{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JHRNVE42PGYZPDT5EXYIJF722W","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":"85b5c11c8bd4032040def703a7775d89e31715ed408d660a1daa924e38ddc383","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-01T09:22:05Z","title_canon_sha256":"979e9cd42213038a4501189f16509823a80d0faa903ae907c650c905581ed719"},"schema_version":"1.0","source":{"id":"1509.00187","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00187","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00187v1","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00187","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"pith_short_12","alias_value":"JHRNVE42PGYZ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JHRNVE42PGYZPDT5","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JHRNVE42","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:110150a9294bc7ca5ef7d674cbe94214a10f5cb8960647ff940660e4d7045d48","target":"graph","created_at":"2026-05-18T00:19:54Z","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 prove that SAut(Fn), the unique subgroup of index two in the automorphism group of a free group of rank n, admits no non-trivial linear representation of degree d<n for any field of characteristic not equal to two.","authors_text":"Olga Varghese","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-01T09:22:05Z","title":"Low dimensional linear representations of SAut(Fn)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00187","kind":"arxiv","version":1},"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:fca15d489f2521916ed479aac88ab25904539bec795c27f94377fc69daa7cd1a","target":"record","created_at":"2026-05-18T00:19:54Z","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":"85b5c11c8bd4032040def703a7775d89e31715ed408d660a1daa924e38ddc383","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-01T09:22:05Z","title_canon_sha256":"979e9cd42213038a4501189f16509823a80d0faa903ae907c650c905581ed719"},"schema_version":"1.0","source":{"id":"1509.00187","kind":"arxiv","version":1}},"canonical_sha256":"49e2da939a79b1978e7d25f08497fad58fa7b92846278b2914f465031c66129b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49e2da939a79b1978e7d25f08497fad58fa7b92846278b2914f465031c66129b","first_computed_at":"2026-05-18T00:19:54.046881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:54.046881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qmk/QjjzmasN5c+rRS+0N1yReTe2W9JV9ZI0xjWJDY0ajgBTanpQOgbAenFzQ+pXlnaMQoZTGyp0iorHGc2YCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:54.047652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00187","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fca15d489f2521916ed479aac88ab25904539bec795c27f94377fc69daa7cd1a","sha256:110150a9294bc7ca5ef7d674cbe94214a10f5cb8960647ff940660e4d7045d48"],"state_sha256":"4ce424c7035c70b6b38c99d726f3fe2c75fd7ec54cb48044286d2191ffe39872"}