{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JOTHBX6MW7FHSNYFWHCITP4WKW","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":"bb7e0a4a0b700ee981906570a46323bd4e35a90ac2a8038a7e7152d5a0d8bbf4","cross_cats_sorted":["math.DS","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-01T15:50:30Z","title_canon_sha256":"4cbec417a42190a6c4913d844cf0e073f4e2cb0211ae137b6ade2bda83894ddc"},"schema_version":"1.0","source":{"id":"1308.0250","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0250","created_at":"2026-05-17T23:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0250v2","created_at":"2026-05-17T23:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0250","created_at":"2026-05-17T23:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"JOTHBX6MW7FH","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JOTHBX6MW7FHSNYF","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JOTHBX6M","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:009c491f014c1c821c3846f016f62f70f3413367f3f4f102fa70091abb85d27b","target":"graph","created_at":"2026-05-17T23:53:15Z","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 if \\Gamma is subgroup of Diff_{+}^{1+\\epsilon}(I) and N is a natural number such that every non-identity element of \\Gamma has at most N fixed points then \\Gamma is solvable. If in addition \\Gamma is a subgroup of Diff_{+}^{2}(I) then we can claim that \\Gamma is metaabelian.","authors_text":"Azer Akhmedov","cross_cats":["math.DS","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-01T15:50:30Z","title":"Extension of H\\\"older's Theorem in Diff_{+}^{1+\\epsilon}(I)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0250","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:aff39e9048ce9a2ed81d2d72ee6df194fb8e7428e23ef7e1626a5acfee2efd75","target":"record","created_at":"2026-05-17T23:53:15Z","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":"bb7e0a4a0b700ee981906570a46323bd4e35a90ac2a8038a7e7152d5a0d8bbf4","cross_cats_sorted":["math.DS","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-01T15:50:30Z","title_canon_sha256":"4cbec417a42190a6c4913d844cf0e073f4e2cb0211ae137b6ade2bda83894ddc"},"schema_version":"1.0","source":{"id":"1308.0250","kind":"arxiv","version":2}},"canonical_sha256":"4ba670dfccb7ca793705b1c489bf965584a805b73a0fcd1cbd791c4d0de8067c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ba670dfccb7ca793705b1c489bf965584a805b73a0fcd1cbd791c4d0de8067c","first_computed_at":"2026-05-17T23:53:15.218134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:15.218134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QCTRf0+RPHY1jvJH43cFASnX4Mc3WhYddg/abxp2ToY+8/fNTiyuieXyU72aGL2o7/7s+ov87QO6ud02L6IpCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:15.218614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0250","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aff39e9048ce9a2ed81d2d72ee6df194fb8e7428e23ef7e1626a5acfee2efd75","sha256:009c491f014c1c821c3846f016f62f70f3413367f3f4f102fa70091abb85d27b"],"state_sha256":"e24a1f3c367d929a24e0b51b10f45a3a71353f92249bf70045fb0f06d898cab2"}