{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AKXJDPCLCYFHEAJQGK5YI5VVYK","short_pith_number":"pith:AKXJDPCL","canonical_record":{"source":{"id":"1212.3005","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-12T22:34:00Z","cross_cats_sorted":[],"title_canon_sha256":"3f4a70efae60ec1f8d81bc401b3d0fdffce434db13390d0623041a23d919a75f","abstract_canon_sha256":"e224c68ace9a8054f5298d6ea8b73b298a3fdf3c846939c7f3c7f29acdeb2a0e"},"schema_version":"1.0"},"canonical_sha256":"02ae91bc4b160a72013032bb8476b5c2b6eb9d2eccb50b0058b75cf624a82b26","source":{"kind":"arxiv","id":"1212.3005","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3005","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3005v2","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3005","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"pith_short_12","alias_value":"AKXJDPCLCYFH","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AKXJDPCLCYFHEAJQ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AKXJDPCL","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AKXJDPCLCYFHEAJQGK5YI5VVYK","target":"record","payload":{"canonical_record":{"source":{"id":"1212.3005","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-12T22:34:00Z","cross_cats_sorted":[],"title_canon_sha256":"3f4a70efae60ec1f8d81bc401b3d0fdffce434db13390d0623041a23d919a75f","abstract_canon_sha256":"e224c68ace9a8054f5298d6ea8b73b298a3fdf3c846939c7f3c7f29acdeb2a0e"},"schema_version":"1.0"},"canonical_sha256":"02ae91bc4b160a72013032bb8476b5c2b6eb9d2eccb50b0058b75cf624a82b26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:34.098236Z","signature_b64":"g307S4vJDNRu/nzrUdhnXqvLxulF5g8F1mebUAlYCd4gFnQ53likLUtVqBV9LzUf1BiACKvkYXi56DaxrbwEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02ae91bc4b160a72013032bb8476b5c2b6eb9d2eccb50b0058b75cf624a82b26","last_reissued_at":"2026-05-18T03:13:34.097561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:34.097561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.3005","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":"2026-05-18T03:13:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VTmcmUrqOQW6W5Ilc53lBkdsgGndpEIXwGgmwZMbk1NHXWXPj4uTM6er+gjxBIgRWALTfTtBP46rscPrB+6FDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:17:03.857292Z"},"content_sha256":"8b6ad9583071ccc22e6959209c7b744b35e2f382968105cc78de5268b94daf57","schema_version":"1.0","event_id":"sha256:8b6ad9583071ccc22e6959209c7b744b35e2f382968105cc78de5268b94daf57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AKXJDPCLCYFHEAJQGK5YI5VVYK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bad Wadge-like reducibilities on the Baire space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Luca Motto Ros","submitted_at":"2012-12-12T22:34:00Z","abstract_excerpt":"We consider various collections of functions from the Baire space X into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings, and functions which are nonexpansive or Lipschitz with respect to suitable complete ultrametrics on X (compatible with its standard topology). We analyze the degree-structures induced by such sets of functions when used as reducibility notions between subsets of X, and we show that the resulting hierarchies of degrees are much more complicated than the classic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3005","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":"2026-05-18T03:13:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W+yeezqNKV+K7nDeU5zA5rl1ImnBvdZffOeYRF5l6eDNc3jmHa1JG5kgY+H0XNki77S/oTRUgnkrXDy8AGXMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T19:17:03.857678Z"},"content_sha256":"881d190ef63df0b5f9a11e7dddf8cf364226edba62a89222b7eb254bf723a42b","schema_version":"1.0","event_id":"sha256:881d190ef63df0b5f9a11e7dddf8cf364226edba62a89222b7eb254bf723a42b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AKXJDPCLCYFHEAJQGK5YI5VVYK/bundle.json","state_url":"https://pith.science/pith/AKXJDPCLCYFHEAJQGK5YI5VVYK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AKXJDPCLCYFHEAJQGK5YI5VVYK/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":"2026-07-02T19:17:03Z","links":{"resolver":"https://pith.science/pith/AKXJDPCLCYFHEAJQGK5YI5VVYK","bundle":"https://pith.science/pith/AKXJDPCLCYFHEAJQGK5YI5VVYK/bundle.json","state":"https://pith.science/pith/AKXJDPCLCYFHEAJQGK5YI5VVYK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AKXJDPCLCYFHEAJQGK5YI5VVYK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AKXJDPCLCYFHEAJQGK5YI5VVYK","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":"e224c68ace9a8054f5298d6ea8b73b298a3fdf3c846939c7f3c7f29acdeb2a0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-12T22:34:00Z","title_canon_sha256":"3f4a70efae60ec1f8d81bc401b3d0fdffce434db13390d0623041a23d919a75f"},"schema_version":"1.0","source":{"id":"1212.3005","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3005","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3005v2","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3005","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"pith_short_12","alias_value":"AKXJDPCLCYFH","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AKXJDPCLCYFHEAJQ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AKXJDPCL","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:881d190ef63df0b5f9a11e7dddf8cf364226edba62a89222b7eb254bf723a42b","target":"graph","created_at":"2026-05-18T03:13:34Z","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":"We consider various collections of functions from the Baire space X into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings, and functions which are nonexpansive or Lipschitz with respect to suitable complete ultrametrics on X (compatible with its standard topology). We analyze the degree-structures induced by such sets of functions when used as reducibility notions between subsets of X, and we show that the resulting hierarchies of degrees are much more complicated than the classic","authors_text":"Luca Motto Ros","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-12T22:34:00Z","title":"Bad Wadge-like reducibilities on the Baire space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3005","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":"sha256:8b6ad9583071ccc22e6959209c7b744b35e2f382968105cc78de5268b94daf57","target":"record","created_at":"2026-05-18T03:13:34Z","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":"e224c68ace9a8054f5298d6ea8b73b298a3fdf3c846939c7f3c7f29acdeb2a0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-12T22:34:00Z","title_canon_sha256":"3f4a70efae60ec1f8d81bc401b3d0fdffce434db13390d0623041a23d919a75f"},"schema_version":"1.0","source":{"id":"1212.3005","kind":"arxiv","version":2}},"canonical_sha256":"02ae91bc4b160a72013032bb8476b5c2b6eb9d2eccb50b0058b75cf624a82b26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02ae91bc4b160a72013032bb8476b5c2b6eb9d2eccb50b0058b75cf624a82b26","first_computed_at":"2026-05-18T03:13:34.097561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:34.097561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g307S4vJDNRu/nzrUdhnXqvLxulF5g8F1mebUAlYCd4gFnQ53likLUtVqBV9LzUf1BiACKvkYXi56DaxrbwEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:34.098236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3005","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b6ad9583071ccc22e6959209c7b744b35e2f382968105cc78de5268b94daf57","sha256:881d190ef63df0b5f9a11e7dddf8cf364226edba62a89222b7eb254bf723a42b"],"state_sha256":"866872910515e9a598899e2c5d1009ac14fa7196190e6b82e3aaff28277f5704"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WXjT4aHxr9YKcTcHO0WEO//p3c2kUjZYTWx4z4vDzgGeLlsKd+gax+BkewWDt60oM6BJkvKz99sB0tcuYBPnDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T19:17:03.859742Z","bundle_sha256":"7a74a9a6baf51b767d8d91335c6e538860867b7164a6e85e3cb2b68319e4533a"}}