{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SEUNKWSRHOLHR6ZQUZ2CAYAPRJ","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":"76776c6436099328791054eb66ca1d0ba6ce60323e1ac9c0e9037ede43aff4cd","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-11-27T21:00:08Z","title_canon_sha256":"eb79940d3d6d470d654ed49026e7afbf26ad41cfeeba375dbc0305db707ae216"},"schema_version":"1.0","source":{"id":"1311.7150","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7150","created_at":"2026-05-18T01:35:33Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7150v2","created_at":"2026-05-18T01:35:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7150","created_at":"2026-05-18T01:35:33Z"},{"alias_kind":"pith_short_12","alias_value":"SEUNKWSRHOLH","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SEUNKWSRHOLHR6ZQ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SEUNKWSR","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:e79377b2d5fe3912769c2ae9d380bee41e550fb5e864eb59d344c12f77b87d03","target":"graph","created_at":"2026-05-18T01:35:33Z","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":"For k >= 1, let Torelli_g^1(k) be the k-th term in the Johnson filtration of the mapping class group of a genus g surface with one boundary component. We prove that for all k, there exists some G_k >= 0 such that Torelli_g^1(k) is generated by elements which are supported on subsurfaces whose genus is at most G_k. We also prove similar theorems for the Johnson filtration of Aut(F_n) and for certain mod-p analogues of the Johnson filtrations of both the mapping class group and of Aut(F_n). The main tools used in the proofs are the related theories of FI-modules (due to the first author together","authors_text":"Andrew Putman, Thomas Church","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-11-27T21:00:08Z","title":"Generating the Johnson filtration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7150","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":"sha256:0167701bfc21fffea46179af76a804391882297ccdcaedff22fc2b80f26b510f","target":"record","created_at":"2026-05-18T01:35:33Z","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":"76776c6436099328791054eb66ca1d0ba6ce60323e1ac9c0e9037ede43aff4cd","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-11-27T21:00:08Z","title_canon_sha256":"eb79940d3d6d470d654ed49026e7afbf26ad41cfeeba375dbc0305db707ae216"},"schema_version":"1.0","source":{"id":"1311.7150","kind":"arxiv","version":2}},"canonical_sha256":"9128d55a513b9678fb30a67420600f8a4ae1fa4569bdc49e8fe1a5cf20c768d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9128d55a513b9678fb30a67420600f8a4ae1fa4569bdc49e8fe1a5cf20c768d1","first_computed_at":"2026-05-18T01:35:33.070954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:33.070954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q9ZNJuMiEnmzeBU5aMlubiaHo+X9gG8FrI2DlltqNVWcf2kC1Brew/Ri/eNOuXbAh9zz/R34iHJwxdrnJBMfCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:33.071415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7150","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0167701bfc21fffea46179af76a804391882297ccdcaedff22fc2b80f26b510f","sha256:e79377b2d5fe3912769c2ae9d380bee41e550fb5e864eb59d344c12f77b87d03"],"state_sha256":"8adaa747fd4a07d39eeb2e6d2b6af6114f9a07bbbb98f5b17b8470dbc5295277"}