{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LYO2RBGTAIRXXOININ4ZF3VX3G","short_pith_number":"pith:LYO2RBGT","canonical_record":{"source":{"id":"1609.07319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-23T11:32:22Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"cd91f7cd5b299474925b93320b557c65e8256bf94ff3e23797046855cfdfb19e","abstract_canon_sha256":"df2b9efa0ef56fccdf0cce96206234901680f21eecaf564fc0d9e2e6b32ae003"},"schema_version":"1.0"},"canonical_sha256":"5e1da884d302237bb90d437992eeb7d9bbfb007e73f44bbfb854cda6a212e6b2","source":{"kind":"arxiv","id":"1609.07319","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07319","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07319v1","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07319","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"LYO2RBGTAIRX","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LYO2RBGTAIRXXOIN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LYO2RBGT","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LYO2RBGTAIRXXOININ4ZF3VX3G","target":"record","payload":{"canonical_record":{"source":{"id":"1609.07319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-23T11:32:22Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"cd91f7cd5b299474925b93320b557c65e8256bf94ff3e23797046855cfdfb19e","abstract_canon_sha256":"df2b9efa0ef56fccdf0cce96206234901680f21eecaf564fc0d9e2e6b32ae003"},"schema_version":"1.0"},"canonical_sha256":"5e1da884d302237bb90d437992eeb7d9bbfb007e73f44bbfb854cda6a212e6b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:01.719633Z","signature_b64":"JwbQBiMqmcjxv6/QVZHYePmm1CgGDVMB8muv/z0XGDkMTT+nr3UH8i1EKqaoG7JemJo+u4IsGnx7ASDG/ERrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e1da884d302237bb90d437992eeb7d9bbfb007e73f44bbfb854cda6a212e6b2","last_reissued_at":"2026-05-18T01:04:01.718819Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:01.718819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.07319","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":"2026-05-18T01:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vluTE/1vgMol/vPUTiIFdSw1Dw+fvfGbd00D/QxvnOxvppFw1Dh641gb6s436ZWXeqgalB40N8ljTB+Mbz2iCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T23:15:30.060527Z"},"content_sha256":"552976cfdebd19836ff09c574eff946cc50b3b551eba0ba58c533fed45635c63","schema_version":"1.0","event_id":"sha256:552976cfdebd19836ff09c574eff946cc50b3b551eba0ba58c533fed45635c63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LYO2RBGTAIRXXOININ4ZF3VX3G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equidistribution in S-arithmetic and adelic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Antonin Guilloux (IMJ-PRG, UPMC)","submitted_at":"2016-09-23T11:32:22Z","abstract_excerpt":"We give an introduction to adelic mixing and its applications for mathematicians knowing about the mixing of the geodesic flow on hyperbolic surfaces. We focus on the example of the Hecke trees in the modular surface."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07319","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":""},"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":"2026-05-18T01:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2x3SG1EkFL1ZgCe0W0kwnD1hnLZFGAVC5/XxFUAuEX/mc0vLmKeJn4Mh5WJwb9lzKhpbu7dyCfZK96vhyJ8JAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T23:15:30.061208Z"},"content_sha256":"4362d4a43e43b7cd60e2da4627cbfaf8684d7eeea6cae5b8085095f579ac767a","schema_version":"1.0","event_id":"sha256:4362d4a43e43b7cd60e2da4627cbfaf8684d7eeea6cae5b8085095f579ac767a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LYO2RBGTAIRXXOININ4ZF3VX3G/bundle.json","state_url":"https://pith.science/pith/LYO2RBGTAIRXXOININ4ZF3VX3G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LYO2RBGTAIRXXOININ4ZF3VX3G/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":"2026-05-24T23:15:30Z","links":{"resolver":"https://pith.science/pith/LYO2RBGTAIRXXOININ4ZF3VX3G","bundle":"https://pith.science/pith/LYO2RBGTAIRXXOININ4ZF3VX3G/bundle.json","state":"https://pith.science/pith/LYO2RBGTAIRXXOININ4ZF3VX3G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LYO2RBGTAIRXXOININ4ZF3VX3G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LYO2RBGTAIRXXOININ4ZF3VX3G","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":"df2b9efa0ef56fccdf0cce96206234901680f21eecaf564fc0d9e2e6b32ae003","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-23T11:32:22Z","title_canon_sha256":"cd91f7cd5b299474925b93320b557c65e8256bf94ff3e23797046855cfdfb19e"},"schema_version":"1.0","source":{"id":"1609.07319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07319","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07319v1","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07319","created_at":"2026-05-18T01:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"LYO2RBGTAIRX","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LYO2RBGTAIRXXOIN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LYO2RBGT","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:4362d4a43e43b7cd60e2da4627cbfaf8684d7eeea6cae5b8085095f579ac767a","target":"graph","created_at":"2026-05-18T01:04:01Z","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 give an introduction to adelic mixing and its applications for mathematicians knowing about the mixing of the geodesic flow on hyperbolic surfaces. We focus on the example of the Hecke trees in the modular surface.","authors_text":"Antonin Guilloux (IMJ-PRG, UPMC)","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-23T11:32:22Z","title":"Equidistribution in S-arithmetic and adelic spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07319","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":"sha256:552976cfdebd19836ff09c574eff946cc50b3b551eba0ba58c533fed45635c63","target":"record","created_at":"2026-05-18T01:04:01Z","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":"df2b9efa0ef56fccdf0cce96206234901680f21eecaf564fc0d9e2e6b32ae003","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-23T11:32:22Z","title_canon_sha256":"cd91f7cd5b299474925b93320b557c65e8256bf94ff3e23797046855cfdfb19e"},"schema_version":"1.0","source":{"id":"1609.07319","kind":"arxiv","version":1}},"canonical_sha256":"5e1da884d302237bb90d437992eeb7d9bbfb007e73f44bbfb854cda6a212e6b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e1da884d302237bb90d437992eeb7d9bbfb007e73f44bbfb854cda6a212e6b2","first_computed_at":"2026-05-18T01:04:01.718819Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:01.718819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JwbQBiMqmcjxv6/QVZHYePmm1CgGDVMB8muv/z0XGDkMTT+nr3UH8i1EKqaoG7JemJo+u4IsGnx7ASDG/ERrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:01.719633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:552976cfdebd19836ff09c574eff946cc50b3b551eba0ba58c533fed45635c63","sha256:4362d4a43e43b7cd60e2da4627cbfaf8684d7eeea6cae5b8085095f579ac767a"],"state_sha256":"5bb8017599f1da5608e4d8e2e442a4100ff8f8ea18b5f2fab984cd14f7f64779"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQbV6CgqrsIUF6OV6019f5mPzRzyb4BhSEdmXacUi4nNqLwWInF2Pb6w+o8IGY4jWL2L5zmPVujk1kfhtFHECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T23:15:30.067193Z","bundle_sha256":"f54ee9b8c7480c3f767864b44032864af0515402ce05c4a9fb8c408b9dfa11ea"}}