{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6A7VTOTJKPPBBVURYCS4Z6C6VV","short_pith_number":"pith:6A7VTOTJ","canonical_record":{"source":{"id":"1406.2084","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-06-09T06:09:34Z","cross_cats_sorted":[],"title_canon_sha256":"ed15a8132d03ee21ea6bd97f5019f8454818c2a2fc2dca7d62d7052611b13f39","abstract_canon_sha256":"839f2a0667a68773d86a1da2d84f2cc5b72306faf68efbb0444ff98ed7a83d2a"},"schema_version":"1.0"},"canonical_sha256":"f03f59ba6953de10d691c0a5ccf85ead692a099f7849b700b3c59228e99f0e34","source":{"kind":"arxiv","id":"1406.2084","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2084","created_at":"2026-05-18T02:21:51Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2084v2","created_at":"2026-05-18T02:21:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2084","created_at":"2026-05-18T02:21:51Z"},{"alias_kind":"pith_short_12","alias_value":"6A7VTOTJKPPB","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6A7VTOTJKPPBBVUR","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6A7VTOTJ","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6A7VTOTJKPPBBVURYCS4Z6C6VV","target":"record","payload":{"canonical_record":{"source":{"id":"1406.2084","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-06-09T06:09:34Z","cross_cats_sorted":[],"title_canon_sha256":"ed15a8132d03ee21ea6bd97f5019f8454818c2a2fc2dca7d62d7052611b13f39","abstract_canon_sha256":"839f2a0667a68773d86a1da2d84f2cc5b72306faf68efbb0444ff98ed7a83d2a"},"schema_version":"1.0"},"canonical_sha256":"f03f59ba6953de10d691c0a5ccf85ead692a099f7849b700b3c59228e99f0e34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:51.842260Z","signature_b64":"MUDu6YZPxJQDWrVneHOdWNT1ROXF/UrRUzvMo8e+w0W6Xfg5tPJ4q1LeeuHzrls5qaQZ6k3hzMxSSmGljNijDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f03f59ba6953de10d691c0a5ccf85ead692a099f7849b700b3c59228e99f0e34","last_reissued_at":"2026-05-18T02:21:51.841714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:51.841714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.2084","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":"2026-05-18T02:21:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7XQcjT4qKVyXjp1aKUKbcreTtz8Tibtc5PWgXeNds8d2bkoI+fmw6l1my/8wS0O7l2FHUjdqikIoXNlKgW1uCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:30:14.966932Z"},"content_sha256":"f1fd6f51d7b05b2af4c1239982022d02db699bb011cd795f8df93559dc5820b9","schema_version":"1.0","event_id":"sha256:f1fd6f51d7b05b2af4c1239982022d02db699bb011cd795f8df93559dc5820b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6A7VTOTJKPPBBVURYCS4Z6C6VV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectra of Tukey types of ultrafilters on Boolean algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jennifer A. Brown, Natasha Dobrinen","submitted_at":"2014-06-09T06:09:34Z","abstract_excerpt":"Extending recent investigations on the structure of Tukey types of ultrafilters on $\\mathcal{P}(\\omega)$ to Boolean algebras in general, we classify the spectra of Tukey types of ultrafilters for several classes of Boolean algebras, including interval algebras, tree algebras, and pseudo-tree algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2084","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":"2026-05-18T02:21:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6mIZ0LEckHdaNc0o0s7ABLrYBUEYnGT+Jq6Bf0dy6PxwrwZ+lo/xifHa7q9PkoXpq3kg5UTtj7PsGuue9ldHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:30:14.967953Z"},"content_sha256":"dfbb6a7c15298afc3cd0a910061154ef376f39e2d84de9438da8a6c38c2697ec","schema_version":"1.0","event_id":"sha256:dfbb6a7c15298afc3cd0a910061154ef376f39e2d84de9438da8a6c38c2697ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6A7VTOTJKPPBBVURYCS4Z6C6VV/bundle.json","state_url":"https://pith.science/