{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:GCCUP2GWG7IW7YGV5IOGZP4FSO","short_pith_number":"pith:GCCUP2GW","canonical_record":{"source":{"id":"2205.15352","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-05-30T18:01:31Z","cross_cats_sorted":["math.AG","math.NT","math.RT"],"title_canon_sha256":"6fd0705313b919a84241ab9ab47a6931a2d8fd1e3519e8d3f53e4da12f645a2d","abstract_canon_sha256":"ad45b13d09fb34982407d2566b2d96f387dab4399b8e2815af96059449b1c0e5"},"schema_version":"1.0"},"canonical_sha256":"308547e8d637d16fe0d5ea1c6cbf8593874fca56f11f7fae8aafc85746647305","source":{"kind":"arxiv","id":"2205.15352","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.15352","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"arxiv_version","alias_value":"2205.15352v4","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.15352","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"pith_short_12","alias_value":"GCCUP2GWG7IW","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"pith_short_16","alias_value":"GCCUP2GWG7IW7YGV","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"pith_short_8","alias_value":"GCCUP2GW","created_at":"2026-07-05T10:18:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:GCCUP2GWG7IW7YGV5IOGZP4FSO","target":"record","payload":{"canonical_record":{"source":{"id":"2205.15352","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-05-30T18:01:31Z","cross_cats_sorted":["math.AG","math.NT","math.RT"],"title_canon_sha256":"6fd0705313b919a84241ab9ab47a6931a2d8fd1e3519e8d3f53e4da12f645a2d","abstract_canon_sha256":"ad45b13d09fb34982407d2566b2d96f387dab4399b8e2815af96059449b1c0e5"},"schema_version":"1.0"},"canonical_sha256":"308547e8d637d16fe0d5ea1c6cbf8593874fca56f11f7fae8aafc85746647305","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:18:30.455127Z","signature_b64":"D3Z+UGDtnxRebh/7O9FoRc7/xilosVx1kj232WUTfjV2UAzK+F6CnevxvWJ0CctCGHABQPDZCSg2oxGxqRsWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"308547e8d637d16fe0d5ea1c6cbf8593874fca56f11f7fae8aafc85746647305","last_reissued_at":"2026-07-05T10:18:30.454599Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:18:30.454599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.15352","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":"2026-07-05T10:18:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0DqjnZRd9qq10XcPK8vQVSNo9p6os/lxLuvUZO79K+BVaa35JtYhmysW6ftOkVqBqKLNaOO7mf7WRLj8rZDEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T10:31:16.657776Z"},"content_sha256":"24ce35da0357c0c97a5e95435a9b1c1cdcee1cf2a6612053c03067e6363a3344","schema_version":"1.0","event_id":"sha256:24ce35da0357c0c97a5e95435a9b1c1cdcee1cf2a6612053c03067e6363a3344"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:GCCUP2GWG7IW7YGV5IOGZP4FSO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Canonical representations of surface groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.NT","math.RT"],"primary_cat":"math.GT","authors_text":"Aaron Landesman, Daniel Litt","submitted_at":"2022-05-30T18:01:31Z","abstract_excerpt":"Let $\\Sigma_{g,n}$ be an orientable surface of genus $g$ with $n$ punctures. We study actions of the mapping class group of $\\Sigma_{g,n}$ via Hodge-theoretic and arithmetic techniques. We show that if $$\\rho: \\pi_1(\\Sigma_{g,n})\\to GL_r(\\mathbb{C})$$ is a representation whose conjugacy class has finite orbit under the mapping class group, and $r<\\sqrt{g+1}$, then $\\rho$ has finite image. This answers questions of Junho Peter Whang and Mark Kisin. We give applications of our methods to the Putman-Wieland conjecture, the Fontaine-Mazur conjecture, and a question of Esnault-Kerz.\n  The proofs re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.15352","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.15352/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":"2026-07-05T10:18:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j+PwVwgmVE4cU/Mg7eMLYGC32io4CeqXZ5Npj+gpY/xn/q4pTVgDlQqR2EpEJK5eIcN++jW3VwchXN9JT1NCAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T10:31:16.658303Z"},"content_sha256":"71a04a21be93b6273476a984af460aeacc54e7edd016c330b54938c677181294","schema_version":"1.0","event_id":"sha256:71a04a21be93b6273476a984af460aeacc54e7edd016c330b54938c677181294"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GCCUP2GWG7IW7YGV5IOGZP4FSO/bundle.json","state_url":"https://pith.science