{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SYUNGZGDY64DH5ZPDBXCJSSQVU","short_pith_number":"pith:SYUNGZGD","canonical_record":{"source":{"id":"1604.08872","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-04-29T15:22:09Z","cross_cats_sorted":[],"title_canon_sha256":"001f92276ac725eb3208aa17c253ce6d186be780e1767ba7e07f4dab80e31c0e","abstract_canon_sha256":"5438531448105d2f47db6fd4a323a1a977663e2ed76622e3bf6b2c0ace9885bb"},"schema_version":"1.0"},"canonical_sha256":"9628d364c3c7b833f72f186e24ca50ad1c3afad28cb307d2c0fef494a3e30c2a","source":{"kind":"arxiv","id":"1604.08872","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08872","created_at":"2026-05-18T01:16:01Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08872v1","created_at":"2026-05-18T01:16:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08872","created_at":"2026-05-18T01:16:01Z"},{"alias_kind":"pith_short_12","alias_value":"SYUNGZGDY64D","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SYUNGZGDY64DH5ZP","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SYUNGZGD","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SYUNGZGDY64DH5ZPDBXCJSSQVU","target":"record","payload":{"canonical_record":{"source":{"id":"1604.08872","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-04-29T15:22:09Z","cross_cats_sorted":[],"title_canon_sha256":"001f92276ac725eb3208aa17c253ce6d186be780e1767ba7e07f4dab80e31c0e","abstract_canon_sha256":"5438531448105d2f47db6fd4a323a1a977663e2ed76622e3bf6b2c0ace9885bb"},"schema_version":"1.0"},"canonical_sha256":"9628d364c3c7b833f72f186e24ca50ad1c3afad28cb307d2c0fef494a3e30c2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:01.537866Z","signature_b64":"XDn9FKz7Q+UUWqrFaSdUNiXjmSX2iYzNO8tPRQZbdkzSYUnfoXyPDExbU58tms2eViUP4KEP92xTu828Ik+hCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9628d364c3c7b833f72f186e24ca50ad1c3afad28cb307d2c0fef494a3e30c2a","last_reissued_at":"2026-05-18T01:16:01.537212Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:01.537212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.08872","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":"2026-05-18T01:16:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"26J9hgG5boTgEGuxz/MhwkSUtvFo3sPxncgxzgx520/JoNU0X4a+wzIN1y9qIr61DNOMIkyEJW2pA8wPqRcOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:01:54.557346Z"},"content_sha256":"824b0412e77e1b47d8248831c5e9d6cbcb715a7b4c27b0aad1522205f3cdd060","schema_version":"1.0","event_id":"sha256:824b0412e77e1b47d8248831c5e9d6cbcb715a7b4c27b0aad1522205f3cdd060"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SYUNGZGDY64DH5ZPDBXCJSSQVU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On sequential analytic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Alexander Shibakov","submitted_at":"2016-04-29T15:22:09Z","abstract_excerpt":"We answer a question of S.~Todor\\v{c}evi\\'c and C.~Uzc\\'ategui from \\cite{TU1} by showing that the only possible sequential orders of sequential analytic groups are $1$ and $\\omega_1$. Other results on the structure of sequential analytic spaces and their relation to other classes of spaces are given as well. In particular, we provide a full topological classification of sequential analytic groups by showing that all such groups are either metrizable or $k_\\omega$-spaces, which, together with a result by Zelenyuk, implies that there are exactly $\\omega_1$ non homeomorphic analytic sequential g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08872","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":"2026-05-18T01:16:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wqWNAA/Hpbhyi/PMXCKgIpJS+FLYgzLD0AoeMsVLm+QrlVzeqIvKb+UvXDB4lhMjaYBFE09ufw8W5DKK2rKsAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:01:54.557696Z"},"content_sha256":"fa4023467799fa02dc8787d8dcf123263a1cece3792c51fc2871ad4de3446fff","schema_version":"1.0","event_id":"sha256:fa4023467799fa02dc8787d8dcf123263a1cece3792c51fc2871ad4de3446fff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SYUNGZGDY64DH5ZPDBXCJSSQVU/bundle.json","state_url":"https://pith.science