{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XYREMQILJASR5UCBM6N7AUH7LB","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":"c2068f7250b442fffbf7c8ba792cfae398b6b192aa4dd2743eca3271911f8c61","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-30T01:46:15Z","title_canon_sha256":"16d1acafc720275c799addbe983aa663534dcd61174d7bb84c5ec789b4cdfa9f"},"schema_version":"1.0","source":{"id":"2607.28682","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28682","created_at":"2026-08-03T00:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28682v1","created_at":"2026-08-03T00:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28682","created_at":"2026-08-03T00:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"XYREMQILJASR","created_at":"2026-08-03T00:12:09Z"},{"alias_kind":"pith_short_16","alias_value":"XYREMQILJASR5UCB","created_at":"2026-08-03T00:12:09Z"},{"alias_kind":"pith_short_8","alias_value":"XYREMQIL","created_at":"2026-08-03T00:12:09Z"}],"graph_snapshots":[{"event_id":"sha256:be43a9078975a528348fc9deef29cb37be66a86159e8460e8539c860d266a6c4","target":"graph","created_at":"2026-08-03T00:12:09Z","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/2607.28682/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove Schur-positivity for a family of symmetric functions.","authors_text":"Peter J. McNamara","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-30T01:46:15Z","title":"On a Schur-positive function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28682","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:ccbab40d85cfa47e1b21428b1180f29399192f8b8b3492ba1f86c4894c0a81ef","target":"record","created_at":"2026-08-03T00:12:09Z","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":"c2068f7250b442fffbf7c8ba792cfae398b6b192aa4dd2743eca3271911f8c61","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-30T01:46:15Z","title_canon_sha256":"16d1acafc720275c799addbe983aa663534dcd61174d7bb84c5ec789b4cdfa9f"},"schema_version":"1.0","source":{"id":"2607.28682","kind":"arxiv","version":1}},"canonical_sha256":"be2246410b48251ed041679bf050ff5868e5006ac956af2a0e09a9a55b4f8958","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be2246410b48251ed041679bf050ff5868e5006ac956af2a0e09a9a55b4f8958","first_computed_at":"2026-08-03T00:12:09.852836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T00:12:09.852836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iw/ZmQafS23nGG6XI5d188PrSnjPSq9mrgoCjanU5FbPdFXVSV4a2VDK7ouXHHkF4I+x36unTRbZJVFrEqXgBQ==","signature_status":"signed_v1","signed_at":"2026-08-03T00:12:09.854979Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.28682","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccbab40d85cfa47e1b21428b1180f29399192f8b8b3492ba1f86c4894c0a81ef","sha256:be43a9078975a528348fc9deef29cb37be66a86159e8460e8539c860d266a6c4"],"state_sha256":"a5e8ebdef8f00dcd87197b0e5035b2b033865f43ffe54cad3716d2687c521f81"}