{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AD3GZWBGGAE3J3ULD7OVTZHKIF","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":"666db94408337604441601dda71e049e2e89ae13d7bdf1b9b884f0960185d013","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-21T22:17:23Z","title_canon_sha256":"2ec8a46297a6fe7bee2a5c7dc947d8dea0b6c30edd5fcd2491ca07ef4b270f09"},"schema_version":"1.0","source":{"id":"1509.06414","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06414","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06414v3","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06414","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"AD3GZWBGGAE3","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AD3GZWBGGAE3J3UL","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AD3GZWBG","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:6dc66854afa987f038e7d55a8c1fb3bf807be31824c8610dc27c77cea81f98e7","target":"graph","created_at":"2026-05-18T01:03:31Z","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 asymptotic properties of the modular representation theory of symmetric groups and investigate modular analogs of stabilization phenomena in characteristic zero. The main results are equivalences of categories between certain abelian subcategories of representations of $S_n$ and $S_m$ for different $n$ and $m$. We apply these results to obtain a structural result for $FI$-modules, and to prove a result conjectured by Deligne in a recent letter to Ostrik.","authors_text":"Nate Harman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-21T22:17:23Z","title":"Stability and periodicity in the modular representation theory of symmetric groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06414","kind":"arxiv","version":3},"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:e917f3c6918a089a7385689f96ae38ccd18744de78561db20cb6a44fcb9c9b9f","target":"record","created_at":"2026-05-18T01:03:31Z","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":"666db94408337604441601dda71e049e2e89ae13d7bdf1b9b884f0960185d013","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-21T22:17:23Z","title_canon_sha256":"2ec8a46297a6fe7bee2a5c7dc947d8dea0b6c30edd5fcd2491ca07ef4b270f09"},"schema_version":"1.0","source":{"id":"1509.06414","kind":"arxiv","version":3}},"canonical_sha256":"00f66cd8263009b4ee8b1fdd59e4ea41719f4afe4b7593b54186c4ac0e83d99f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00f66cd8263009b4ee8b1fdd59e4ea41719f4afe4b7593b54186c4ac0e83d99f","first_computed_at":"2026-05-18T01:03:31.059164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:31.059164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4qgpDmo0aYJNK8SJ9TAlBEESfBBFploJSvJQgmEOYafL6R/cqM0DymeBx9YVD1z+I1CxljCHygWXT0giNAVoBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:31.059684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06414","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e917f3c6918a089a7385689f96ae38ccd18744de78561db20cb6a44fcb9c9b9f","sha256:6dc66854afa987f038e7d55a8c1fb3bf807be31824c8610dc27c77cea81f98e7"],"state_sha256":"04b54df938b14da651347f5eab595e3c17f3de60a5bba6e8005f60f0b0322898"}