{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:G7GCWWE2UEVI3A5MNVUEE74N2D","short_pith_number":"pith:G7GCWWE2","schema_version":"1.0","canonical_sha256":"37cc2b589aa12a8d83ac6d68427f8dd0ed617a4a6dd05d76e35f8955d3be4da4","source":{"kind":"arxiv","id":"2605.25468","version":1},"attestation_state":"computed","paper":{"title":"Uniformization as Tannakian Reconstruction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Mao Sheng, Xiaojin Lin","submitted_at":"2026-05-25T06:19:22Z","abstract_excerpt":"We formulate hyperbolic uniformization as a Tannakian reconstruction theorem. For a hyperbolic log-orbi curve C, we construct an intrinsic canonical maximal parahoric PSL2-Higgs object. A tensor-functorial parahoric non-abelian Hodge-Riemann-Hilbert correspondence identifies its Betti realization with a representation of the orbifold fundamental group whose image is the uniformizing cofinite Fuchsian lattice. This construction quasi-inverts the compactified quotient functor from cofinite Fuchsian lattices in PSL2(R) to hyperbolic log-orbi curves. We also prove a Galois enhancement, identifying"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.25468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-05-25T06:19:22Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"5653d37d1737b332244f0e941546338cbd7c6c34c6ce6d99e4d0c9f0513b018e","abstract_canon_sha256":"544c5da9fc009ea8a40b167ae9404c409e061cb11cb4e82f48cffa44f03678fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:04:37.703796Z","signature_b64":"GtNIbgFdE7ksadtqvF7yi2I9ELacHqGD9S4Ah34wpacZbpVmlLMJ4Qrp42laVD3fW40Em9CVM5qUb6VtcHyXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37cc2b589aa12a8d83ac6d68427f8dd0ed617a4a6dd05d76e35f8955d3be4da4","last_reissued_at":"2026-05-26T02:04:37.702903Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:04:37.702903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniformization as Tannakian Reconstruction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Mao Sheng, Xiaojin Lin","submitted_at":"2026-05-25T06:19:22Z","abstract_excerpt":"We formulate hyperbolic uniformization as a Tannakian reconstruction theorem. For a hyperbolic log-orbi curve C, we construct an intrinsic canonical maximal parahoric PSL2-Higgs object. A tensor-functorial parahoric non-abelian Hodge-Riemann-Hilbert correspondence identifies its Betti realization with a representation of the orbifold fundamental group whose image is the uniformizing cofinite Fuchsian lattice. This construction quasi-inverts the compactified quotient functor from cofinite Fuchsian lattices in PSL2(R) to hyperbolic log-orbi curves. We also prove a Galois enhancement, identifying"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25468","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25468/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.25468","created_at":"2026-05-26T02:04:37.703030+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.25468v1","created_at":"2026-05-26T02:04:37.703030+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25468","created_at":"2026-05-26T02:04:37.703030+00:00"},{"alias_kind":"pith_short_12","alias_value":"G7GCWWE2UEVI","created_at":"2026-05-26T02:04:37.703030+00:00"},{"alias_kind":"pith_short_16","alias_value":"G7GCWWE2UEVI3A5M","created_at":"2026-05-26T02:04:37.703030+00:00"},{"alias_kind":"pith_short_8","alias_value":"G7GCWWE2","created_at":"2026-05-26T02:04:37.703030+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/G7GCWWE2UEVI3A5MNVUEE74N2D","json":"https://pith.science/pith/G7GCWWE2UEVI3A5MNVUEE74N2D.json","graph_json":"https://pith.science/api/pith-number/G7GCWWE2UEVI3A5MNVUEE74N2D/graph.json","events_json":"https://pith.science/api/pith-number/G7GCWWE2UEVI3A5MNVUEE74N2D/events.json","paper":"https://pith.science/paper/G7GCWWE2"},"agent_actions":{"view_html":"https://pith.science/pith/G7GCWWE2UEVI3A5MNVUEE74N2D","download_json":"https://pith.science/pith/G7GCWWE2UEVI3A5MNVUEE74N2D.json","view_paper":"https://pith.science/paper/G7GCWWE2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.25468&json=true","fetch_graph":"https://pith.science/api/pith-number/G7GCWWE2UEVI3A5MNVUEE74N2D/graph.json","fetch_events":"https://pith.science/api/pith-number/G7GCWWE2UEVI3A5MNVUEE74N2D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G7GCWWE2UEVI3A5MNVUEE74N2D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G7GCWWE2UEVI3A5MNVUEE74N2D/action/storage_attestation","attest_author":"https://pith.science/pith/G7GCWWE2UEVI3A5MNVUEE74N2D/action/author_attestation","sign_citation":"https://pith.science/pith/G7GCWWE2UEVI3A5MNVUEE74N2D/action/citation_signature","submit_replication":"https://pith.science/pith/G7GCWWE2UEVI3A5MNVUEE74N2D/action/replication_record"}},"created_at":"2026-05-26T02:04:37.703030+00:00","updated_at":"2026-05-26T02:04:37.703030+00:00"}