{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WUX62A2UV2W7YZ62WQ3OMELGQV","short_pith_number":"pith:WUX62A2U","canonical_record":{"source":{"id":"1307.5417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-07-20T12:33:27Z","cross_cats_sorted":[],"title_canon_sha256":"04d5fc2e9d6b4e83a03410587e38b3efa20dd0df88cf8c52fd901a857945b23a","abstract_canon_sha256":"a1c13c30a7c1f618d24936d5167bd9acc84530d0bd89d527c509529fbbe5922d"},"schema_version":"1.0"},"canonical_sha256":"b52fed0354aeadfc67dab436e61166854393a975933138dea89d8fe6010d1866","source":{"kind":"arxiv","id":"1307.5417","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5417","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5417v1","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5417","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"WUX62A2UV2W7","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WUX62A2UV2W7YZ62","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WUX62A2U","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WUX62A2UV2W7YZ62WQ3OMELGQV","target":"record","payload":{"canonical_record":{"source":{"id":"1307.5417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-07-20T12:33:27Z","cross_cats_sorted":[],"title_canon_sha256":"04d5fc2e9d6b4e83a03410587e38b3efa20dd0df88cf8c52fd901a857945b23a","abstract_canon_sha256":"a1c13c30a7c1f618d24936d5167bd9acc84530d0bd89d527c509529fbbe5922d"},"schema_version":"1.0"},"canonical_sha256":"b52fed0354aeadfc67dab436e61166854393a975933138dea89d8fe6010d1866","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:55.841886Z","signature_b64":"4kES/3R4imCcgwcDAlRpcr4vKerldIkeSwiDGzUzmaD8dj3foUNbZK+xZlD2C+1OIWEN/yurBAufRyPiOAttAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b52fed0354aeadfc67dab436e61166854393a975933138dea89d8fe6010d1866","last_reissued_at":"2026-05-18T03:17:55.841181Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:55.841181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.5417","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":"2026-05-18T03:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zpTX4KEFpyFVzB2mC3xuaWjqTrpgu+ZwqOkebP55bF23v2IVPBhQylZB5wXpYoMfjW93yuGYRDq5arRQU8fxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:28:15.944805Z"},"content_sha256":"33c5b063c7c776607006be6f06a565476d2c42120fad0d8613300f0d5a9ebe96","schema_version":"1.0","event_id":"sha256:33c5b063c7c776607006be6f06a565476d2c42120fad0d8613300f0d5a9ebe96"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WUX62A2UV2W7YZ62WQ3OMELGQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$p$-Groups for which each outer $p$-automorphism centralizes only $p$ elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alireza Abdollahi, S. Mohsen Ghoraishi","submitted_at":"2013-07-20T12:33:27Z","abstract_excerpt":"An automorphism of a group is called outer if it is not an inner automorphism.\n  Let $G$ be a finite $p$-group. Then for every outer $p$-automorphism $\\phi$ of $G$ the subgroup $C_G(\\phi)=\\{x\\in G \\;|\\; x^\\phi=x\\}$ has order $p$ if and only if $G$ is of order at most $p^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5417","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":"2026-05-18T03:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MH2JzmoCV4Z7FSHAnM5iJAmaYBHWP11GoRb+Suv9Vc1/MUxJX1zsyocdcAMM3gu/iN+u1qMoAwHccmtSyNKuCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:28:15.945531Z"},"content_sha256":"8d0b4f26e60b09eb4ea3272acd74fb2bebc14ebceaccad08eb4c3450e4ec3b6d","schema_version":"1.0","event_id":"sha256:8d0b4f26e60b09eb4ea3272acd74fb2bebc14ebceaccad08eb4c3450e4ec3b6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WUX62A2UV2W7YZ62WQ3OMELGQV/bundle.json","state_url":"https://pith.science/pith/WUX62A2UV2W7YZ62WQ3OMELGQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WUX62A2UV2W7YZ62WQ3OMELGQV/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":"2026-06-08T18:28:15Z","links":{"resolver":"https://pith.science/pith/WUX62A2UV2W7YZ62WQ3OMELGQV","bundle":"https://pith.science/pith/WUX62A2UV2W7YZ62WQ3OMELGQV/bundle.json","state":"https://pith.science/pith/WUX62A2UV2W7YZ62WQ3OMELGQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WUX62A2UV2W7YZ62WQ3OMELGQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WUX62A2UV2W7YZ62WQ3OMELGQV","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":"a1c13c30a7c1f618d24936d5167bd9acc84530d0bd89d527c509529fbbe5922d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-07-20T12:33:27Z","title_canon_sha256":"04d5fc2e9d6b4e83a03410587e38b3efa20dd0df88cf8c52fd901a857945b23a"},"schema_version":"1.0","source":{"id":"1307.5417","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5417","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5417v1","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5417","created_at":"2026-05-18T03:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"WUX62A2UV2W7","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WUX62A2UV2W7YZ62","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WUX62A2U","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:8d0b4f26e60b09eb4ea3272acd74fb2bebc14ebceaccad08eb4c3450e4ec3b6d","target":"graph","created_at":"2026-05-18T03:17:55Z","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":"An automorphism of a group is called outer if it is not an inner automorphism.\n  Let $G$ be a finite $p$-group. Then for every outer $p$-automorphism $\\phi$ of $G$ the subgroup $C_G(\\phi)=\\{x\\in G \\;|\\; x^\\phi=x\\}$ has order $p$ if and only if $G$ is of order at most $p^2$.","authors_text":"Alireza Abdollahi, S. Mohsen Ghoraishi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-07-20T12:33:27Z","title":"$p$-Groups for which each outer $p$-automorphism centralizes only $p$ elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5417","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":"sha256:33c5b063c7c776607006be6f06a565476d2c42120fad0d8613300f0d5a9ebe96","target":"record","created_at":"2026-05-18T03:17:55Z","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":"a1c13c30a7c1f618d24936d5167bd9acc84530d0bd89d527c509529fbbe5922d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-07-20T12:33:27Z","title_canon_sha256":"04d5fc2e9d6b4e83a03410587e38b3efa20dd0df88cf8c52fd901a857945b23a"},"schema_version":"1.0","source":{"id":"1307.5417","kind":"arxiv","version":1}},"canonical_sha256":"b52fed0354aeadfc67dab436e61166854393a975933138dea89d8fe6010d1866","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b52fed0354aeadfc67dab436e61166854393a975933138dea89d8fe6010d1866","first_computed_at":"2026-05-18T03:17:55.841181Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:55.841181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4kES/3R4imCcgwcDAlRpcr4vKerldIkeSwiDGzUzmaD8dj3foUNbZK+xZlD2C+1OIWEN/yurBAufRyPiOAttAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:55.841886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5417","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33c5b063c7c776607006be6f06a565476d2c42120fad0d8613300f0d5a9ebe96","sha256:8d0b4f26e60b09eb4ea3272acd74fb2bebc14ebceaccad08eb4c3450e4ec3b6d"],"state_sha256":"44918a9f8abd46e4752437241aa86bfe71601bd40e154fc6de74c5e6e7f1c138"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qHJj+OKzPCM0eo9KsOUjpE82Gh0RiZu67b9PWKv1D0kHU7GY1n+tQStIzUqVAm4Bdq+sHfei7phUAqqgIaDfAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:28:15.949768Z","bundle_sha256":"2c8546f1d63d278749923913ca63a4013e360720a68d82d5a4eaf088484d83c2"}}