK8BpzwruDopRMuQ2oJ3GvFMhxjnDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:22.783450Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.3928","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2fa802234d380ed9ecafc7783a20497beb46762350bf33af31c97a1b07ff1fc","sha256:cec75f79d0cdd9eacd7143602d1bf874bfb3e7028fbdf1dc6b58c0624b2f3c57"],"state_sha256":"dbe8cb0f0fe5fb55673f2b5e6746653d158f885470ccb416b1ab963f0b771a71"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mLRDLgc6nrX2HRKHL5BA74XwqDkHiZKUsjPvCZF/uKXndhy1LajGqG2Ad69uLixV2eX2mWYiBT9spUx88GsuDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:05:14.869487Z","bundle_sha256":"9b888b00b7f365071b040390dc2c1d3c7338c0861a03f93ef632095903233694"}}