{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EZLSAIPL5PIY4M2BKMAF25RLEE","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":"628b8657fb4b64569d41953609d6c2af3bc20435a8d899b1f8e7c670a512d625","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-04-12T13:08:17Z","title_canon_sha256":"4eee68b7f2baee5d266166ef42405f839fcbb7f2022db426f489fb2623e545b0"},"schema_version":"1.0","source":{"id":"2504.09204","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.09204","created_at":"2026-07-05T11:02:43Z"},{"alias_kind":"arxiv_version","alias_value":"2504.09204v2","created_at":"2026-07-05T11:02:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.09204","created_at":"2026-07-05T11:02:43Z"},{"alias_kind":"pith_short_12","alias_value":"EZLSAIPL5PIY","created_at":"2026-07-05T11:02:43Z"},{"alias_kind":"pith_short_16","alias_value":"EZLSAIPL5PIY4M2B","created_at":"2026-07-05T11:02:43Z"},{"alias_kind":"pith_short_8","alias_value":"EZLSAIPL","created_at":"2026-07-05T11:02:43Z"}],"graph_snapshots":[{"event_id":"sha256:f27113304b9400cf66e761ac570d51714fc9b49f4a4682216d161c5cf1487d80","target":"graph","created_at":"2026-07-05T11:02:43Z","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/2504.09204/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $R$ be a reduced irreducible root system, $h$ its Coxeter number and $m$ a positive integer smaller than $h$. Choose of base of $R$, whence a corresponding height function, and let $R(m)$ be the set of roots whose height is a multiple of $m$. In a recent paper, S. Nadimpalli, S. Pattanayak and D. Prasad studied, for the purposes of character theory at torsion elements, the root systems $R(m)$; in particular, they introduced a constant $d_m$ which is always the dimension of a representation of the semisimple, simply-connected group with root system dual to $R(m)$ and equals $1$ if the roots","authors_text":"Patrick Polo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-04-12T13:08:17Z","title":"Classification of the root systems $R(m)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09204","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":"sha256:793cbdb1dca87c7cc1bbc7d9416d0c6b4e87ce0b77e3d749165ca2275748111f","target":"record","created_at":"2026-07-05T11:02:43Z","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":"628b8657fb4b64569d41953609d6c2af3bc20435a8d899b1f8e7c670a512d625","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-04-12T13:08:17Z","title_canon_sha256":"4eee68b7f2baee5d266166ef42405f839fcbb7f2022db426f489fb2623e545b0"},"schema_version":"1.0","source":{"id":"2504.09204","kind":"arxiv","version":2}},"canonical_sha256":"26572021ebebd18e334153005d762b21225e619fd846d74b2a39536da0efc901","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26572021ebebd18e334153005d762b21225e619fd846d74b2a39536da0efc901","first_computed_at":"2026-07-05T11:02:43.160077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:02:43.160077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o/4Z0KTzBmae3bQy52NfpHgsG7dLIKp2Wht8UFp6ciPoVgoMy1zd+t7bdLpvDd6/PfcFV5lEL9xSLfZlQRjyDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:02:43.160717Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.09204","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:793cbdb1dca87c7cc1bbc7d9416d0c6b4e87ce0b77e3d749165ca2275748111f","sha256:f27113304b9400cf66e761ac570d51714fc9b49f4a4682216d161c5cf1487d80"],"state_sha256":"923922c5712c1014685936a6cf2629a4bd803782be5769a2117402d8a22ba8e9"}