{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CQBWIZW6C3UHZPMAI5MPKNRN5D","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":"eec3c9177c498835b295ad84d6788a0220dd536f1b584b4be5ef12cf7270ac5d","cross_cats_sorted":["math.CO","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-12T00:42:17Z","title_canon_sha256":"f2ae2148fd02ed5f82ce851e88ba0724e882ef4bc6ea091b1be2e366b7d08813"},"schema_version":"1.0","source":{"id":"1108.2542","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2542","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2542v2","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2542","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"pith_short_12","alias_value":"CQBWIZW6C3UH","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CQBWIZW6C3UHZPMA","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CQBWIZW6","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:a73e9e799b16d237676deed1c7041f0d14e251e5736fc00171b847a4091f0e74","target":"graph","created_at":"2026-05-18T03:32:45Z","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":"The main purpose of the paper is to construct a sequence of graphs of constant degree with indefinitely growing girths admitting embeddings into $\\ell_1$ with uniformly bounded distortions. This result answers the problem posed by N. Linial, A. Magen, and A. Naor (2002).","authors_text":"Mikhail I. Ostrovskii","cross_cats":["math.CO","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-12T00:42:17Z","title":"Low-distortion embeddings of graphs with large girth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2542","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":"sha256:5d3e481579b1b96fddd4d30beea8208fdc7310ba3f434e562ccfb3425cec13bc","target":"record","created_at":"2026-05-18T03:32:45Z","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":"eec3c9177c498835b295ad84d6788a0220dd536f1b584b4be5ef12cf7270ac5d","cross_cats_sorted":["math.CO","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-12T00:42:17Z","title_canon_sha256":"f2ae2148fd02ed5f82ce851e88ba0724e882ef4bc6ea091b1be2e366b7d08813"},"schema_version":"1.0","source":{"id":"1108.2542","kind":"arxiv","version":2}},"canonical_sha256":"14036466de16e87cbd804758f5362de8e02e9ccdbc9f7bfdb1f095a03b7cdb97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14036466de16e87cbd804758f5362de8e02e9ccdbc9f7bfdb1f095a03b7cdb97","first_computed_at":"2026-05-18T03:32:45.580389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:45.580389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"imEO+Yyc99ed09cOnYKy8jcangyezUkqNRnzI8cxtuus+LX7bo8g1u/Qw1k2dfis/ASgkQnTOgViBAHt6Mz2Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:45.581197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2542","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d3e481579b1b96fddd4d30beea8208fdc7310ba3f434e562ccfb3425cec13bc","sha256:a73e9e799b16d237676deed1c7041f0d14e251e5736fc00171b847a4091f0e74"],"state_sha256":"f58d2ea88ffd56be4e157c2a80ab4af5dd5e0ffdd1c54b3c268bd6a615308150"}