pith/6A7VTOTJKPPBBVURYCS4Z6C6VV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6A7VTOTJKPPBBVURYCS4Z6C6VV/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":"2026-06-08T18:30:14Z","links":{"resolver":"https://pith.science/pith/6A7VTOTJKPPBBVURYCS4Z6C6VV","bundle":"https://pith.science/pith/6A7VTOTJKPPBBVURYCS4Z6C6VV/bundle.json","state":"https://pith.science/pith/6A7VTOTJKPPBBVURYCS4Z6C6VV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6A7VTOTJKPPBBVURYCS4Z6C6VV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6A7VTOTJKPPBBVURYCS4Z6C6VV","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":"839f2a0667a68773d86a1da2d84f2cc5b72306faf68efbb0444ff98ed7a83d2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-06-09T06:09:34Z","title_canon_sha256":"ed15a8132d03ee21ea6bd97f5019f8454818c2a2fc2dca7d62d7052611b13f39"},"schema_version":"1.0","source":{"id":"1406.2084","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2084","created_at":"2026-05-18T02:21:51Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2084v2","created_at":"2026-05-18T02:21:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2084","created_at":"2026-05-18T02:21:51Z"},{"alias_kind":"pith_short_12","alias_value":"6A7VTOTJKPPB","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6A7VTOTJKPPBBVUR","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6A7VTOTJ","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:dfbb6a7c15298afc3cd0a910061154ef376f39e2d84de9438da8a6c38c2697ec","target":"graph","created_at":"2026-05-18T02:21:51Z","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":"Extending recent investigations on the structure of Tukey types of ultrafilters on $\\mathcal{P}(\\omega)$ to Boolean algebras in general, we classify the spectra of Tukey types of ultrafilters for several classes of Boolean algebras, including interval algebras, tree algebras, and pseudo-tree algebras.","authors_text":"Jennifer A. Brown, Natasha Dobrinen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-06-09T06:09:34Z","title":"Spectra of Tukey types of ultrafilters on Boolean algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2084","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:f1fd6f51d7b05b2af4c1239982022d02db699bb011cd795f8df93559dc5820b9","target":"record","created_at":"2026-05-18T02:21:51Z","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":"839f2a0667a68773d86a1da2d84f2cc5b72306faf68efbb0444ff98ed7a83d2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-06-09T06:09:34Z","title_canon_sha256":"ed15a8132d03ee21ea6bd97f5019f8454818c2a2fc2dca7d62d7052611b13f39"},"schema_version":"1.0","source":{"id":"1406.2084","kind":"arxiv","version":2}},"canonical_sha256":"f03f59ba6953de10d691c0a5ccf85ead692a099f7849b700b3c59228e99f0e34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f03f59ba6953de10d691c0a5ccf85ead692a099f7849b700b3c59228e99f0e34","first_computed_at":"2026-05-18T02:21:51.841714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:51.841714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MUDu6YZPxJQDWrVneHOdWNT1ROXF/UrRUzvMo8e+w0W6Xfg5tPJ4q1LeeuHzrls5qaQZ6k3hzMxSSmGljNijDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:51.842260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.2084","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1fd6f51d7b05b2af4c1239982022d02db699bb011cd795f8df93559dc5820b9","sha256:dfbb6a7c15298afc3cd0a910061154ef376f39e2d84de9438da8a6c38c2697ec"],"state_sha256":"1c63f0d02203ddbad5af3bda42cba6bd7a5ab0be4ca24f3b33c70036b2138463"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f6NExlrsyXlHaXtUNQjnWiLUDBAGt/6AxIAy69+u2vIHeUJcP8TRvbj9mqn7q5j3itgBnFcHs/HqtwqKycSqCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:30:14.972360Z","bundle_sha256":"93558b92b1297ed0575e129ddfa71a15a01bf2aaf5934b718e128d42e85eea47"}}