{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DB3QCKXPQSVR5BA3G6JW5XXRMH","short_pith_number":"pith:DB3QCKXP","canonical_record":{"source":{"id":"1511.06054","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-11-19T03:56:13Z","cross_cats_sorted":[],"title_canon_sha256":"48a2a584814a11482cff453b5fc3779f4a3e8a8d4e9b23c6f9a54d67ed2181e1","abstract_canon_sha256":"fc3849c4f1e4481a5a82758e61cac08c9e85c425de2f9669df5ab7f1887041ec"},"schema_version":"1.0"},"canonical_sha256":"1877012aef84ab1e841b37936edef161c78eb1cc2053bd7bec8261bf2f1a1fe2","source":{"kind":"arxiv","id":"1511.06054","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06054","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06054v4","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06054","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"DB3QCKXPQSVR","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DB3QCKXPQSVR5BA3","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DB3QCKXP","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DB3QCKXPQSVR5BA3G6JW5XXRMH","target":"record","payload":{"canonical_record":{"source":{"id":"1511.06054","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-11-19T03:56:13Z","cross_cats_sorted":[],"title_canon_sha256":"48a2a584814a11482cff453b5fc3779f4a3e8a8d4e9b23c6f9a54d67ed2181e1","abstract_canon_sha256":"fc3849c4f1e4481a5a82758e61cac08c9e85c425de2f9669df5ab7f1887041ec"},"schema_version":"1.0"},"canonical_sha256":"1877012aef84ab1e841b37936edef161c78eb1cc2053bd7bec8261bf2f1a1fe2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:44.801788Z","signature_b64":"7tA27EjiDcUc17E1pfqAv/+/Jyb+jGqzMfUix8T5CnFxoXnBqLBFBQioJM/UfXqJ/G+4dykyA2sSs7Zu1lVVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1877012aef84ab1e841b37936edef161c78eb1cc2053bd7bec8261bf2f1a1fe2","last_reissued_at":"2026-05-17T23:52:44.801207Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:44.801207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.06054","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nsH5kqKo31UfNMr/B0m0l+bZejfSOsjTlM7RatXqFRzmzS8dBh+iBTs7natI3ilC9xl0fxpDF059F1+ViOsPDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:39:11.839072Z"},"content_sha256":"d634a92df3793eaa0f37888a31c79580fd94f5e7d90f90ce6559a5fb0c20eb2d","schema_version":"1.0","event_id":"sha256:d634a92df3793eaa0f37888a31c79580fd94f5e7d90f90ce6559a5fb0c20eb2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DB3QCKXPQSVR5BA3G6JW5XXRMH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Teichm\\\"uller spaces and quantum trace map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Thang T. Q. L\\^e","submitted_at":"2015-11-19T03:56:13Z","abstract_excerpt":"We show how the quantum trace map of Bonahon and Wong can be constructed in a natural way using the skein algebra of Muller, which is an extension of the Kauffman bracket skein algebra of surfaces. We also show that the quantum Teichm\\\"uller space of a marked surface, defined by Chekhov-Fock (and Kashaev) in an abstract way, can be realized as a concrete subalgebra of the skew field of the skein algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06054","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ah9mRj8Q+XAPOH7I8S1oEN1VHYjQjdFonDQ6g3mCUq1GdjkfEc8KUxMPJaqzN1GC1R7Wt1NjXXciuG08ZWC9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:39:11.839457Z"},"content_sha256":"cecc814ad3ecef772f3ca1f2bfc97ed6ae6a247053a0dc7055bbd6e2ea43cb97","schema_version":"1.0","event_id":"sha256:cecc814ad3ecef772f3ca1f2bfc97ed6ae6a247053a0dc7055bbd6e2ea43cb97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DB3QCKXPQSVR5BA3G6JW5XXRMH/bundle.json","state_url":"https://pith.science/pith/DB3QCKXPQSVR5BA3G6JW5XXRMH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DB3QCKXPQSVR5BA3G6JW5XXRMH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T19:39:11Z","links":{"resolver":"https://pith.science/pith/DB3QCKXPQSVR5BA3G6JW5XXRMH","bundle":"https://pith.science/pith/DB3QCKXPQSVR5BA3G6JW5XXRMH/bundle.json","state":"https://pith.science/pith/DB3QCKXPQSVR5BA3G6JW5XXRMH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DB3QCKXPQSVR5BA3G6JW5XXRMH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DB3QCKXPQSVR5BA3G6JW5XXRMH","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":"fc3849c4f1e4481a5a82758e61cac08c9e85c425de2f9669df5ab7f1887041ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-11-19T03:56:13Z","title_canon_sha256":"48a2a584814a11482cff453b5fc3779f4a3e8a8d4e9b23c6f9a54d67ed2181e1"},"schema_version":"1.0","source":{"id":"1511.06054","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06054","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06054v4","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06054","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"DB3QCKXPQSVR","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DB3QCKXPQSVR5BA3","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DB3QCKXP","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:cecc814ad3ecef772f3ca1f2bfc97ed6ae6a247053a0dc7055bbd6e2ea43cb97","target":"graph","created_at":"2026-05-17T23:52:44Z","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":"We show how the quantum trace map of Bonahon and Wong can be constructed in a natural way using the skein algebra of Muller, which is an extension of the Kauffman bracket skein algebra of surfaces. We also show that the quantum Teichm\\\"uller space of a marked surface, defined by Chekhov-Fock (and Kashaev) in an abstract way, can be realized as a concrete subalgebra of the skew field of the skein algebra.","authors_text":"Thang T. Q. L\\^e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-11-19T03:56:13Z","title":"Quantum Teichm\\\"uller spaces and quantum trace map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06054","kind":"arxiv","version":4},"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:d634a92df3793eaa0f37888a31c79580fd94f5e7d90f90ce6559a5fb0c20eb2d","target":"record","created_at":"2026-05-17T23:52:44Z","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":"fc3849c4f1e4481a5a82758e61cac08c9e85c425de2f9669df5ab7f1887041ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-11-19T03:56:13Z","title_canon_sha256":"48a2a584814a11482cff453b5fc3779f4a3e8a8d4e9b23c6f9a54d67ed2181e1"},"schema_version":"1.0","source":{"id":"1511.06054","kind":"arxiv","version":4}},"canonical_sha256":"1877012aef84ab1e841b37936edef161c78eb1cc2053bd7bec8261bf2f1a1fe2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1877012aef84ab1e841b37936edef161c78eb1cc2053bd7bec8261bf2f1a1fe2","first_computed_at":"2026-05-17T23:52:44.801207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:44.801207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7tA27EjiDcUc17E1pfqAv/+/Jyb+jGqzMfUix8T5CnFxoXnBqLBFBQioJM/UfXqJ/G+4dykyA2sSs7Zu1lVVBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:44.801788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.06054","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d634a92df3793eaa0f37888a31c79580fd94f5e7d90f90ce6559a5fb0c20eb2d","sha256:cecc814ad3ecef772f3ca1f2bfc97ed6ae6a247053a0dc7055bbd6e2ea43cb97"],"state_sha256":"da3d333b348a5d4b7c75b47b90ea1b4f746cf43fa5c196de8dec3f9a34ec0138"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7qI25mMmpSagxM6hUWvUhAIIROX2IqdO6efD5MiP96gPT3n+y8XOd7mD5gnM91DOD1+ltNc1TnZf7RRY17g0Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:39:11.842251Z","bundle_sha256":"5bfe15683296b8e051f604669afd360bde9620b14e9a2b920b4d909f9b36170e"}}