{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YR2NGW64X6JZL7TXNPLI3SRKUQ","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":"a73582038fda05f00ce741c006fe830a5e7c4dedb35ba539227a26b270eb374b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-02T01:16:30Z","title_canon_sha256":"17b2edecb9e3b8b058085d46addb9c12377ec3bdde0be4c1f43462f9e46e230b"},"schema_version":"1.0","source":{"id":"2607.01577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01577","created_at":"2026-07-03T01:17:02Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01577v1","created_at":"2026-07-03T01:17:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01577","created_at":"2026-07-03T01:17:02Z"},{"alias_kind":"pith_short_12","alias_value":"YR2NGW64X6JZ","created_at":"2026-07-03T01:17:02Z"},{"alias_kind":"pith_short_16","alias_value":"YR2NGW64X6JZL7TX","created_at":"2026-07-03T01:17:02Z"},{"alias_kind":"pith_short_8","alias_value":"YR2NGW64","created_at":"2026-07-03T01:17:02Z"}],"graph_snapshots":[{"event_id":"sha256:28b9ec673bb6948981be932b8e33d619b9dcde07f99cb47415743a90da5aedc7","target":"graph","created_at":"2026-07-03T01:17:02Z","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/2607.01577/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The transformation of the $h$-vector of a finite simplicial complex under an $\\mathcal{F}$-uniform subdivision is encoded by a transformation matrix. Mu and Welker conjectured that the transformation matrix of the barycentric subdivision is totally positive. In this paper, we give a new combinatorial proof of this conjecture. We also prove the total positivity of the transformation matrix of the interval subdivision. In addition, we establish a sufficient condition for the transformation matrix of a uniform subdivision to be totally positive of order $2$ (TP$_2$), thereby partially answering a","authors_text":"Jianxi Mao, Yanxin Liu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-02T01:16:30Z","title":"Total positivity of transformation matrices for uniform subdivisions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01577","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:ef14e30ffd3693549473aab8f6d38ed55fe694d34e7cf4c607c178e2bdaeecf0","target":"record","created_at":"2026-07-03T01:17:02Z","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":"a73582038fda05f00ce741c006fe830a5e7c4dedb35ba539227a26b270eb374b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-02T01:16:30Z","title_canon_sha256":"17b2edecb9e3b8b058085d46addb9c12377ec3bdde0be4c1f43462f9e46e230b"},"schema_version":"1.0","source":{"id":"2607.01577","kind":"arxiv","version":1}},"canonical_sha256":"c474d35bdcbf9395fe776bd68dca2aa41b471d55d8c5541decf46467555b9b42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c474d35bdcbf9395fe776bd68dca2aa41b471d55d8c5541decf46467555b9b42","first_computed_at":"2026-07-03T01:17:02.362364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:02.362364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/ay2zDRDA07Uthy7GxXzmupOPR19L070+YZzQHPD7HCGOMFAkhL0JO38AtcZMiCKT3kZN441nyluAu1sJJH1Aw==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:02.362800Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef14e30ffd3693549473aab8f6d38ed55fe694d34e7cf4c607c178e2bdaeecf0","sha256:28b9ec673bb6948981be932b8e33d619b9dcde07f99cb47415743a90da5aedc7"],"state_sha256":"b2629545cc3b8f4c625f2570617e11988d79304eeee3ea5e58f8dd743f6ca8f7"}