{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6UO7Z5SX4J57MOSCLE3KYJQHSO","short_pith_number":"pith:6UO7Z5SX","canonical_record":{"source":{"id":"1301.0477","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-03T15:08:21Z","cross_cats_sorted":["math.GN","math.GT"],"title_canon_sha256":"d08a982126971972ffdad2570109f032cc9f070b8b4ae5448f643c8bf2795254","abstract_canon_sha256":"5ff678fd07d3e3276d4c273cf8b28e6f590d3bd5490cff35ea5644f384fe58e2"},"schema_version":"1.0"},"canonical_sha256":"f51dfcf657e27bf63a425936ac260793bfaf6f1d744b4578f574513d97d90fac","source":{"kind":"arxiv","id":"1301.0477","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0477","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0477v2","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0477","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"6UO7Z5SX4J57","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6UO7Z5SX4J57MOSC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6UO7Z5SX","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6UO7Z5SX4J57MOSCLE3KYJQHSO","target":"record","payload":{"canonical_record":{"source":{"id":"1301.0477","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-03T15:08:21Z","cross_cats_sorted":["math.GN","math.GT"],"title_canon_sha256":"d08a982126971972ffdad2570109f032cc9f070b8b4ae5448f643c8bf2795254","abstract_canon_sha256":"5ff678fd07d3e3276d4c273cf8b28e6f590d3bd5490cff35ea5644f384fe58e2"},"schema_version":"1.0"},"canonical_sha256":"f51dfcf657e27bf63a425936ac260793bfaf6f1d744b4578f574513d97d90fac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:06.023297Z","signature_b64":"qERTF9P6mKP408Vw6NOG9oCJUJx6+CIbbSpyQSndeZ1S9oHSup7DvsEzSqp/noVkbkfKcsLLOr6ANxnl06uuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f51dfcf657e27bf63a425936ac260793bfaf6f1d744b4578f574513d97d90fac","last_reissued_at":"2026-05-18T03:36:06.022642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:06.022642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.0477","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":"2026-05-18T03:36:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nvviKlmDi9ypuQk55jOBHolvsOa291FkjC5Qy4ukiP6D0OmCHkCLPszdK0R6aARpTwHDMrdFJW7IjErpnM6pDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:03:53.498765Z"},"content_sha256":"921f5355983a724af2254abc0211e728940be09b5ac85a83368ff90ec8afb885","schema_version":"1.0","event_id":"sha256:921f5355983a724af2254abc0211e728940be09b5ac85a83368ff90ec8afb885"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6UO7Z5SX4J57MOSCLE3KYJQHSO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Overlays and group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.GT"],"primary_cat":"math.AT","authors_text":"Jerzy Dydak","submitted_at":"2013-01-03T15:08:21Z","abstract_excerpt":"Overlays were introduced by R. H. Fox [6] as a subclass of covering maps. We offer a different view of overlays: it resembles the definition of paracompact spaces via star refinements of open covers. One introduces covering structures for covering maps and $p:X\\to Y$ is an overlay if it has a covering structure that has a star refinement.\n  We prove two characterizations of overlays: one using existence and uniqueness of lifts of discrete chains, the second as maps inducing simplicial coverings of nerves of certain covers. We use those characterizations to improve results of Eda-Matijevi\\' c c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0477","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":"2026-05-18T03:36:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p23PHHnkwLxI2Fqcbk5ot/U0ZsFUKIPM/2vUewY1C+9lYEBucmu1v3TqXivCPfgp4gFZqDfDRfjcUwvrj7qSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:03:53.499131Z"},"content_sha256":"f33725e483cc983ce9d6f6ea778b651744a59fc9dc6ac0d40cb273bf706c7aee","schema_version":"1.0","event_id":"sha256:f33725e483cc983ce9d6f6ea778b651744a59fc9dc6ac0d40cb273bf706c7aee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6UO7Z5SX4J57MOSCLE3KYJQHSO/bundle.json","state_url":"https://pith.science/pith/6UO7