{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:CGY4EKQYCPYJTSROF4TIBJPZFK","short_pith_number":"pith:CGY4EKQY","canonical_record":{"source":{"id":"2408.13449","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-08-24T03:17:41Z","cross_cats_sorted":[],"title_canon_sha256":"8f0218b78c9227a481e5eedf42a850d099147931a22a2cbeb08a1b296cfab4fa","abstract_canon_sha256":"64f910be22affb20a85ab6934b942bcc187af4df07d24f5f4523dfd0f83730e3"},"schema_version":"1.0"},"canonical_sha256":"11b1c22a1813f099ca2e2f2680a5f92aaf6d197e65751d6fca8fe680b24c4328","source":{"kind":"arxiv","id":"2408.13449","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.13449","created_at":"2026-05-22T01:03:40Z"},{"alias_kind":"arxiv_version","alias_value":"2408.13449v2","created_at":"2026-05-22T01:03:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.13449","created_at":"2026-05-22T01:03:40Z"},{"alias_kind":"pith_short_12","alias_value":"CGY4EKQYCPYJ","created_at":"2026-05-22T01:03:40Z"},{"alias_kind":"pith_short_16","alias_value":"CGY4EKQYCPYJTSRO","created_at":"2026-05-22T01:03:40Z"},{"alias_kind":"pith_short_8","alias_value":"CGY4EKQY","created_at":"2026-05-22T01:03:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:CGY4EKQYCPYJTSROF4TIBJPZFK","target":"record","payload":{"canonical_record":{"source":{"id":"2408.13449","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-08-24T03:17:41Z","cross_cats_sorted":[],"title_canon_sha256":"8f0218b78c9227a481e5eedf42a850d099147931a22a2cbeb08a1b296cfab4fa","abstract_canon_sha256":"64f910be22affb20a85ab6934b942bcc187af4df07d24f5f4523dfd0f83730e3"},"schema_version":"1.0"},"canonical_sha256":"11b1c22a1813f099ca2e2f2680a5f92aaf6d197e65751d6fca8fe680b24c4328","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:03:40.219206Z","signature_b64":"CGL9WLMFSQp9hSG5ox0weYjsh0pp0Bn0wMTACPvQ/pJ8TnnxAFFK2WX4oZUu8maTGk07MSbGh5+LAonTMDHyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11b1c22a1813f099ca2e2f2680a5f92aaf6d197e65751d6fca8fe680b24c4328","last_reissued_at":"2026-05-22T01:03:40.218192Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:03:40.218192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.13449","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":"2026-05-22T01:03:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YlkqWRh+bZS6x3lpXedvGriRytKC/zhLSDtlRvF5cCRhFkhkdZI3nvuWxC/z/24G9/vMGPPbjxZVd0BtEu/jBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:45:20.320557Z"},"content_sha256":"4595a76829a393f40b10a324f62142cc58ade8830a7c15b66b927b6fc19db5e7","schema_version":"1.0","event_id":"sha256:4595a76829a393f40b10a324f62142cc58ade8830a7c15b66b927b6fc19db5e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:CGY4EKQYCPYJTSROF4TIBJPZFK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on test elements for monomorphisms of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Dongxiao Zhao, Qiang Zhang","submitted_at":"2024-08-24T03:17:41Z","abstract_excerpt":"A word in a group is called a test element if any endomorphism fixing it is necessarily an automorphism. In this note, we give a sufficient condition in geometry to construct test elements for monomorphisms of a free group, by using the Whitehead graph and the action of the free group on its Cayley graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.13449","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.13449/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-22T01:03:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IwNyVPGRUFb0TbUWfCFca/onJ/bEZkZQAHatYBMRg/xHKfXUfDGY3iI2YGZQhhCKu7ZjWWzhA/x1VAjuxSafAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:45:20.321178Z"},"content_sha256":"b8aa9825d243c92f1d99384f3478b78fd74b407f3a4e16446dcde1a1bfd2d4c5","schema_version":"1.0","event_id":"sha256:b8aa9825d243c92f1d99384f3478b78fd74b407f3a4e16446dcde1a1bfd2d4c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CGY4EKQYCPYJTSROF4TIBJPZFK/bundle.json","state_url":"https://pith.science/pith/CGY