{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:WP6W2YB6U7GTGSRA222WKFPLLT","short_pith_number":"pith:WP6W2YB6","canonical_record":{"source":{"id":"2202.11815","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-02-23T22:35:59Z","cross_cats_sorted":["math.GT","math.NT"],"title_canon_sha256":"0b2985148553a3659b832d43bdfd684162a1182355a39cea198105f872f44343","abstract_canon_sha256":"39c6b09f64565a93d074dbb7c0b14ed4f267385a78bb62cf33dd64277f6e66d3"},"schema_version":"1.0"},"canonical_sha256":"b3fd6d603ea7cd334a20d6b56515eb5cdd99c2614cdfb936ff527d4e7dda9779","source":{"kind":"arxiv","id":"2202.11815","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.11815","created_at":"2026-07-05T04:44:10Z"},{"alias_kind":"arxiv_version","alias_value":"2202.11815v3","created_at":"2026-07-05T04:44:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.11815","created_at":"2026-07-05T04:44:10Z"},{"alias_kind":"pith_short_12","alias_value":"WP6W2YB6U7GT","created_at":"2026-07-05T04:44:10Z"},{"alias_kind":"pith_short_16","alias_value":"WP6W2YB6U7GTGSRA","created_at":"2026-07-05T04:44:10Z"},{"alias_kind":"pith_short_8","alias_value":"WP6W2YB6","created_at":"2026-07-05T04:44:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:WP6W2YB6U7GTGSRA222WKFPLLT","target":"record","payload":{"canonical_record":{"source":{"id":"2202.11815","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-02-23T22:35:59Z","cross_cats_sorted":["math.GT","math.NT"],"title_canon_sha256":"0b2985148553a3659b832d43bdfd684162a1182355a39cea198105f872f44343","abstract_canon_sha256":"39c6b09f64565a93d074dbb7c0b14ed4f267385a78bb62cf33dd64277f6e66d3"},"schema_version":"1.0"},"canonical_sha256":"b3fd6d603ea7cd334a20d6b56515eb5cdd99c2614cdfb936ff527d4e7dda9779","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:44:10.773147Z","signature_b64":"9le0Ji70qfGeqUy4ddZ50XxG/CBOBPO0I3JQC9RsMiuRxF6VkkO2oyJJhqHK7F8uAb9eI2+AUJwS19bT5z5OBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3fd6d603ea7cd334a20d6b56515eb5cdd99c2614cdfb936ff527d4e7dda9779","last_reissued_at":"2026-07-05T04:44:10.772630Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:44:10.772630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2202.11815","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:44:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jSzNEuOPbaE96T5PH8oviFipp74dAnVFa4HgmV/3h8M6q0cYystwHQKB0Xqt2qBt7C/ydzogObJ+mJ4l/Z70Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T06:33:37.278718Z"},"content_sha256":"30235ec3a369eb2c894b658988e51061e3b95b5b22a6019cd8c72d15c21f6218","schema_version":"1.0","event_id":"sha256:30235ec3a369eb2c894b658988e51061e3b95b5b22a6019cd8c72d15c21f6218"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:WP6W2YB6U7GTGSRA222WKFPLLT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial effective equidistribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.NT"],"primary_cat":"math.DS","authors_text":"Amir Mohammadi, Elon Lindenstrauss, Zhiren Wang","submitted_at":"2022-02-23T22:35:59Z","abstract_excerpt":"We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\\operatorname{SL}_2(\\mathbb R)$ in arithmetic quotients of $\\operatorname{SL}_2(\\mathbb C)$ and $\\operatorname{SL}_2(\\mathbb R)\\times\\operatorname{SL}_2(\\mathbb R)$. The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.11815","kind":"arxiv","version":3},"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/2202.11815/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":"2026-07-05T04:44:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hN6Q9yXcpmnCO9N6qsuQ/CogpAM2MOqA0DTb2Bw7mJDh1SU1fl9MPxOxG869kesdEanclCCVeCKzSEUi7MNBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T06:33:37.279222Z"},"content_sha256":"169bbaf2a8941d887f88d2407ad65fadee9de9e9327d3810c4bd59515c62e805","schema_version":"1.0","event_id":"sha256:169bbaf2a8941d887f88d2407ad65fadee9de9e9327d3810c4bd59515c62e805"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WP6W2YB6U7GTGSRA222WKFPLLT/bundle.json","state_url":"https://pith.science/pith/WP6W2YB6U7GTGSRA222WKFPLLT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WP6W2YB6U7GTGSRA222WKFPLLT/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":"2026-08-11T06:33:37Z","links":{"resolver":"https://pith.science/pith/WP6W2YB6U7GTGSRA222WKFPLLT","bundle":"https://pith.science/pith/WP6W2YB6U7GTGSRA222WKFPLLT/bundle.json","state":"https://pith.science/pith/WP6W2YB6U7GTGSRA222WKFPLLT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WP6W2YB6U7GTGSRA222WKFPLLT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:WP6W2YB6U7GTGSRA222WKFPLLT","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":"39c6b09f64565a93d074dbb7c0b14ed4f267385a78bb62cf33dd64277f6e66d3","cross_cats_sorted":["math.GT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-02-23T22:35:59Z","title_canon_sha256":"0b2985148553a3659b832d43bdfd684162a1182355a39cea198105f872f44343"},"schema_version":"1.0","source":{"id":"2202.11815","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.11815","created_at":"2026-07-05T04:44:10Z"},{"alias_kind":"arxiv_version","alias_value":"2202.11815v3","created_at":"2026-07-05T04:44:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.11815","created_at":"2026-07-05T04:44:10Z"},{"alias_kind":"pith_short_12","alias_value":"WP6W2YB6U7GT","created_at":"2026-07-05T04:44:10Z"},{"alias_kind":"pith_short_16","alias_value":"WP6W2YB6U7GTGSRA","created_at":"2026-07-05T04:44:10Z"},{"alias_kind":"pith_short_8","alias_value":"WP6W2YB6","created_at":"2026-07-05T04:44:10Z"}],"graph_snapshots":[{"event_id":"sha256:169bbaf2a8941d887f88d2407ad65fadee9de9e9327d3810c4bd59515c62e805","target":"graph","created_at":"2026-07-05T04:44:10Z","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/2202.11815/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\\operatorname{SL}_2(\\mathbb R)$ in arithmetic quotients of $\\operatorname{SL}_2(\\mathbb C)$ and $\\operatorname{SL}_2(\\mathbb R)\\times\\operatorname{SL}_2(\\mathbb R)$. The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.","authors_text":"Amir Mohammadi, Elon Lindenstrauss, Zhiren Wang","cross_cats":["math.GT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-02-23T22:35:59Z","title":"Polynomial effective equidistribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.11815","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":"sha256:30235ec3a369eb2c894b658988e51061e3b95b5b22a6019cd8c72d15c21f6218","target":"record","created_at":"2026-07-05T04:44:10Z","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":"39c6b09f64565a93d074dbb7c0b14ed4f267385a78bb62cf33dd64277f6e66d3","cross_cats_sorted":["math.GT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-02-23T22:35:59Z","title_canon_sha256":"0b2985148553a3659b832d43bdfd684162a1182355a39cea198105f872f44343"},"schema_version":"1.0","source":{"id":"2202.11815","kind":"arxiv","version":3}},"canonical_sha256":"b3fd6d603ea7cd334a20d6b56515eb5cdd99c2614cdfb936ff527d4e7dda9779","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3fd6d603ea7cd334a20d6b56515eb5cdd99c2614cdfb936ff527d4e7dda9779","first_computed_at":"2026-07-05T04:44:10.772630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:44:10.772630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9le0Ji70qfGeqUy4ddZ50XxG/CBOBPO0I3JQC9RsMiuRxF6VkkO2oyJJhqHK7F8uAb9eI2+AUJwS19bT5z5OBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:44:10.773147Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.11815","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30235ec3a369eb2c894b658988e51061e3b95b5b22a6019cd8c72d15c21f6218","sha256:169bbaf2a8941d887f88d2407ad65fadee9de9e9327d3810c4bd59515c62e805"],"state_sha256":"ece501981cbfa873a96efa4f3bc7fdf52bfc5ba646f25fb4bc52afa7088b6d10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bc9LRwN+B0C0boY9Nww6stKMqwrV579jTW5f7g/V+9G+7UueBu1tkAg6IDB+EGovq+5TDYi1qKZ+khxTXR3SDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T06:33:37.284734Z","bundle_sha256":"481a4d665f22a86f791a49489917e39bc6dcaa85196c2ba190b8620f18ebbdf5"}}