{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:AASAXOJJITSSD4KXKOD7GYSAUT","short_pith_number":"pith:AASAXOJJ","canonical_record":{"source":{"id":"1903.08041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-03-19T15:06:07Z","cross_cats_sorted":[],"title_canon_sha256":"51442d9f65f4046d08f45ea37d520ff91d8b0a48d8e00ebcf72ef0bee5f1cc4b","abstract_canon_sha256":"d5cd0e86aa0fc49f45c864397be3e9d6d96b335fd68ff1f87c20d1b73a0c58c9"},"schema_version":"1.0"},"canonical_sha256":"00240bb92944e521f1575387f36240a4e7e07e669d3edf7556daa0ffe0d54956","source":{"kind":"arxiv","id":"1903.08041","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.08041","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1903.08041v1","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.08041","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"AASAXOJJITSS","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AASAXOJJITSSD4KX","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AASAXOJJ","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:AASAXOJJITSSD4KXKOD7GYSAUT","target":"record","payload":{"canonical_record":{"source":{"id":"1903.08041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-03-19T15:06:07Z","cross_cats_sorted":[],"title_canon_sha256":"51442d9f65f4046d08f45ea37d520ff91d8b0a48d8e00ebcf72ef0bee5f1cc4b","abstract_canon_sha256":"d5cd0e86aa0fc49f45c864397be3e9d6d96b335fd68ff1f87c20d1b73a0c58c9"},"schema_version":"1.0"},"canonical_sha256":"00240bb92944e521f1575387f36240a4e7e07e669d3edf7556daa0ffe0d54956","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:53.101827Z","signature_b64":"IBufWHcLO28HIk0+0DQ76O7x4OzhkeWlW8R5tssL7jH0L9/v9n3leGbeol/im7I6zP6TzN9xe3BKKtqchpZXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00240bb92944e521f1575387f36240a4e7e07e669d3edf7556daa0ffe0d54956","last_reissued_at":"2026-05-17T23:50:53.101108Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:53.101108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.08041","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":"2026-05-17T23:50:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yL1Bz/YRWhpcKvaepum5aclAH/Ix9UlFW1R7ScsVunGcx4abplfUfJvqgUZOxj5PSeMVhVPdLtD6d3Bhd5brBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:10:41.678091Z"},"content_sha256":"598b677bd46e7b90b5baa8b8a47fb23ab4558242dd09d778fa84043a52ea5901","schema_version":"1.0","event_id":"sha256:598b677bd46e7b90b5baa8b8a47fb23ab4558242dd09d778fa84043a52ea5901"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:AASAXOJJITSSD4KXKOD7GYSAUT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Countably compact groups and sequential order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Alexander Shibakov, Dmitri Shakhmatov","submitted_at":"2019-03-19T15:06:07Z","abstract_excerpt":"We use $\\diamondsuit$ to construct, for every $\\alpha\\leq\\omega_1$ a sequential countably compact topological group of sequential order $\\alpha$. This establishes the independence of the existence of sequential countably compact non Fr\\'echet groups from the usual axioms of ZFC and answers several questions of D.~Shakhmatov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08041","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":"2026-05-17T23:50:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9lESZR35Bo1u6+ZXNPkxIy7TVgioHtTbzSZ2TSq1sujQydXWUtG4mIjabojHkSmuHST3uVh34ElZyhwHpgZCBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:10:41.678446Z"},"content_sha256":"11beb5735315691c0cdba249daeee5697af06c35d2bec0f14efa3d24447f11da","schema_version":"1.0","event_id":"sha256:11beb5735315691c0cdba249daeee5697af06c35d2bec0f14efa3d24447f11da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AASAXOJJITSSD4KXKOD7GYSAUT/bundle.json","state_url":"https://pith.science/pith/AASAXOJJITSSD4KXKOD7GYSAUT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AASAXOJJITSSD4KXKOD7GYSAUT/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":"2026-06-01T15:10:41Z","links":{"resolver":"https://pith.science/pith/AASAXOJJITSSD4KXKOD7GYSAUT","bundle":"https://pith.science/pith/AASAXOJJITSSD4KXKOD7GYSAUT/bundle.json","state":"https://pith.science/pith/AASAXOJJITSSD4KXKOD7GYSAUT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AASAXOJJITSSD4KXKOD7GYSAUT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AASAXOJJITSSD4KXKOD7GYSAUT","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":"d5cd0e86aa0fc49f45c864397be3e9d6d96b335fd68ff1f87c20d1b73a0c58c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-03-19T15:06:07Z","title_canon_sha256":"51442d9f65f4046d08f45ea37d520ff91d8b0a48d8e00ebcf72ef0bee5f1cc4b"},"schema_version":"1.0","source":{"id":"1903.08041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.08041","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1903.08041v1","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.08041","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"AASAXOJJITSS","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AASAXOJJITSSD4KX","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AASAXOJJ","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:11beb5735315691c0cdba249daeee5697af06c35d2bec0f14efa3d24447f11da","target":"graph","created_at":"2026-05-17T23:50:53Z","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 use $\\diamondsuit$ to construct, for every $\\alpha\\leq\\omega_1$ a sequential countably compact topological group of sequential order $\\alpha$. This establishes the independence of the existence of sequential countably compact non Fr\\'echet groups from the usual axioms of ZFC and answers several questions of D.~Shakhmatov.","authors_text":"Alexander Shibakov, Dmitri Shakhmatov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-03-19T15:06:07Z","title":"Countably compact groups and sequential order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08041","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":"sha256:598b677bd46e7b90b5baa8b8a47fb23ab4558242dd09d778fa84043a52ea5901","target":"record","created_at":"2026-05-17T23:50:53Z","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":"d5cd0e86aa0fc49f45c864397be3e9d6d96b335fd68ff1f87c20d1b73a0c58c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-03-19T15:06:07Z","title_canon_sha256":"51442d9f65f4046d08f45ea37d520ff91d8b0a48d8e00ebcf72ef0bee5f1cc4b"},"schema_version":"1.0","source":{"id":"1903.08041","kind":"arxiv","version":1}},"canonical_sha256":"00240bb92944e521f1575387f36240a4e7e07e669d3edf7556daa0ffe0d54956","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00240bb92944e521f1575387f36240a4e7e07e669d3edf7556daa0ffe0d54956","first_computed_at":"2026-05-17T23:50:53.101108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:53.101108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IBufWHcLO28HIk0+0DQ76O7x4OzhkeWlW8R5tssL7jH0L9/v9n3leGbeol/im7I6zP6TzN9xe3BKKtqchpZXAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:53.101827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.08041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:598b677bd46e7b90b5baa8b8a47fb23ab4558242dd09d778fa84043a52ea5901","sha256:11beb5735315691c0cdba249daeee5697af06c35d2bec0f14efa3d24447f11da"],"state_sha256":"d837b568797c710aa328b304dbfc28ca0605c3ae0b864a7a3c94196aa80f8b96"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"20v04lk5Lh/pv1blJs48U/6NNrygJJd/ARC92yX0vb/F4gzMaZ3Z8ywCAW/BKjtfyzmYkfOdZ/nW6QqgJP1ICg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T15:10:41.680266Z","bundle_sha256":"d79f8dd583b58420549ee86874023cd98e253a6d04720774e43816d7034d2a59"}}