{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:6W43VXF6HQXWKSIYOONYOWUNTS","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":"34eecff12d2d6b9fb5d15bfe34cb2c6471a8105e49a85cbae3bfe85fb57852ef","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-10-27T12:30:42Z","title_canon_sha256":"f805cafbcd85250d3ff1863f7d3c86ced7279570236996bf447d4c8fb8aa805a"},"schema_version":"1.0","source":{"id":"2310.18093","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.18093","created_at":"2026-07-05T07:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"2310.18093v2","created_at":"2026-07-05T07:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.18093","created_at":"2026-07-05T07:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"6W43VXF6HQXW","created_at":"2026-07-05T07:51:34Z"},{"alias_kind":"pith_short_16","alias_value":"6W43VXF6HQXWKSIY","created_at":"2026-07-05T07:51:34Z"},{"alias_kind":"pith_short_8","alias_value":"6W43VXF6","created_at":"2026-07-05T07:51:34Z"}],"graph_snapshots":[{"event_id":"sha256:344902755acee3d7a565c7fcad9a436db683cf9999f035b4058740f0959739de","target":"graph","created_at":"2026-07-05T07:51:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.18093/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For closed hyperbolic $3$-manifolds $M$ with volume less than a constant $V$, we prove an inequality regarding the geometric $L^2$-norm and the topological Thurston norm, which is qualitatively sharp and verifies a conjecture of Brock and Dunfield in this case. Generically, we show that the $L^2$-norm is less than a constant $c(V)$ times the Thurston norm by showing that any least area closed surface is disjoint from the thin part.\n  We then study the connection between the Thurston norm, best Lipschitz circle-valued maps, and maximal stretch laminations, building on the recent work of Daskalo","authors_text":"Xiaolong Hans Han","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-10-27T12:30:42Z","title":"Thurston norms, $L^2$-norms, geodesic laminations, and Lipschitz maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.18093","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":"sha256:1d7fd1d54ad5536da90401ca961060dd6096bb0c024df23f0a066c950bb901b8","target":"record","created_at":"2026-07-05T07:51:34Z","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":"34eecff12d2d6b9fb5d15bfe34cb2c6471a8105e49a85cbae3bfe85fb57852ef","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-10-27T12:30:42Z","title_canon_sha256":"f805cafbcd85250d3ff1863f7d3c86ced7279570236996bf447d4c8fb8aa805a"},"schema_version":"1.0","source":{"id":"2310.18093","kind":"arxiv","version":2}},"canonical_sha256":"f5b9badcbe3c2f654918739b875a8d9c8ccb25f6be2e1a530c0bedbc5f844ea2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5b9badcbe3c2f654918739b875a8d9c8ccb25f6be2e1a530c0bedbc5f844ea2","first_computed_at":"2026-07-05T07:51:34.639137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:51:34.639137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JefC4jrqYtsrylsUWqmtsicg3OL5Z6xJzNxYALOU6n8w8CDw5qvJCrXsQsOCJ5xB93lYMO0Bw9Ub/P9PLglJDA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:51:34.639583Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.18093","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d7fd1d54ad5536da90401ca961060dd6096bb0c024df23f0a066c950bb901b8","sha256:344902755acee3d7a565c7fcad9a436db683cf9999f035b4058740f0959739de"],"state_sha256":"e27d1d9a7fe8308785af5fea780afdae4d3a45a0c3adda5a0d53ae2ad637fe56"}