Z5SX4J57MOSCLE3KYJQHSO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6UO7Z5SX4J57MOSCLE3KYJQHSO/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":"2026-06-23T19:03:53Z","links":{"resolver":"https://pith.science/pith/6UO7Z5SX4J57MOSCLE3KYJQHSO","bundle":"https://pith.science/pith/6UO7Z5SX4J57MOSCLE3KYJQHSO/bundle.json","state":"https://pith.science/pith/6UO7Z5SX4J57MOSCLE3KYJQHSO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6UO7Z5SX4J57MOSCLE3KYJQHSO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6UO7Z5SX4J57MOSCLE3KYJQHSO","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":"5ff678fd07d3e3276d4c273cf8b28e6f590d3bd5490cff35ea5644f384fe58e2","cross_cats_sorted":["math.GN","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-03T15:08:21Z","title_canon_sha256":"d08a982126971972ffdad2570109f032cc9f070b8b4ae5448f643c8bf2795254"},"schema_version":"1.0","source":{"id":"1301.0477","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0477","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0477v2","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0477","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"6UO7Z5SX4J57","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6UO7Z5SX4J57MOSC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6UO7Z5SX","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:f33725e483cc983ce9d6f6ea778b651744a59fc9dc6ac0d40cb273bf706c7aee","target":"graph","created_at":"2026-05-18T03:36:06Z","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":"Overlays were introduced by R. H. Fox [6] as a subclass of covering maps. We offer a different view of overlays: it resembles the definition of paracompact spaces via star refinements of open covers. One introduces covering structures for covering maps and $p:X\\to Y$ is an overlay if it has a covering structure that has a star refinement.\n  We prove two characterizations of overlays: one using existence and uniqueness of lifts of discrete chains, the second as maps inducing simplicial coverings of nerves of certain covers. We use those characterizations to improve results of Eda-Matijevi\\' c c","authors_text":"Jerzy Dydak","cross_cats":["math.GN","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-03T15:08:21Z","title":"Overlays and group actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0477","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":"sha256:921f5355983a724af2254abc0211e728940be09b5ac85a83368ff90ec8afb885","target":"record","created_at":"2026-05-18T03:36:06Z","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":"5ff678fd07d3e3276d4c273cf8b28e6f590d3bd5490cff35ea5644f384fe58e2","cross_cats_sorted":["math.GN","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-01-03T15:08:21Z","title_canon_sha256":"d08a982126971972ffdad2570109f032cc9f070b8b4ae5448f643c8bf2795254"},"schema_version":"1.0","source":{"id":"1301.0477","kind":"arxiv","version":2}},"canonical_sha256":"f51dfcf657e27bf63a425936ac260793bfaf6f1d744b4578f574513d97d90fac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f51dfcf657e27bf63a425936ac260793bfaf6f1d744b4578f574513d97d90fac","first_computed_at":"2026-05-18T03:36:06.022642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:06.022642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qERTF9P6mKP408Vw6NOG9oCJUJx6+CIbbSpyQSndeZ1S9oHSup7DvsEzSqp/noVkbkfKcsLLOr6ANxnl06uuBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:06.023297Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.0477","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:921f5355983a724af2254abc0211e728940be09b5ac85a83368ff90ec8afb885","sha256:f33725e483cc983ce9d6f6ea778b651744a59fc9dc6ac0d40cb273bf706c7aee"],"state_sha256":"0df048cff7b56044baaa195f5707e0559bf86c9be1293f0e07c32bd83ea90e89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"55/mbxdwxkZJ2raf+CIUlRDQ0LO1CVxXoP+FbzdxORiN5BJz/t+FUoNo2smrWSxEkL+6qlKa8nMmCpsgwFV3DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:03:53.501294Z","bundle_sha256":"cdaaaad95a69a6eaa97c3847f6ae480bf9e22f2feab78304b02906bde4bc407e"}}