{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:64OIYBMFFVLKWGCTJDAM2XTRIJ","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":"3082a5363158858889237dc397fe4102c64795bb651a75e5754c346bfb7c4e7e","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-09-11T19:05:05Z","title_canon_sha256":"a64b71223c3ab19ca77cef3a80fb15cd6b2203184fa1aa5f8087a32378c2e221"},"schema_version":"1.0","source":{"id":"2409.07575","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.07575","created_at":"2026-07-05T10:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"2409.07575v2","created_at":"2026-07-05T10:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.07575","created_at":"2026-07-05T10:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"64OIYBMFFVLK","created_at":"2026-07-05T10:22:49Z"},{"alias_kind":"pith_short_16","alias_value":"64OIYBMFFVLKWGCT","created_at":"2026-07-05T10:22:49Z"},{"alias_kind":"pith_short_8","alias_value":"64OIYBMF","created_at":"2026-07-05T10:22:49Z"}],"graph_snapshots":[{"event_id":"sha256:45e1d2b06ea7be280a3cef07db45bb3566e459335c9e3f1af4e6919cd2cd1a6e","target":"graph","created_at":"2026-07-05T10:22:49Z","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/2409.07575/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $p\\ge 5$ be a prime and let $P$ be a Sylow $p$-subgroup of a finite symmetric group. To every irreducible character of $P$ we associate a collection of labelled, complete $p$-ary trees. The main results of this article describe Sylow branching coefficients for symmetric groups for all irreducible characters of $P$ in terms of some combinatorial properties of these trees, extending previous work on the linear characters of $P$.","authors_text":"Eugenio Giannelli, Stacey Law","cross_cats":["math.CO","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-09-11T19:05:05Z","title":"Sylow branching trees for symmetric groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.07575","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:af48cb2c11654ace53e284f36de207638945a703fbe105f342836050b7aeeb8b","target":"record","created_at":"2026-07-05T10:22:49Z","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":"3082a5363158858889237dc397fe4102c64795bb651a75e5754c346bfb7c4e7e","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-09-11T19:05:05Z","title_canon_sha256":"a64b71223c3ab19ca77cef3a80fb15cd6b2203184fa1aa5f8087a32378c2e221"},"schema_version":"1.0","source":{"id":"2409.07575","kind":"arxiv","version":2}},"canonical_sha256":"f71c8c05852d56ab185348c0cd5e714267f643557cf745ea3881e4ac1c963c36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f71c8c05852d56ab185348c0cd5e714267f643557cf745ea3881e4ac1c963c36","first_computed_at":"2026-07-05T10:22:49.700326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:22:49.700326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xHRxSaGlvPwEdj9YHGYdgTF95bJq8YyyTfY7FtZZ9uEDfOZt7Dy4aTSEqBln849L3cZtYoa/VjcR9bkeb4LHAA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:22:49.702406Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.07575","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af48cb2c11654ace53e284f36de207638945a703fbe105f342836050b7aeeb8b","sha256:45e1d2b06ea7be280a3cef07db45bb3566e459335c9e3f1af4e6919cd2cd1a6e"],"state_sha256":"f4729cf61e91c2b095c9bd0da832768110593a1725b19f3fdbc04f9b598a81d6"}