{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PIQDSSX4TDEZPNGIZ2TXQORQCC","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":"73eb96f3f616aad82fb52332271041e6cd4878ee7304b766e366dba5362eeeb8","cross_cats_sorted":["math.GR","math.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GN","submitted_at":"2026-05-25T05:49:59Z","title_canon_sha256":"9daa40d91f16b4427f2aae9b07c1e95e485febd5ec31fedc0f20b19db68dc458"},"schema_version":"1.0","source":{"id":"2605.25445","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25445","created_at":"2026-05-26T02:04:35Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25445v1","created_at":"2026-05-26T02:04:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25445","created_at":"2026-05-26T02:04:35Z"},{"alias_kind":"pith_short_12","alias_value":"PIQDSSX4TDEZ","created_at":"2026-05-26T02:04:35Z"},{"alias_kind":"pith_short_16","alias_value":"PIQDSSX4TDEZPNGI","created_at":"2026-05-26T02:04:35Z"},{"alias_kind":"pith_short_8","alias_value":"PIQDSSX4","created_at":"2026-05-26T02:04:35Z"}],"graph_snapshots":[{"event_id":"sha256:27eed262e29e920fefe1b37079e7a4271df1e20998d7cf78db36229a88374fb2","target":"graph","created_at":"2026-05-26T02:04:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.25445/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the local topological structure of non-metrizable topological groups through the lens of Tukey order and cofinal types. Motivated by recent advances in topological groups admitting an $\\omega^\\omega$-base, we introduce the \\emph{fineness index}, denoted $\\f(P)$, for arbitrary directed partially ordered sets. This cardinal invariant fundamentally generalizes the bounding number $\\mathfrak{b}$ by capturing the exact threshold where a poset evades domination by its countable subsets, thereby establishing a universal lower bound for the character of topological groups with a $P$-bas","authors_text":"Dekui Peng, Xuan Gong","cross_cats":["math.GR","math.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GN","submitted_at":"2026-05-25T05:49:59Z","title":"Cofinal types of topological groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25445","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":"sha256:826e765fcfa33a827503053c34f1fb583a1e067b58c5f3994de3ce2ebe4f9373","target":"record","created_at":"2026-05-26T02:04:35Z","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":"73eb96f3f616aad82fb52332271041e6cd4878ee7304b766e366dba5362eeeb8","cross_cats_sorted":["math.GR","math.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GN","submitted_at":"2026-05-25T05:49:59Z","title_canon_sha256":"9daa40d91f16b4427f2aae9b07c1e95e485febd5ec31fedc0f20b19db68dc458"},"schema_version":"1.0","source":{"id":"2605.25445","kind":"arxiv","version":1}},"canonical_sha256":"7a20394afc98c997b4c8cea7783a3010a3348908e3c915ad8a031be2749d90b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a20394afc98c997b4c8cea7783a3010a3348908e3c915ad8a031be2749d90b9","first_computed_at":"2026-05-26T02:04:35.670515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:35.670515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nkx3xj2zazpowN4dWx9zu5ENpfw9YspRkzxTjzoV26MR/8DGnu95470uhZEDPHRsh2hQbOEdZ8qPUlZNdjZLDQ==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:35.671348Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25445","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:826e765fcfa33a827503053c34f1fb583a1e067b58c5f3994de3ce2ebe4f9373","sha256:27eed262e29e920fefe1b37079e7a4271df1e20998d7cf78db36229a88374fb2"],"state_sha256":"eba33666b3b9b1d2685c311a068d64d708dd9cb1b0d76115200e59dc21c3b512"}