{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:U7DYUYP4NS7RHAJEMAAU5IXB2S","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":"1ce85b08c1e28a70ad80381fa4e34756687b79e8bf6d485d386a96646db2d535","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-18T08:23:39Z","title_canon_sha256":"9cf43c235b3edb0cfa0d878e241b51c80b56d048f4be276d0825a77b09dabc52"},"schema_version":"1.0","source":{"id":"1212.4261","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4261","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4261v3","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4261","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"U7DYUYP4NS7R","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U7DYUYP4NS7RHAJE","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U7DYUYP4","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:5579741dd3ea6895f423bf4e0f0c7a3e6fc1506fa822bd7b0e6988bc9f0b6a3e","target":"graph","created_at":"2026-05-18T01:31:46Z","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 organize the quantum hyperbolic invariants (QHI) of $3$-manifolds into sequences of rational functions indexed by the odd integers $N\\geq 3$ and defined on moduli spaces of geometric structures refining the character varieties. In the case of one-cusped hyperbolic $3$-manifolds $M$ we generalize the QHI and get rational functions $\\mathcal{H}_N^{h_f,h_c,k_c}$ depending on a finite set of cohomological data $(h_f,h_c,k_c)$ called {\\it weights}. These functions are regular on a determined Abelian covering of degree $N^2$ of a Zariski open subset, canonically associated to $M$, of the geometri","authors_text":"Riccardo Benedetti, Stephane Baseilhac","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-18T08:23:39Z","title":"Analytic families of quantum hyperbolic invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4261","kind":"arxiv","version":3},"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":"sha256:95a728cf612dbd0c686b9e73bf0e729de5d1c6213bcf7f70eae5b42dc99e7154","target":"record","created_at":"2026-05-18T01:31:46Z","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":"1ce85b08c1e28a70ad80381fa4e34756687b79e8bf6d485d386a96646db2d535","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-18T08:23:39Z","title_canon_sha256":"9cf43c235b3edb0cfa0d878e241b51c80b56d048f4be276d0825a77b09dabc52"},"schema_version":"1.0","source":{"id":"1212.4261","kind":"arxiv","version":3}},"canonical_sha256":"a7c78a61fc6cbf13812460014ea2e1d4b521f80b13a78074858aacb5140d6dd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7c78a61fc6cbf13812460014ea2e1d4b521f80b13a78074858aacb5140d6dd9","first_computed_at":"2026-05-18T01:31:46.880618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:46.880618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7zZbl+OxB8pT0OLNwuPeOrfST3T+pGnt6ar4dawIHoLQq3/+kRVm4GAa03ljFG44sC9mquQ7EYySPlKFKaSUAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:46.881104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4261","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95a728cf612dbd0c686b9e73bf0e729de5d1c6213bcf7f70eae5b42dc99e7154","sha256:5579741dd3ea6895f423bf4e0f0c7a3e6fc1506fa822bd7b0e6988bc9f0b6a3e"],"state_sha256":"3c46a8f9b3f75ec8cfcb85dd3b60873fd5d4c51c75e14b8b911612fdbf16a1a9"}