{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Y5BW2KUZAJPFNPNRO5Y2M5NSCV","short_pith_number":"pith:Y5BW2KUZ","canonical_record":{"source":{"id":"1207.6377","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-07-26T19:21:23Z","cross_cats_sorted":[],"title_canon_sha256":"d998fe9efeff916ab21597b246b5a1c3bf07e7c57967e5f41aad6dabc8ea2506","abstract_canon_sha256":"71712c708f2953753d6f7d7a90adb9359e4959d4000a2078c727da53af4412fa"},"schema_version":"1.0"},"canonical_sha256":"c7436d2a99025e56bdb17771a675b2155edb7a08aa7cf3d97a123f5cf6956def","source":{"kind":"arxiv","id":"1207.6377","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6377","created_at":"2026-05-18T00:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6377v2","created_at":"2026-05-18T00:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6377","created_at":"2026-05-18T00:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"Y5BW2KUZAJPF","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y5BW2KUZAJPFNPNR","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y5BW2KUZ","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Y5BW2KUZAJPFNPNRO5Y2M5NSCV","target":"record","payload":{"canonical_record":{"source":{"id":"1207.6377","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-07-26T19:21:23Z","cross_cats_sorted":[],"title_canon_sha256":"d998fe9efeff916ab21597b246b5a1c3bf07e7c57967e5f41aad6dabc8ea2506","abstract_canon_sha256":"71712c708f2953753d6f7d7a90adb9359e4959d4000a2078c727da53af4412fa"},"schema_version":"1.0"},"canonical_sha256":"c7436d2a99025e56bdb17771a675b2155edb7a08aa7cf3d97a123f5cf6956def","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:28.306457Z","signature_b64":"/rb1BumRWwWvKDiHDiAOpf5Ypggw/3iN8/UQcCdg65Bp9PNQpWKyNzDxlSDbzoKWSYHJGR4nAanmhTuUpCf+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7436d2a99025e56bdb17771a675b2155edb7a08aa7cf3d97a123f5cf6956def","last_reissued_at":"2026-05-18T00:59:28.305943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:28.305943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.6377","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":"2026-05-18T00:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YN/41it8qa1TRimC1hxB3e/UQ8oBMrhML/6/Diui+meMfxnUfrDXMzdeuh3ZiItXxEvbMoDoCWEL0Y/Yvr5vDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:30:00.481092Z"},"content_sha256":"0eeda6fc033d14e937efd0e33d74ed74f9bf05cf181e014050224ad9aefd6304","schema_version":"1.0","event_id":"sha256:0eeda6fc033d14e937efd0e33d74ed74f9bf05cf181e014050224ad9aefd6304"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Y5BW2KUZAJPFNPNRO5Y2M5NSCV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cardinal functions on continuous images of orderable compacta and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Ahmad Farhat","submitted_at":"2012-07-26T19:21:23Z","abstract_excerpt":"The class of Hausdorff spaces that are continuous images of compact orderable spaces is studied by analyzing the relationship between the elements of this class and compact orderable spaces in a back-and-forth fashion. Structure results for this class are then obtained, as well as continuum-theoretic embedding results. Applications to Boolean algebras are also demonstrated, specifically concerning the relationship between interval algebras and pseudo-tree algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6377","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":"2026-05-18T00:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"14KDL5vVF1+U2BZmiNrUo7VI9GZ0DUYW8mKLxWoKVPWp60wBoJCpAM0twmiwiHtx/CVeEqnd3rjQMWzPSKQTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:30:00.481455Z"},"content_sha256":"88b4f567df26de3190a92ca8e48b29feee2c132e00b344c408b359e7d171b335","schema_version":"1.0","event_id":"sha256:88b4f567df26de3190a92ca8e48b29feee2c132e00b344c408b359e7d171b335"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y5BW2KUZAJPFNPNRO5Y2M5NSCV/bundle.json","state_url":"https://pith.science/pith/Y5BW2KUZAJPFNPNRO5Y2M5NSCV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y5BW2KUZAJPFNPNRO5Y2M5NSCV/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":"2026-06-25T13:30:00Z","links":{"resolver":"https://pith.science/pith/Y5BW2KUZAJPFNPNRO5Y2M5NSCV","bundle":"https://pith.science/pith/Y5BW2KUZAJPFNPNRO5Y2M5NSCV/bundle.json","state":"https://pith.science/pith/Y5BW2KUZAJPFNPNRO5Y2M5NSCV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y5BW2KUZAJPFNPNRO5Y2M5NSCV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y5BW2KUZAJPFNPNRO5Y2M5NSCV","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":"71712c708f2953753d6f7d7a90adb9359e4959d4000a2078c727da53af4412fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-07-26T19:21:23Z","title_canon_sha256":"d998fe9efeff916ab21597b246b5a1c3bf07e7c57967e5f41aad6dabc8ea2506"},"schema_version":"1.0","source":{"id":"1207.6377","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6377","created_at":"2026-05-18T00:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6377v2","created_at":"2026-05-18T00:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6377","created_at":"2026-05-18T00:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"Y5BW2KUZAJPF","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y5BW2KUZAJPFNPNR","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y5BW2KUZ","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:88b4f567df26de3190a92ca8e48b29feee2c132e00b344c408b359e7d171b335","target":"graph","created_at":"2026-05-18T00:59:28Z","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":"The class of Hausdorff spaces that are continuous images of compact orderable spaces is studied by analyzing the relationship between the elements of this class and compact orderable spaces in a back-and-forth fashion. Structure results for this class are then obtained, as well as continuum-theoretic embedding results. Applications to Boolean algebras are also demonstrated, specifically concerning the relationship between interval algebras and pseudo-tree algebras.","authors_text":"Ahmad Farhat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-07-26T19:21:23Z","title":"Cardinal functions on continuous images of orderable compacta and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6377","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":"sha256:0eeda6fc033d14e937efd0e33d74ed74f9bf05cf181e014050224ad9aefd6304","target":"record","created_at":"2026-05-18T00:59:28Z","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":"71712c708f2953753d6f7d7a90adb9359e4959d4000a2078c727da53af4412fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-07-26T19:21:23Z","title_canon_sha256":"d998fe9efeff916ab21597b246b5a1c3bf07e7c57967e5f41aad6dabc8ea2506"},"schema_version":"1.0","source":{"id":"1207.6377","kind":"arxiv","version":2}},"canonical_sha256":"c7436d2a99025e56bdb17771a675b2155edb7a08aa7cf3d97a123f5cf6956def","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7436d2a99025e56bdb17771a675b2155edb7a08aa7cf3d97a123f5cf6956def","first_computed_at":"2026-05-18T00:59:28.305943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:28.305943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/rb1BumRWwWvKDiHDiAOpf5Ypggw/3iN8/UQcCdg65Bp9PNQpWKyNzDxlSDbzoKWSYHJGR4nAanmhTuUpCf+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:28.306457Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6377","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0eeda6fc033d14e937efd0e33d74ed74f9bf05cf181e014050224ad9aefd6304","sha256:88b4f567df26de3190a92ca8e48b29feee2c132e00b344c408b359e7d171b335"],"state_sha256":"860a3bdbedd6a42cecaf64519d1abea2306f669da4e141314bec01554b260c5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kcEpYGazEzUm9+sORSz2Xu9yBCcRkEU0LfXeEvS666jDG0TVEoskdCzuf4z8m47ZFbVnsddSoopOCEnSnMb2AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T13:30:00.483379Z","bundle_sha256":"b6301657abd21c983d7a346c030ed621ffdeaf52b28f47fe4775bd11e3e70570"}}