{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:G3UVCPTGKIWINXM2K6YNTSYTKX","short_pith_number":"pith:G3UVCPTG","canonical_record":{"source":{"id":"2509.03820","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2025-09-04T02:11:30Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"4d84952c24d153a86206ca52d57383a0c0273f893da69f6152afed562f89d8ff","abstract_canon_sha256":"2f80c81e1f694e6d2b89ddbe6657c4783849db8f8cf6ef2c78e066adc9e2655c"},"schema_version":"1.0"},"canonical_sha256":"36e9513e66522c86dd9a57b0d9cb1355deceea3275c3f3da054442925ac33495","source":{"kind":"arxiv","id":"2509.03820","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.03820","created_at":"2026-07-05T12:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"2509.03820v1","created_at":"2026-07-05T12:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.03820","created_at":"2026-07-05T12:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"G3UVCPTGKIWI","created_at":"2026-07-05T12:04:47Z"},{"alias_kind":"pith_short_16","alias_value":"G3UVCPTGKIWINXM2","created_at":"2026-07-05T12:04:47Z"},{"alias_kind":"pith_short_8","alias_value":"G3UVCPTG","created_at":"2026-07-05T12:04:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:G3UVCPTGKIWINXM2K6YNTSYTKX","target":"record","payload":{"canonical_record":{"source":{"id":"2509.03820","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2025-09-04T02:11:30Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"4d84952c24d153a86206ca52d57383a0c0273f893da69f6152afed562f89d8ff","abstract_canon_sha256":"2f80c81e1f694e6d2b89ddbe6657c4783849db8f8cf6ef2c78e066adc9e2655c"},"schema_version":"1.0"},"canonical_sha256":"36e9513e66522c86dd9a57b0d9cb1355deceea3275c3f3da054442925ac33495","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:04:47.135786Z","signature_b64":"77Aw6jt5yeLrwa51hI4XqGsMunpfiPoy9tIbsS6PV+5JfB/xlAr6OsRZ9vll5oEzmeEf+SfwEMNnXUjJKA+lDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36e9513e66522c86dd9a57b0d9cb1355deceea3275c3f3da054442925ac33495","last_reissued_at":"2026-07-05T12:04:47.135230Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:04:47.135230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.03820","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:04:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TcdXBXepvBUIGjaovBIWyYPCK0+njS9NKl7V74ihyFgZ5j4vLC9+jVPKqU+OWPX0MdUXtZ/mG5AUMiGye4fHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T08:29:03.024177Z"},"content_sha256":"3fe10a8b17390b9500d44d2ae7c9753dba5d8d20b6328dea06f940a1de56354c","schema_version":"1.0","event_id":"sha256:3fe10a8b17390b9500d44d2ae7c9753dba5d8d20b6328dea06f940a1de56354c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:G3UVCPTGKIWINXM2K6YNTSYTKX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The algebraic modular functor conjecture in type $A_n$ quantum Teichm\\\"uller theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Alexander Shapiro, Gus Schrader","submitted_at":"2025-09-04T02:11:30Z","abstract_excerpt":"Fock and Goncharov introduced a quantization of higher Teichm\\\"uller theory using cluster Poisson varieties and their noncommutative deformations, associating to a complex semisimple Lie group $G$ and a marked surface $S$ a quantum algebra $\\mathbb{L}_{G,S}$ equipped with an action of the surface mapping class group. They conjectured that these quantizations form an algebraic analog of a modular functor: cutting a surface along a simple closed curve should correspond to a canonical gluing isomorphism for the associated algebras. In this paper we prove this conjecture for $G = \\mathrm{PGL}_{n+1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.03820","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/2509.03820/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:04:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C+wO/Jw9AAbB3jZu65OPFYI8KHd2ZaNIJmbpX4uMjsEzkUuci5PoJUuO41nMt4/po7HMhcLMBcta/w2BWhyOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T08:29:03.024681Z"},"content_sha256":"af8da883ab416338c37e0b94f9806d42334c70a4fb9c0de87c1ab5398144b74e","schema_version":"1.0","event_id":"sha256:af8da883ab416338c37e0b94f9806d42334c70a4fb9c0de87c1ab5398144b74e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G3UVCPTGKIWINXM2K6YNTSYTKX/bundle.json","state_url":"https://pith.science/pith/G3UVCPTGKIWINXM2K6YNTSYTKX