{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OJKZ3FQOJVBWJPOS6RJW6SP6XZ","short_pith_number":"pith:OJKZ3FQO","canonical_record":{"source":{"id":"1008.0318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-02T14:40:46Z","cross_cats_sorted":[],"title_canon_sha256":"b2b5fc5ad651b72c162cd34e523322ff5e160ba7e039b8f1b5c75c56d6d8e497","abstract_canon_sha256":"d77830752a63359829e007aa9c55d42b77c0c5fed5ae72b7e164b5eb89d969b3"},"schema_version":"1.0"},"canonical_sha256":"72559d960e4d4364bdd2f4536f49febe5beb7f9c6c94d44b14afe875b355690b","source":{"kind":"arxiv","id":"1008.0318","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0318","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0318v1","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0318","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"pith_short_12","alias_value":"OJKZ3FQOJVBW","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OJKZ3FQOJVBWJPOS","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OJKZ3FQO","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OJKZ3FQOJVBWJPOS6RJW6SP6XZ","target":"record","payload":{"canonical_record":{"source":{"id":"1008.0318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-02T14:40:46Z","cross_cats_sorted":[],"title_canon_sha256":"b2b5fc5ad651b72c162cd34e523322ff5e160ba7e039b8f1b5c75c56d6d8e497","abstract_canon_sha256":"d77830752a63359829e007aa9c55d42b77c0c5fed5ae72b7e164b5eb89d969b3"},"schema_version":"1.0"},"canonical_sha256":"72559d960e4d4364bdd2f4536f49febe5beb7f9c6c94d44b14afe875b355690b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:18.881972Z","signature_b64":"5niPkybOGuArbvrY4dO0764q0SB7GlPDYOC6KVhedicoq0Jxyc2YgwpGWfRCnX9H/WVdcniZGJTnW5zbDqBfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72559d960e4d4364bdd2f4536f49febe5beb7f9c6c94d44b14afe875b355690b","last_reissued_at":"2026-05-18T02:55:18.881368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:18.881368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.0318","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":"2026-05-18T02:55:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5MCM1ZpKrj91aV4pU4Copjf//FBy4cPvxaqjqVAi1gxKVaPEKzbogK4nQdhWckDM9leKU4hhFpLt8ODUGJEJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:52:51.296692Z"},"content_sha256":"506bab74ca9dae82d6aede97822af08ebe6937dd308bb991c28f0baf7ab58004","schema_version":"1.0","event_id":"sha256:506bab74ca9dae82d6aede97822af08ebe6937dd308bb991c28f0baf7ab58004"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OJKZ3FQOJVBWJPOS6RJW6SP6XZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized uniform covering maps relative to subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"B. Labuz","submitted_at":"2010-08-02T14:40:46Z","abstract_excerpt":"In \"Rips complexes and covers in the uniform category\" \\cite{Rips} the authors define, following James \\cite{J}, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. Conditions for the existence of universal uniform covering maps and generalized uniform covering maps are given. This paper extends these results by investigating the existence of these covering maps relative to subgroups of the uniform fundamental group and the fundamental group of the base space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0318","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":"2026-05-18T02:55:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9JN7EYLloxRgsTa2sTgy9mr1BuPTNe8abut9LBidLC9FC+/KsR8+BDivFC8FGtJf41N6SkPOJ6OQr87HPug7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:52:51.297033Z"},"content_sha256":"a5fbfb9232e91f71e9ac8bffbe2a6d7c57bec03243f92b25cb9a840a3fc4280e","schema_version":"1.0","event_id":"sha256:a5fbfb9232e91f71e9ac8bffbe2a6d7c57bec03243f92b25cb9a840a3fc4280e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OJKZ3FQOJVBWJPOS6RJW6SP6XZ/bundle.json","state_url":"https://pith.science/pith/OJKZ3FQOJVBWJPOS6RJW6SP6XZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OJKZ3FQOJVBWJPOS6RJW6SP6XZ/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":"2026-05-29T16:52:51Z","links":{"resolver":"https://pith.science/pith/OJKZ3FQOJVBWJPOS6RJW6SP6XZ","bundle":"https://pith.science/pith/OJKZ3FQOJVBWJPOS6RJW6SP6XZ/bundle.json","state":"https://pith.science/pith/OJKZ3FQOJVBWJPOS6RJW6SP6XZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OJKZ3FQOJVBWJPOS6RJW6SP6XZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OJKZ3FQOJVBWJPOS6RJW6SP6XZ","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":"d77830752a63359829e007aa9c55d42b77c0c5fed5ae72b7e164b5eb89d969b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-02T14:40:46Z","title_canon_sha256":"b2b5fc5ad651b72c162cd34e523322ff5e160ba7e039b8f1b5c75c56d6d8e497"},"schema_version":"1.0","source":{"id":"1008.0318","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0318","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0318v1","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0318","created_at":"2026-05-18T02:55:18Z"},{"alias_kind":"pith_short_12","alias_value":"OJKZ3FQOJVBW","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OJKZ3FQOJVBWJPOS","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OJKZ3FQO","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:a5fbfb9232e91f71e9ac8bffbe2a6d7c57bec03243f92b25cb9a840a3fc4280e","target":"graph","created_at":"2026-05-18T02:55:18Z","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 \"Rips complexes and covers in the uniform category\" \\cite{Rips} the authors define, following James \\cite{J}, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. Conditions for the existence of universal uniform covering maps and generalized uniform covering maps are given. This paper extends these results by investigating the existence of these covering maps relative to subgroups of the uniform fundamental group and the fundamental group of the base space.","authors_text":"B. Labuz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-02T14:40:46Z","title":"Generalized uniform covering maps relative to subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0318","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":"sha256:506bab74ca9dae82d6aede97822af08ebe6937dd308bb991c28f0baf7ab58004","target":"record","created_at":"2026-05-18T02:55:18Z","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":"d77830752a63359829e007aa9c55d42b77c0c5fed5ae72b7e164b5eb89d969b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-08-02T14:40:46Z","title_canon_sha256":"b2b5fc5ad651b72c162cd34e523322ff5e160ba7e039b8f1b5c75c56d6d8e497"},"schema_version":"1.0","source":{"id":"1008.0318","kind":"arxiv","version":1}},"canonical_sha256":"72559d960e4d4364bdd2f4536f49febe5beb7f9c6c94d44b14afe875b355690b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72559d960e4d4364bdd2f4536f49febe5beb7f9c6c94d44b14afe875b355690b","first_computed_at":"2026-05-18T02:55:18.881368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:18.881368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5niPkybOGuArbvrY4dO0764q0SB7GlPDYOC6KVhedicoq0Jxyc2YgwpGWfRCnX9H/WVdcniZGJTnW5zbDqBfDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:18.881972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.0318","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:506bab74ca9dae82d6aede97822af08ebe6937dd308bb991c28f0baf7ab58004","sha256:a5fbfb9232e91f71e9ac8bffbe2a6d7c57bec03243f92b25cb9a840a3fc4280e"],"state_sha256":"a656b93a5dc0c81e2a6906482c1189730758b7f3ca278bbfe8df6a956dbe5fe4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jLcazt7mMouwBBK203qbcXOP1DUsvCftLLUd1yJyJ0CVqaPWGMfZNEqJS+xqlDO5HXezbaBSH+7/puYpxCNLCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T16:52:51.298976Z","bundle_sha256":"970d161ab31f398878500e592e736767052d2f6ba8f50455bf7dc452029274f0"}}