{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PNSXDYMVFXRG3ZCM5ZBQPBGKUS","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":"92a718a569ed19c97e5ed3754339cf2c055bfec677cda8ea79ff2ebf03fbc00d","cross_cats_sorted":["hep-th","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-08-12T19:57:16Z","title_canon_sha256":"2eb53a03b431147cd89b52b6f33966fa805cad30f1a4537cd921fb8c38474ee5"},"schema_version":"1.0","source":{"id":"1508.03038","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03038","created_at":"2026-05-18T01:22:14Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03038v2","created_at":"2026-05-18T01:22:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03038","created_at":"2026-05-18T01:22:14Z"},{"alias_kind":"pith_short_12","alias_value":"PNSXDYMVFXRG","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PNSXDYMVFXRG3ZCM","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PNSXDYMV","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:65fd42613d4289efbea4c578f73fd2c489d3d22e40eb52f19e55476e90f38286","target":"graph","created_at":"2026-05-18T01:22:14Z","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"},"paper":{"abstract_excerpt":"We study the central hyperplane arrangement whose hyperplanes are the vanishing loci of the weights of the first and the second fundamental representations of $\\mathfrak{gl}_n$ restricted to the dual fundamental Weyl chamber. We obtain generating functions that count flats and faces of a given dimension. This counting is interpreted in physics as the enumeration of the phases of the Coulomb and mixed Coulomb-Higgs branches of a five dimensional gauge theory with 8 supercharges in presence of hypermultiplets transforming in the fundamental and antisymmetric representation of a U(n) gauge group ","authors_text":"Alfred G. No\\\"el, Mboyo Esole, Ravi Jagadeesan, Steven Glenn Jackson","cross_cats":["hep-th","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-08-12T19:57:16Z","title":"Incidence Geometry in a Weyl Chamber I: $GL_n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03038","kind":"arxiv","version":2},"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:d3b878317bfd97d6b529970ddb7f50b7e600d1931e9fbc0a252320791043c0d9","target":"record","created_at":"2026-05-18T01:22:14Z","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":"92a718a569ed19c97e5ed3754339cf2c055bfec677cda8ea79ff2ebf03fbc00d","cross_cats_sorted":["hep-th","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-08-12T19:57:16Z","title_canon_sha256":"2eb53a03b431147cd89b52b6f33966fa805cad30f1a4537cd921fb8c38474ee5"},"schema_version":"1.0","source":{"id":"1508.03038","kind":"arxiv","version":2}},"canonical_sha256":"7b6571e1952de26de44cee430784caa488f9221cc9b305ad47db702f6f574452","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b6571e1952de26de44cee430784caa488f9221cc9b305ad47db702f6f574452","first_computed_at":"2026-05-18T01:22:14.351606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:14.351606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gd259XNwIT9mJdJ+4kVlnuJV5BIlAqHcVPZkSYG4httrHSCOR8iJjci5OaSJJKGxWSP+kL760KBnARyw/UKwDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:14.352367Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03038","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3b878317bfd97d6b529970ddb7f50b7e600d1931e9fbc0a252320791043c0d9","sha256:65fd42613d4289efbea4c578f73fd2c489d3d22e40eb52f19e55476e90f38286"],"state_sha256":"2353b51aa1800f3d253b10659f197488ad14577d563e06f84d71ebb798923cfd"}