{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YKJWKMRDR5QUTMN7742CYNLR4I","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":"87d9c349a8eeb91d26c9b0800c40122017c10ea662cef7060722c332765f36f3","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-22T12:39:04Z","title_canon_sha256":"5d8a619c2bf2ec4e64e002ad881ef6478906cf28cb4f9ebd92ff4a33dcf828b5"},"schema_version":"1.0","source":{"id":"0910.4305","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.4305","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"0910.4305v5","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.4305","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"YKJWKMRDR5QU","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YKJWKMRDR5QUTMN7","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YKJWKMRD","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:fae455c4d8f58fd2e09cbdab0fb3302a039a4b4fd0b8b00033bfe3499d4ce980","target":"graph","created_at":"2026-05-18T03:36:06Z","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 $2g-2+n>0$, the Teichm\\\"uller modular group $\\Gamma_{g,n}$ of a compact Riemann surface of genus $g$ with $n$ points removed $S_{g,n}$ is the group of homotopy classes of diffeomorphisms of $S_{g,n}$ which preserve the orientation of $S_{g,n}$ and a given order of its punctures. Let $\\Pi_{g,n}$ be the fundamental group of $S_{g,n}$, with a given base point, and $\\hat{\\Pi}_{g,n}$ its profinite completion. There is then a natural faithful representation $\\Gamma_{g,n}\\hookrightarrow Out(\\hat{\\Pi}_{g,n})$. The procongruence completion $\\check{\\Gamma}_{g,n}$ of the Teichm\\\"uller group is define","authors_text":"Marco Boggi","cross_cats":["math.GR","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-22T12:39:04Z","title":"On the procongruence completion of the Teichm\\\"uller modular group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4305","kind":"arxiv","version":5},"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":"sha256:203782f0d50e76d483bd06b389b47da042e2684abf6dcbc2bdad7d9823f80601","target":"record","created_at":"2026-05-18T03:36:06Z","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":"87d9c349a8eeb91d26c9b0800c40122017c10ea662cef7060722c332765f36f3","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-22T12:39:04Z","title_canon_sha256":"5d8a619c2bf2ec4e64e002ad881ef6478906cf28cb4f9ebd92ff4a33dcf828b5"},"schema_version":"1.0","source":{"id":"0910.4305","kind":"arxiv","version":5}},"canonical_sha256":"c2936532238f6149b1bfff342c3571e20ddba5f06d9ebffaf05238a43d28ed47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2936532238f6149b1bfff342c3571e20ddba5f06d9ebffaf05238a43d28ed47","first_computed_at":"2026-05-18T03:36:06.760459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:06.760459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TtZZ+4STpLfX7MLQS3SLrqHZqhv3oycAani4UGDwSWRTbzCkyG7Uj3VcUTV72hxtzYCTIomOqD868HaVgFtmAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:06.761097Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.4305","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:203782f0d50e76d483bd06b389b47da042e2684abf6dcbc2bdad7d9823f80601","sha256:fae455c4d8f58fd2e09cbdab0fb3302a039a4b4fd0b8b00033bfe3499d4ce980"],"state_sha256":"deafc7cc2dcff31e5b346c03fd4af28f74b33e391a279c4abaaa00ad43be905b"}