{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KQ53ISODNGVV75BW6YI5UYMVXH","short_pith_number":"pith:KQ53ISOD","schema_version":"1.0","canonical_sha256":"543bb449c369ab5ff436f611da6195b9f7c3fd703047e6d0710a010ee20c1ac8","source":{"kind":"arxiv","id":"1601.05070","version":2},"attestation_state":"computed","paper":{"title":"Incidence Geometry in a Weyl Chamber II: $SL_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO"],"primary_cat":"math.RT","authors_text":"Alfred G. No\\\"el, Mboyo Esole, Ravi Jagadeesan, Steven Glenn Jackson","submitted_at":"2016-01-19T20:35:32Z","abstract_excerpt":"We study the polyhedral geometry of the hyperplanes orthogonal to the weights of the first and the second fundamental representations of $sl_n$ inside the dual fundamental Weyl chamber. We obtain generating functions that enumerate the flats and the faces of a fixed dimension. In addition, we describe the extreme rays of the incidence geometry and classify simplicial faces.\n  From the perspective of supersymmetric gauge theories with 8 supercharges in five dimensional spacetime, the poset of flats is isomorphic to the network of mixed Coulomb-Higgs branches. On the other hand, the poset of fac"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1601.05070","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-01-19T20:35:32Z","cross_cats_sorted":["hep-th","math.CO"],"title_canon_sha256":"3569c8269e7e0d6ac6f48e2a2c67eebe8ca0deeb0dc7a1a7759807137fa0e815","abstract_canon_sha256":"72498cb5d6d7176cf65853bc84b7a5af82b731255512460a9507f75196c334c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:09.918067Z","signature_b64":"UiYI7w8BXbumUfSww0a/KDKtqdpZeJSRU1n9V6fRfSpAUtD4SjXYANf6HfLpqJeQD4fcuFNisL6ijBbB2ipoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"543bb449c369ab5ff436f611da6195b9f7c3fd703047e6d0710a010ee20c1ac8","last_reissued_at":"2026-05-18T01:22:09.917478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:09.917478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Incidence Geometry in a Weyl Chamber II: $SL_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO"],"primary_cat":"math.RT","authors_text":"Alfred G. No\\\"el, Mboyo Esole, Ravi Jagadeesan, Steven Glenn Jackson","submitted_at":"2016-01-19T20:35:32Z","abstract_excerpt":"We study the polyhedral geometry of the hyperplanes orthogonal to the weights of the first and the second fundamental representations of $sl_n$ inside the dual fundamental Weyl chamber. We obtain generating functions that enumerate the flats and the faces of a fixed dimension. In addition, we describe the extreme rays of the incidence geometry and classify simplicial faces.\n  From the perspective of supersymmetric gauge theories with 8 supercharges in five dimensional spacetime, the poset of flats is isomorphic to the network of mixed Coulomb-Higgs branches. On the other hand, the poset of fac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05070","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1601.05070","created_at":"2026-05-18T01:22:09.917561+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.05070v2","created_at":"2026-05-18T01:22:09.917561+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05070","created_at":"2026-05-18T01:22:09.917561+00:00"},{"alias_kind":"pith_short_12","alias_value":"KQ53ISODNGVV","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KQ53ISODNGVV75BW","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KQ53ISOD","created_at":"2026-05-18T12:30:25.849896+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KQ53ISODNGVV75BW6YI5UYMVXH","json":"https://pith.science/pith/KQ53ISODNGVV75BW6YI5UYMVXH.json","graph_json":"https://pith.science/api/pith-number/KQ53ISODNGVV75BW6YI5UYMVXH/graph.json","events_json":"https://pith.science/api/pith-number/KQ53ISODNGVV75BW6YI5UYMVXH/events.json","paper":"https://pith.science/paper/KQ53ISOD"},"agent_actions":{"view_html":"https://pith.science/pith/KQ53ISODNGVV75BW6YI5UYMVXH","download_json":"https://pith.science/pith/KQ53ISODNGVV75BW6YI5UYMVXH.json","view_paper":"https://pith.science/paper/KQ53ISOD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.05070&json=true","fetch_graph":"https://pith.science/api/pith-number/KQ53ISODNGVV75BW6YI5UYMVXH/graph.json","fetch_events":"https://pith.science/api/pith-number/KQ53ISODNGVV75BW6YI5UYMVXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KQ53ISODNGVV75BW6YI5UYMVXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KQ53ISODNGVV75BW6YI5UYMVXH/action/storage_attestation","attest_author":"https://pith.science/pith/KQ53ISODNGVV75BW6YI5UYMVXH/action/author_attestation","sign_citation":"https://pith.science/pith/KQ53ISODNGVV75BW6YI5UYMVXH/action/citation_signature","submit_replication":"https://pith.science/pith/KQ53ISODNGVV75BW6YI5UYMVXH/action/replication_record"}},"created_at":"2026-05-18T01:22:09.917561+00:00","updated_at":"2026-05-18T01:22:09.917561+00:00"}