{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:F4SQNJRPNP4OOKESBQW2SUPSIZ","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":"fe22a66be31e9e6ff3fa906bedb7fd079cee8cdd843608791c1916af45fb7657","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-17T09:10:31Z","title_canon_sha256":"dbd909bdf53a0b923efa86f3c6658643b455ba34f2729a96921291da94c332c2"},"schema_version":"1.0","source":{"id":"2605.17337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17337","created_at":"2026-05-20T00:03:52Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17337v1","created_at":"2026-05-20T00:03:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17337","created_at":"2026-05-20T00:03:52Z"},{"alias_kind":"pith_short_12","alias_value":"F4SQNJRPNP4O","created_at":"2026-05-20T00:03:52Z"},{"alias_kind":"pith_short_16","alias_value":"F4SQNJRPNP4OOKES","created_at":"2026-05-20T00:03:52Z"},{"alias_kind":"pith_short_8","alias_value":"F4SQNJRP","created_at":"2026-05-20T00:03:52Z"}],"graph_snapshots":[{"event_id":"sha256:e1255e4f5865dc2d5ccc7a76d480a252b21761a43dba834ad8a64298f6dcb4d7","target":"graph","created_at":"2026-05-20T00:03:52Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We determine the minimal equivariant embedding dimension of orthogonal groups acting on real flag manifolds and unitary groups acting on complex flag manifolds. The minimal embedding dimension is achieved at isospectral model."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The isospectral model is assumed to realize the absolute minimal dimension among all possible equivariant embeddings; if a lower-dimensional equivariant embedding exists outside this construction, the claimed minimality fails."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Minimal equivariant embedding dimensions for real and complex flag manifolds are computed and realized via isospectral models."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The minimal dimension for equivariant embeddings of real and complex flag manifolds into Euclidean space is achieved by the isospectral model."}],"snapshot_sha256":"e62590213f05c4d0161f126f3bb9d567cd1b7cc3d750e44ba53e6ce5ca205f23"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"a9f5b04745ca58bc07897909bddad7b68d74f1848dec8dcdf504ff7ff82eadde"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:20.114941Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T23:21:25.180253Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.804759Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.739629Z","status":"skipped","version":"1.0.0"}],"endpoint":"/pith/2605.17337/integrity.json","findings":[],"snapshot_sha256":"ddaf7269b621d68cca3f3f5f8fed0dc3b0158b7cbaad2d133cb7248776a38fc4","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine the minimal equivariant embedding dimension of orthgonal groups acting on real flag manifolds and unitary groups acting on complex flag manifolds. The minimal embedding dimension is achieved at isospectral model.","authors_text":"Hang Yin, Zhongzi Wang","cross_cats":[],"headline":"The minimal dimension for equivariant embeddings of real and complex flag manifolds into Euclidean space is achieved by the isospectral model.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-17T09:10:31Z","title":"Minimal dimension equivariant embeddings of real and complex flag manifolds into Euclidean spaces"},"references":{"count":14,"internal_anchors":0,"resolved_work":14,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Lim, Lek-Heng and Ye, ke , title=","work_id":"ebc8e164-b630-4937-ba78-e2a0948df222","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Wang, Rongbial Thomas and Lim, Lek-Heng and Ye, ke , title =","work_id":"19366055-990d-4eee-805f-23ed8fdb9a39","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Hirsch , title =","work_id":"512d5a5f-56d4-4560-9887-efbd1c753cd3","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Lectures on the orbit method , year =","work_id":"e48b5977-98c8-45ec-80d0-431a3f3981ba","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"2022 , author =","work_id":"6823bb53-2541-4296-b50e-999139c6bfff","year":2022}],"snapshot_sha256":"5878283760b6214090e85c2843d8f80b314ba27a23e8da3436ffcb690cae8e6b"},"source":{"id":"2605.17337","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T23:11:37.206185Z","id":"36424ee0-b839-4028-a7b3-165df127ef26","model_set":{"reader":"grok-4.3"},"one_line_summary":"Minimal equivariant embedding dimensions for real and complex flag manifolds are computed and realized via isospectral models.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The minimal dimension for equivariant embeddings of real and complex flag manifolds into Euclidean space is achieved by the isospectral model.","strongest_claim":"We determine the minimal equivariant embedding dimension of orthogonal groups acting on real flag manifolds and unitary groups acting on complex flag manifolds. The minimal embedding dimension is achieved at isospectral model.","weakest_assumption":"The isospectral model is assumed to realize the absolute minimal dimension among all possible equivariant embeddings; if a lower-dimensional equivariant embedding exists outside this construction, the claimed minimality fails."}},"verdict_id":"36424ee0-b839-4028-a7b3-165df127ef26"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5e3c68bd467650955f835ed8612c632e1d59716686aab0b907575b240cd7a99c","target":"record","created_at":"2026-05-20T00:03:52Z","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":"fe22a66be31e9e6ff3fa906bedb7fd079cee8cdd843608791c1916af45fb7657","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-17T09:10:31Z","title_canon_sha256":"dbd909bdf53a0b923efa86f3c6658643b455ba34f2729a96921291da94c332c2"},"schema_version":"1.0","source":{"id":"2605.17337","kind":"arxiv","version":1}},"canonical_sha256":"2f2506a62f6bf8e728920c2da951f24673a85a29b8ba517666b0ce11004a9bb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f2506a62f6bf8e728920c2da951f24673a85a29b8ba517666b0ce11004a9bb2","first_computed_at":"2026-05-20T00:03:52.935368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:52.935368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tZKduHcyXdR9y0QClciGyunxKF5hM01I1n9AZK0WDjISTWzFqUZxJjGlQXq0O1oaY9DVzLSaIDMBnVpsuJMGCg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:52.936286Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e3c68bd467650955f835ed8612c632e1d59716686aab0b907575b240cd7a99c","sha256:e1255e4f5865dc2d5ccc7a76d480a252b21761a43dba834ad8a64298f6dcb4d7"],"state_sha256":"76e47f4df2e483395accc099dd73ad6c21c1685b476be687af7f72b45ece33de"}