{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:6MIVPKWPK7NAH2K2WEBTB6YHYF","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":"b0fcf445e4cdce077189a2b1514a6bf7e417fb04d57772a23518b7b0295b6eb4","cross_cats_sorted":["math.GT","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2007-06-07T02:19:38Z","title_canon_sha256":"4c7a31daa42283a031095c45df3217e34be58760ce3ff5648b077fab9f951e4d"},"schema_version":"1.0","source":{"id":"0706.0940","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.0940","created_at":"2026-05-18T03:52:53Z"},{"alias_kind":"arxiv_version","alias_value":"0706.0940v2","created_at":"2026-05-18T03:52:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.0940","created_at":"2026-05-18T03:52:53Z"},{"alias_kind":"pith_short_12","alias_value":"6MIVPKWPK7NA","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"6MIVPKWPK7NAH2K2","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"6MIVPKWP","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:ddca0a84709dc5960fd8527423abc7b4600d60517b1cf468c253e5dd754c20b3","target":"graph","created_at":"2026-05-18T03:52:53Z","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":"In this paper, which is the continuation of [EFW2], we complete the proof of the quasi-isometric rigidity of Sol and the lamplighter groups. The results were announced in [EFW1].","authors_text":"Alex Eskin, David Fisher, Kevin Whyte","cross_cats":["math.GT","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2007-06-07T02:19:38Z","title":"Coarse differentiation of quasi-isometries II: Rigidity for Sol and Lamplighter groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0940","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":"sha256:9928746e7dd04f2206365fd2c00fee9195c12cfd49a039251b258fe28fc2449e","target":"record","created_at":"2026-05-18T03:52:53Z","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":"b0fcf445e4cdce077189a2b1514a6bf7e417fb04d57772a23518b7b0295b6eb4","cross_cats_sorted":["math.GT","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2007-06-07T02:19:38Z","title_canon_sha256":"4c7a31daa42283a031095c45df3217e34be58760ce3ff5648b077fab9f951e4d"},"schema_version":"1.0","source":{"id":"0706.0940","kind":"arxiv","version":2}},"canonical_sha256":"f31157aacf57da03e95ab10330fb07c17cfae0878684df81fd842be15d49654e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f31157aacf57da03e95ab10330fb07c17cfae0878684df81fd842be15d49654e","first_computed_at":"2026-05-18T03:52:53.627353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:53.627353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y3A12bZnRDZEuTdZ6+FLlx5aLJUt4xhP6EIfm/Zi9Z2iggfCnn4bqMDTE53OJILWLUcOMhd17jT+1hJIvhsJDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:53.628217Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.0940","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9928746e7dd04f2206365fd2c00fee9195c12cfd49a039251b258fe28fc2449e","sha256:ddca0a84709dc5960fd8527423abc7b4600d60517b1cf468c253e5dd754c20b3"],"state_sha256":"a98e53a27df2c097a227e6c02b7a62cf9c1b0eb3381a0e4380eee6332e0d336e"}