/pith/GCCUP2GWG7IW7YGV5IOGZP4FSO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GCCUP2GWG7IW7YGV5IOGZP4FSO/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":"2026-08-12T10:31:16Z","links":{"resolver":"https://pith.science/pith/GCCUP2GWG7IW7YGV5IOGZP4FSO","bundle":"https://pith.science/pith/GCCUP2GWG7IW7YGV5IOGZP4FSO/bundle.json","state":"https://pith.science/pith/GCCUP2GWG7IW7YGV5IOGZP4FSO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GCCUP2GWG7IW7YGV5IOGZP4FSO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:GCCUP2GWG7IW7YGV5IOGZP4FSO","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":"ad45b13d09fb34982407d2566b2d96f387dab4399b8e2815af96059449b1c0e5","cross_cats_sorted":["math.AG","math.NT","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-05-30T18:01:31Z","title_canon_sha256":"6fd0705313b919a84241ab9ab47a6931a2d8fd1e3519e8d3f53e4da12f645a2d"},"schema_version":"1.0","source":{"id":"2205.15352","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.15352","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"arxiv_version","alias_value":"2205.15352v4","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.15352","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"pith_short_12","alias_value":"GCCUP2GWG7IW","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"pith_short_16","alias_value":"GCCUP2GWG7IW7YGV","created_at":"2026-07-05T10:18:30Z"},{"alias_kind":"pith_short_8","alias_value":"GCCUP2GW","created_at":"2026-07-05T10:18:30Z"}],"graph_snapshots":[{"event_id":"sha256:71a04a21be93b6273476a984af460aeacc54e7edd016c330b54938c677181294","target":"graph","created_at":"2026-07-05T10:18:30Z","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/2205.15352/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\Sigma_{g,n}$ be an orientable surface of genus $g$ with $n$ punctures. We study actions of the mapping class group of $\\Sigma_{g,n}$ via Hodge-theoretic and arithmetic techniques. We show that if $$\\rho: \\pi_1(\\Sigma_{g,n})\\to GL_r(\\mathbb{C})$$ is a representation whose conjugacy class has finite orbit under the mapping class group, and $r<\\sqrt{g+1}$, then $\\rho$ has finite image. This answers questions of Junho Peter Whang and Mark Kisin. We give applications of our methods to the Putman-Wieland conjecture, the Fontaine-Mazur conjecture, and a question of Esnault-Kerz.\n  The proofs re","authors_text":"Aaron Landesman, Daniel Litt","cross_cats":["math.AG","math.NT","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-05-30T18:01:31Z","title":"Canonical representations of surface groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.15352","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":"sha256:24ce35da0357c0c97a5e95435a9b1c1cdcee1cf2a6612053c03067e6363a3344","target":"record","created_at":"2026-07-05T10:18:30Z","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":"ad45b13d09fb34982407d2566b2d96f387dab4399b8e2815af96059449b1c0e5","cross_cats_sorted":["math.AG","math.NT","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-05-30T18:01:31Z","title_canon_sha256":"6fd0705313b919a84241ab9ab47a6931a2d8fd1e3519e8d3f53e4da12f645a2d"},"schema_version":"1.0","source":{"id":"2205.15352","kind":"arxiv","version":4}},"canonical_sha256":"308547e8d637d16fe0d5ea1c6cbf8593874fca56f11f7fae8aafc85746647305","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"308547e8d637d16fe0d5ea1c6cbf8593874fca56f11f7fae8aafc85746647305","first_computed_at":"2026-07-05T10:18:30.454599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:18:30.454599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D3Z+UGDtnxRebh/7O9FoRc7/xilosVx1kj232WUTfjV2UAzK+F6CnevxvWJ0CctCGHABQPDZCSg2oxGxqRsWBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:18:30.455127Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.15352","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24ce35da0357c0c97a5e95435a9b1c1cdcee1cf2a6612053c03067e6363a3344","sha256:71a04a21be93b6273476a984af460aeacc54e7edd016c330b54938c677181294"],"state_sha256":"7d0f317beb265f9a9e36b04f2369085f96f1422203aa239ddac183a3d5299c65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LY7bdeefppf/W3RyI8VsAPgOn1ivr2sGIt4tMDqwCd9Dhbh87di9pcBJQmznhKxh+ukiE0FX4H0Ckswx/5AEAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T10:31:16.663598Z","bundle_sha256":"567cd36055939858fdd06ca608acb6b9e335632d0cd82511c64711674cb12428"}}