{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BPVTYT64M42GXYRFKBKSTQW3ZY","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":"d3058d4bb5dfff153b268f64093996529426af2fa3d2009a69c6f1d5704c5bd9","cross_cats_sorted":["math.AG","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-06-24T07:48:19Z","title_canon_sha256":"ef817b74905cc6293539d6a69df9d1739e54b5b0f4cb7ed40df8160458003a71"},"schema_version":"1.0","source":{"id":"2606.25516","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.25516","created_at":"2026-06-25T01:18:07Z"},{"alias_kind":"arxiv_version","alias_value":"2606.25516v1","created_at":"2026-06-25T01:18:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25516","created_at":"2026-06-25T01:18:07Z"},{"alias_kind":"pith_short_12","alias_value":"BPVTYT64M42G","created_at":"2026-06-25T01:18:07Z"},{"alias_kind":"pith_short_16","alias_value":"BPVTYT64M42GXYRF","created_at":"2026-06-25T01:18:07Z"},{"alias_kind":"pith_short_8","alias_value":"BPVTYT64","created_at":"2026-06-25T01:18:07Z"}],"graph_snapshots":[{"event_id":"sha256:8908cf679574bc1e79d2420e78ef2dcc4235385fb8dc26aa3fc1cd256b99d36e","target":"graph","created_at":"2026-06-25T01:18:07Z","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/2606.25516/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define a notion of total positivity for the symmetric space $G/K$ by taking the Hausdorff closure of the image of Lusztig's totally positive part $G_{>0}$ in $G/K$. We introduce double Bruhat cells for the symmetric space and define their totally positive pieces. We prove a cell decomposition of the totally nonnegative symmetric space, give explicit positive parametrizations of all cells, establish closure relations, and show that the transition maps between the two natural families of parametrizations are subtraction-free.","authors_text":"Huanchen Bao","cross_cats":["math.AG","math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25516","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":"sha256:1f588399fb1c87b4de3e2ea5163dbcea3cf2ece2233c79de1e1c82b7bfe97276","target":"record","created_at":"2026-06-25T01:18:07Z","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":"d3058d4bb5dfff153b268f64093996529426af2fa3d2009a69c6f1d5704c5bd9","cross_cats_sorted":["math.AG","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-06-24T07:48:19Z","title_canon_sha256":"ef817b74905cc6293539d6a69df9d1739e54b5b0f4cb7ed40df8160458003a71"},"schema_version":"1.0","source":{"id":"2606.25516","kind":"arxiv","version":1}},"canonical_sha256":"0beb3c4fdc67346be225505529c2dbce047ce1e83e0f896e399250f7f08e2f67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0beb3c4fdc67346be225505529c2dbce047ce1e83e0f896e399250f7f08e2f67","first_computed_at":"2026-06-25T01:18:07.567342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T01:18:07.567342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/ifdV3/+VA1c8l0+8jZvqpU+v9CST//N93QWov0gLYWX/XnAF655yea+x1nkmvVJvoQJdKyM+QkjpVz3mfAsBA==","signature_status":"signed_v1","signed_at":"2026-06-25T01:18:07.567739Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.25516","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f588399fb1c87b4de3e2ea5163dbcea3cf2ece2233c79de1e1c82b7bfe97276","sha256:8908cf679574bc1e79d2420e78ef2dcc4235385fb8dc26aa3fc1cd256b99d36e"],"state_sha256":"b9e27b385105c201282041e8e4caf4ad6fe70eafbf3ff60e0d91ec1aec8bb3f7"}