/pith/SYUNGZGDY64DH5ZPDBXCJSSQVU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SYUNGZGDY64DH5ZPDBXCJSSQVU/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":"2026-06-24T20:01:54Z","links":{"resolver":"https://pith.science/pith/SYUNGZGDY64DH5ZPDBXCJSSQVU","bundle":"https://pith.science/pith/SYUNGZGDY64DH5ZPDBXCJSSQVU/bundle.json","state":"https://pith.science/pith/SYUNGZGDY64DH5ZPDBXCJSSQVU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SYUNGZGDY64DH5ZPDBXCJSSQVU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SYUNGZGDY64DH5ZPDBXCJSSQVU","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":"5438531448105d2f47db6fd4a323a1a977663e2ed76622e3bf6b2c0ace9885bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-04-29T15:22:09Z","title_canon_sha256":"001f92276ac725eb3208aa17c253ce6d186be780e1767ba7e07f4dab80e31c0e"},"schema_version":"1.0","source":{"id":"1604.08872","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08872","created_at":"2026-05-18T01:16:01Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08872v1","created_at":"2026-05-18T01:16:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08872","created_at":"2026-05-18T01:16:01Z"},{"alias_kind":"pith_short_12","alias_value":"SYUNGZGDY64D","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SYUNGZGDY64DH5ZP","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SYUNGZGD","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:fa4023467799fa02dc8787d8dcf123263a1cece3792c51fc2871ad4de3446fff","target":"graph","created_at":"2026-05-18T01:16:01Z","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 answer a question of S.~Todor\\v{c}evi\\'c and C.~Uzc\\'ategui from \\cite{TU1} by showing that the only possible sequential orders of sequential analytic groups are $1$ and $\\omega_1$. Other results on the structure of sequential analytic spaces and their relation to other classes of spaces are given as well. In particular, we provide a full topological classification of sequential analytic groups by showing that all such groups are either metrizable or $k_\\omega$-spaces, which, together with a result by Zelenyuk, implies that there are exactly $\\omega_1$ non homeomorphic analytic sequential g","authors_text":"Alexander Shibakov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-04-29T15:22:09Z","title":"On sequential analytic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08872","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":"sha256:824b0412e77e1b47d8248831c5e9d6cbcb715a7b4c27b0aad1522205f3cdd060","target":"record","created_at":"2026-05-18T01:16:01Z","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":"5438531448105d2f47db6fd4a323a1a977663e2ed76622e3bf6b2c0ace9885bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-04-29T15:22:09Z","title_canon_sha256":"001f92276ac725eb3208aa17c253ce6d186be780e1767ba7e07f4dab80e31c0e"},"schema_version":"1.0","source":{"id":"1604.08872","kind":"arxiv","version":1}},"canonical_sha256":"9628d364c3c7b833f72f186e24ca50ad1c3afad28cb307d2c0fef494a3e30c2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9628d364c3c7b833f72f186e24ca50ad1c3afad28cb307d2c0fef494a3e30c2a","first_computed_at":"2026-05-18T01:16:01.537212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:01.537212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XDn9FKz7Q+UUWqrFaSdUNiXjmSX2iYzNO8tPRQZbdkzSYUnfoXyPDExbU58tms2eViUP4KEP92xTu828Ik+hCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:01.537866Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.08872","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:824b0412e77e1b47d8248831c5e9d6cbcb715a7b4c27b0aad1522205f3cdd060","sha256:fa4023467799fa02dc8787d8dcf123263a1cece3792c51fc2871ad4de3446fff"],"state_sha256":"27994d0321d21161f236de14ae507ab70f09f01faa61d955291ab74b37950ba5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tgbb22lnFD9+nEEafAE/k0aWbnOr0NvK/RrbcAupwHyR0nUakx5rBkIQpFt0SLxCI52eLlg17mOoPYSN5jf/Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:01:54.559906Z","bundle_sha256":"d4c110f2b743682f19881cec5ea4b9a0eae9af17a39d27b398feb2d8aa3bb38b"}}