4EKQYCPYJTSROF4TIBJPZFK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CGY4EKQYCPYJTSROF4TIBJPZFK/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":"2026-06-11T03:45:20Z","links":{"resolver":"https://pith.science/pith/CGY4EKQYCPYJTSROF4TIBJPZFK","bundle":"https://pith.science/pith/CGY4EKQYCPYJTSROF4TIBJPZFK/bundle.json","state":"https://pith.science/pith/CGY4EKQYCPYJTSROF4TIBJPZFK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CGY4EKQYCPYJTSROF4TIBJPZFK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CGY4EKQYCPYJTSROF4TIBJPZFK","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":"64f910be22affb20a85ab6934b942bcc187af4df07d24f5f4523dfd0f83730e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-08-24T03:17:41Z","title_canon_sha256":"8f0218b78c9227a481e5eedf42a850d099147931a22a2cbeb08a1b296cfab4fa"},"schema_version":"1.0","source":{"id":"2408.13449","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.13449","created_at":"2026-05-22T01:03:40Z"},{"alias_kind":"arxiv_version","alias_value":"2408.13449v2","created_at":"2026-05-22T01:03:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.13449","created_at":"2026-05-22T01:03:40Z"},{"alias_kind":"pith_short_12","alias_value":"CGY4EKQYCPYJ","created_at":"2026-05-22T01:03:40Z"},{"alias_kind":"pith_short_16","alias_value":"CGY4EKQYCPYJTSRO","created_at":"2026-05-22T01:03:40Z"},{"alias_kind":"pith_short_8","alias_value":"CGY4EKQY","created_at":"2026-05-22T01:03:40Z"}],"graph_snapshots":[{"event_id":"sha256:b8aa9825d243c92f1d99384f3478b78fd74b407f3a4e16446dcde1a1bfd2d4c5","target":"graph","created_at":"2026-05-22T01:03:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2408.13449/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A word in a group is called a test element if any endomorphism fixing it is necessarily an automorphism. In this note, we give a sufficient condition in geometry to construct test elements for monomorphisms of a free group, by using the Whitehead graph and the action of the free group on its Cayley graph.","authors_text":"Dongxiao Zhao, Qiang Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-08-24T03:17:41Z","title":"A note on test elements for monomorphisms of free groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.13449","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":"sha256:4595a76829a393f40b10a324f62142cc58ade8830a7c15b66b927b6fc19db5e7","target":"record","created_at":"2026-05-22T01:03:40Z","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":"64f910be22affb20a85ab6934b942bcc187af4df07d24f5f4523dfd0f83730e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-08-24T03:17:41Z","title_canon_sha256":"8f0218b78c9227a481e5eedf42a850d099147931a22a2cbeb08a1b296cfab4fa"},"schema_version":"1.0","source":{"id":"2408.13449","kind":"arxiv","version":2}},"canonical_sha256":"11b1c22a1813f099ca2e2f2680a5f92aaf6d197e65751d6fca8fe680b24c4328","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11b1c22a1813f099ca2e2f2680a5f92aaf6d197e65751d6fca8fe680b24c4328","first_computed_at":"2026-05-22T01:03:40.218192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:03:40.218192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CGL9WLMFSQp9hSG5ox0weYjsh0pp0Bn0wMTACPvQ/pJ8TnnxAFFK2WX4oZUu8maTGk07MSbGh5+LAonTMDHyBA==","signature_status":"signed_v1","signed_at":"2026-05-22T01:03:40.219206Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.13449","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4595a76829a393f40b10a324f62142cc58ade8830a7c15b66b927b6fc19db5e7","sha256:b8aa9825d243c92f1d99384f3478b78fd74b407f3a4e16446dcde1a1bfd2d4c5"],"state_sha256":"c1adf492e623a550f9ec65c0d0dc4984cd765bc302474103c7b15adc38a3c089"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HASFkTNr6t9yy6ptKkDF+cDCu1yV3pWwXKXne8AtpMjWfpQEmQXi4OidFMHQ6iS7QCqJ/adBrDWZ93MIIgmRCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:45:20.324467Z","bundle_sha256":"451b1ad325942bf729744661111274a2fc950ce71e2844df655b1ec4b95f44ee"}}