{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OQ5UBAEVS4O7KC4BMQSC7VOKZW","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":"46cc20e79d51c3ac0f3537e2561593aa09e128ee7d5fecbf868fd4a7b3168512","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-03-21T22:32:16Z","title_canon_sha256":"6730ec0220d8cc6759266ac04432f1ad0ca0949c84b65ce02185bc8eab772faf"},"schema_version":"1.0","source":{"id":"1703.07458","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07458","created_at":"2026-05-17T23:54:11Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07458v2","created_at":"2026-05-17T23:54:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07458","created_at":"2026-05-17T23:54:11Z"},{"alias_kind":"pith_short_12","alias_value":"OQ5UBAEVS4O7","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OQ5UBAEVS4O7KC4B","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OQ5UBAEV","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:0424cf88eb0b6b5bd02baff5d899f4f16155f13f7719cd30b67a34275431e06b","target":"graph","created_at":"2026-05-17T23:54:11Z","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":"Let S be an immersed horizontal surface in a 3-dimensional graph manifold. We show that the fundamental group of the surface S is quadratically distorted whenever the surface is virtually embedded (i.e., separable) and is exponentially distorted when the surface is not virtually embedded.","authors_text":"G. Christopher Hruska, Hoang Thanh Nguyen","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-03-21T22:32:16Z","title":"Distortion of surfaces in graph manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07458","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":"sha256:745db00a085ff7e0007b452554901ef7c53414f7ac669d38c10b795f6dfe31e0","target":"record","created_at":"2026-05-17T23:54:11Z","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":"46cc20e79d51c3ac0f3537e2561593aa09e128ee7d5fecbf868fd4a7b3168512","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-03-21T22:32:16Z","title_canon_sha256":"6730ec0220d8cc6759266ac04432f1ad0ca0949c84b65ce02185bc8eab772faf"},"schema_version":"1.0","source":{"id":"1703.07458","kind":"arxiv","version":2}},"canonical_sha256":"743b408095971df50b8164242fd5cacd8529e8971aed17be9e7f75427b3120ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"743b408095971df50b8164242fd5cacd8529e8971aed17be9e7f75427b3120ae","first_computed_at":"2026-05-17T23:54:11.848836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:11.848836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"udqXpHP7q0C0xyrLf2qhQWfMk45qeQtY0YoIm0dAulAdshgkkstD1OwQnfmioi1vOJYxkf5rcaaDyExxIgySAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:11.849289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07458","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:745db00a085ff7e0007b452554901ef7c53414f7ac669d38c10b795f6dfe31e0","sha256:0424cf88eb0b6b5bd02baff5d899f4f16155f13f7719cd30b67a34275431e06b"],"state_sha256":"aeee25fcd4c2ecf65b56b207e0fee3c5d7852eb0b19e43fc135553477b41012c"}