{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7ZQDWKYMMRTCGRV6BNULBKN5YA","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":"440251ea2bb3c45972d7ff88ee6a5756e65999dc1fcdb2c894b79e61e67c8c99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-24T11:59:57Z","title_canon_sha256":"8199d5e4b7c8375e108521f79734837e49b125b035759412ff033c578facbebe"},"schema_version":"1.0","source":{"id":"1207.5667","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5667","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5667v1","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5667","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"pith_short_12","alias_value":"7ZQDWKYMMRTC","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7ZQDWKYMMRTCGRV6","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7ZQDWKYM","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:0473df18db6c807fca49c0640286f0ffdbd0fdabeb3a95a4ef170d29f7342658","target":"graph","created_at":"2026-05-18T03:50:11Z","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":"This is a short survey of Cheeger and Kleiner's nonembeddability theorem for Heisenberg group into $L^1$.","authors_text":"Pierre Pansu (LM-Orsay)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-24T11:59:57Z","title":"Plongements quasiisom\\'etriques du groupe de Heisenberg dans $L^p$, d'apr\\`es Cheeger, Kleiner, Lee, Naor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5667","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":"sha256:5bce07f97b2694c989e13d1867eb45fc33a9cccf43c4bf739e48152379684e43","target":"record","created_at":"2026-05-18T03:50:11Z","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":"440251ea2bb3c45972d7ff88ee6a5756e65999dc1fcdb2c894b79e61e67c8c99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-24T11:59:57Z","title_canon_sha256":"8199d5e4b7c8375e108521f79734837e49b125b035759412ff033c578facbebe"},"schema_version":"1.0","source":{"id":"1207.5667","kind":"arxiv","version":1}},"canonical_sha256":"fe603b2b0c64662346be0b68b0a9bdc00b0fbee2127c56c4ec59d64f3eacc96b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe603b2b0c64662346be0b68b0a9bdc00b0fbee2127c56c4ec59d64f3eacc96b","first_computed_at":"2026-05-18T03:50:11.673855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:11.673855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dyHJISSR9xzxJYrdzTHel5U6ti80sRv48JqKY/M2voNVOBr3+dkEYO27AHDwUb/syRAZHPA0fLRIIkK5H/1eCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:11.674715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5667","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bce07f97b2694c989e13d1867eb45fc33a9cccf43c4bf739e48152379684e43","sha256:0473df18db6c807fca49c0640286f0ffdbd0fdabeb3a95a4ef170d29f7342658"],"state_sha256":"e3edc0882a27e155eb3a8cacb7277f4663afd932e0d125b4de828b95f421a340"}