{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:QJGKSY7L2DEQXQW7YRBSSPMTGM","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":"2e3cec6476911d8494e2350ae2d642aace1a11570dab324540499b40ad9dbb3a","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"math.AG","submitted_at":"2004-03-15T15:51:46Z","title_canon_sha256":"6925f8920bedb2e156c957caec7e023be62c0dfc6ca5838e565b85bd572c2df0"},"schema_version":"1.0","source":{"id":"math/0403247","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0403247","created_at":"2026-07-04T14:38:25Z"},{"alias_kind":"arxiv_version","alias_value":"math/0403247v1","created_at":"2026-07-04T14:38:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0403247","created_at":"2026-07-04T14:38:25Z"},{"alias_kind":"pith_short_12","alias_value":"QJGKSY7L2DEQ","created_at":"2026-07-04T14:38:25Z"},{"alias_kind":"pith_short_16","alias_value":"QJGKSY7L2DEQXQW7","created_at":"2026-07-04T14:38:25Z"},{"alias_kind":"pith_short_8","alias_value":"QJGKSY7L","created_at":"2026-07-04T14:38:25Z"}],"graph_snapshots":[{"event_id":"sha256:10bef3c230b8478cb28d8b1284bd84c9a4fe4bceda2421d26cd8bfb697069ec9","target":"graph","created_at":"2026-07-04T14:38:25Z","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/math/0403247/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In earlier work, Chekhov and Fock have given a quantization of Teichm\\\"uller space as a Poisson manifold, and the current paper first surveys this material adding further mathematical and other detail, including the underlying geometric work by Penner on classical Teichm\\\"uller theory. In particular, the earlier quantum ordering solution is found to essentially agree with an ``improved'' operator ordering given by serially traversing general edge-paths on a graph in the underlying surface. Now, insofar as Thurston's sphere of projectivized foliations of compact support provides a useful compac","authors_text":"L. Chekhov, R. C. Penner","cross_cats":["hep-th"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2004-03-15T15:51:46Z","title":"On Quantizing Teichm\\\"uller and Thurston theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0403247","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:f256d58dc0259535ca85bbbcbfdae46c3f5057aeee7acce91d0394d37efef3b7","target":"record","created_at":"2026-07-04T14:38:25Z","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":"2e3cec6476911d8494e2350ae2d642aace1a11570dab324540499b40ad9dbb3a","cross_cats_sorted":["hep-th"],"license":"","primary_cat":"math.AG","submitted_at":"2004-03-15T15:51:46Z","title_canon_sha256":"6925f8920bedb2e156c957caec7e023be62c0dfc6ca5838e565b85bd572c2df0"},"schema_version":"1.0","source":{"id":"math/0403247","kind":"arxiv","version":1}},"canonical_sha256":"824ca963ebd0c90bc2dfc443293d933335b1116672e4214deca30855d74d7869","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"824ca963ebd0c90bc2dfc443293d933335b1116672e4214deca30855d74d7869","first_computed_at":"2026-07-04T14:38:25.964399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:38:25.964399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tSqE8naLJTf++Quwz2tn+CkjfHW0qVgpcK1JYvI9u0fv7MqA1baS4kau93w5KodaMEjrUHMDjD+4/52qZ/v6Ag==","signature_status":"signed_v1","signed_at":"2026-07-04T14:38:25.964797Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0403247","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f256d58dc0259535ca85bbbcbfdae46c3f5057aeee7acce91d0394d37efef3b7","sha256:10bef3c230b8478cb28d8b1284bd84c9a4fe4bceda2421d26cd8bfb697069ec9"],"state_sha256":"2eee2f0d23a3b7f14870f3c16f9fdcebb62b65543fe60be736acf6e1121d6114"}