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G3UVCPTGKIWINXM2K6YNTSYTKX/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":"2026-08-08T08:29:03Z","links":{"resolver":"https://pith.science/pith/G3UVCPTGKIWINXM2K6YNTSYTKX","bundle":"https://pith.science/pith/G3UVCPTGKIWINXM2K6YNTSYTKX/bundle.json","state":"https://pith.science/pith/G3UVCPTGKIWINXM2K6YNTSYTKX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G3UVCPTGKIWINXM2K6YNTSYTKX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:G3UVCPTGKIWINXM2K6YNTSYTKX","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":"2f80c81e1f694e6d2b89ddbe6657c4783849db8f8cf6ef2c78e066adc9e2655c","cross_cats_sorted":["math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2025-09-04T02:11:30Z","title_canon_sha256":"4d84952c24d153a86206ca52d57383a0c0273f893da69f6152afed562f89d8ff"},"schema_version":"1.0","source":{"id":"2509.03820","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.03820","created_at":"2026-07-05T12:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"2509.03820v1","created_at":"2026-07-05T12:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.03820","created_at":"2026-07-05T12:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"G3UVCPTGKIWI","created_at":"2026-07-05T12:04:47Z"},{"alias_kind":"pith_short_16","alias_value":"G3UVCPTGKIWINXM2","created_at":"2026-07-05T12:04:47Z"},{"alias_kind":"pith_short_8","alias_value":"G3UVCPTG","created_at":"2026-07-05T12:04:47Z"}],"graph_snapshots":[{"event_id":"sha256:af8da883ab416338c37e0b94f9806d42334c70a4fb9c0de87c1ab5398144b74e","target":"graph","created_at":"2026-07-05T12:04:47Z","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/2509.03820/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Fock and Goncharov introduced a quantization of higher Teichm\\\"uller theory using cluster Poisson varieties and their noncommutative deformations, associating to a complex semisimple Lie group $G$ and a marked surface $S$ a quantum algebra $\\mathbb{L}_{G,S}$ equipped with an action of the surface mapping class group. They conjectured that these quantizations form an algebraic analog of a modular functor: cutting a surface along a simple closed curve should correspond to a canonical gluing isomorphism for the associated algebras. In this paper we prove this conjecture for $G = \\mathrm{PGL}_{n+1","authors_text":"Alexander Shapiro, Gus Schrader","cross_cats":["math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2025-09-04T02:11:30Z","title":"The algebraic modular functor conjecture in type $A_n$ quantum Teichm\\\"uller theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.03820","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":"sha256:3fe10a8b17390b9500d44d2ae7c9753dba5d8d20b6328dea06f940a1de56354c","target":"record","created_at":"2026-07-05T12:04:47Z","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":"2f80c81e1f694e6d2b89ddbe6657c4783849db8f8cf6ef2c78e066adc9e2655c","cross_cats_sorted":["math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2025-09-04T02:11:30Z","title_canon_sha256":"4d84952c24d153a86206ca52d57383a0c0273f893da69f6152afed562f89d8ff"},"schema_version":"1.0","source":{"id":"2509.03820","kind":"arxiv","version":1}},"canonical_sha256":"36e9513e66522c86dd9a57b0d9cb1355deceea3275c3f3da054442925ac33495","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36e9513e66522c86dd9a57b0d9cb1355deceea3275c3f3da054442925ac33495","first_computed_at":"2026-07-05T12:04:47.135230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:04:47.135230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"77Aw6jt5yeLrwa51hI4XqGsMunpfiPoy9tIbsS6PV+5JfB/xlAr6OsRZ9vll5oEzmeEf+SfwEMNnXUjJKA+lDw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:04:47.135786Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.03820","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fe10a8b17390b9500d44d2ae7c9753dba5d8d20b6328dea06f940a1de56354c","sha256:af8da883ab416338c37e0b94f9806d42334c70a4fb9c0de87c1ab5398144b74e"],"state_sha256":"b6dab02b769664ad50f2f31e6a35de2992a3ae4c7473cae4c647e81226d21ab0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LpY/vC8QKHds7NB16q9Of8StyQMUJOTSaY1Mn77kcxA4XLMOb3uEKTOe/KPLt7NARBUB2zXA3rDZASc7g1AuDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T08:29:03.028472Z","bundle_sha256":"199372db40040671fc1ba87da99112ee318bdd791eed0f19fddd3eed9aac8a8d"}}