{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CIL4KVIDDAFMH5HD34BPION2W6","short_pith_number":"pith:CIL4KVID","canonical_record":{"source":{"id":"1205.4930","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-22T14:40:49Z","cross_cats_sorted":[],"title_canon_sha256":"1a114cb1beed8e53990742747ca143d63a5afa8ce2cf5bbd0dbbd85838dea329","abstract_canon_sha256":"fe5575d3fede5fbd8ef831b5a9fb97b2f23b85b086ebcd1402dbc3afd4ed4ebc"},"schema_version":"1.0"},"canonical_sha256":"1217c55503180ac3f4e3df02f439bab7bb5cea83cfb81d5555bcc2704c62e1a4","source":{"kind":"arxiv","id":"1205.4930","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4930","created_at":"2026-05-18T03:55:11Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4930v1","created_at":"2026-05-18T03:55:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4930","created_at":"2026-05-18T03:55:11Z"},{"alias_kind":"pith_short_12","alias_value":"CIL4KVIDDAFM","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CIL4KVIDDAFMH5HD","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CIL4KVID","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CIL4KVIDDAFMH5HD34BPION2W6","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4930","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-22T14:40:49Z","cross_cats_sorted":[],"title_canon_sha256":"1a114cb1beed8e53990742747ca143d63a5afa8ce2cf5bbd0dbbd85838dea329","abstract_canon_sha256":"fe5575d3fede5fbd8ef831b5a9fb97b2f23b85b086ebcd1402dbc3afd4ed4ebc"},"schema_version":"1.0"},"canonical_sha256":"1217c55503180ac3f4e3df02f439bab7bb5cea83cfb81d5555bcc2704c62e1a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:11.278698Z","signature_b64":"x2ufWKrN5+5nNPhH16CDxy8/tHxcp5mQvKgfOoYvpw5LnWkgtOr/abSuG0p+PrA7Qhz+f6QjeZa3LzQpZcTDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1217c55503180ac3f4e3df02f439bab7bb5cea83cfb81d5555bcc2704c62e1a4","last_reissued_at":"2026-05-18T03:55:11.277969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:11.277969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4930","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":"2026-05-18T03:55:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iLRO02scjK+ifoBitBOJVUWUkXnjA/PZcUyRQRj8KDCYV/YmTbY6o1x7STn7bEz9G/v2Sb3F/K//9GXqd2dvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:33:14.177245Z"},"content_sha256":"b62cdca94408e24ad85c9fc033ab08707d513a007606b0c75ce01f41124db5c6","schema_version":"1.0","event_id":"sha256:b62cdca94408e24ad85c9fc033ab08707d513a007606b0c75ce01f41124db5c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CIL4KVIDDAFMH5HD34BPION2W6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit theorems for rank-one Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexander Gorodnik, Felipe A. Ramirez","submitted_at":"2012-05-22T14:40:49Z","abstract_excerpt":"We investigate asymptotic behaviour of averaging operators for actions of simple rank-one Lie groups. It was previously known that these averaging operators converge almost everywhere, and we establish a more precise asymptotic formula that describes their deviations from the limit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4930","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":"2026-05-18T03:55:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bP/jNk0vI1j444uoQeGsTYuMdaEbPLmZwsoTHyydgnQpsgL3IIA7+/f8gZNDcA8gIB54BLswXNwawr67APM+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:33:14.177606Z"},"content_sha256":"59f9685f69f418bd75dec740489acac6a4b2e7f04b9df8b556c0db890d5d3815","schema_version":"1.0","event_id":"sha256:59f9685f69f418bd75dec740489acac6a4b2e7f04b9df8b556c0db890d5d3815"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CIL4KVIDDAFMH5HD34BPION2W6/bundle.json","state_url":"https://pith.science/pith/CIL4KVIDDAFMH5HD34BPION2W6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CIL4KVIDDAFMH5HD34BPION2W6/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":"2026-06-26T11:33:14Z","links":{"resolver":"https://pith.science/pith/CIL4KVIDDAFMH5HD34BPION2W6","bundle":"https://pith.science/pith/CIL4KVIDDAFMH5HD34BPION2W6/bundle.json","state":"https://pith.science/pith/CIL4KVIDDAFMH5HD34BPION2W6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CIL4KVIDDAFMH5HD34BPION2W6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CIL4KVIDDAFMH5HD34BPION2W6","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":"fe5575d3fede5fbd8ef831b5a9fb97b2f23b85b086ebcd1402dbc3afd4ed4ebc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-22T14:40:49Z","title_canon_sha256":"1a114cb1beed8e53990742747ca143d63a5afa8ce2cf5bbd0dbbd85838dea329"},"schema_version":"1.0","source":{"id":"1205.4930","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4930","created_at":"2026-05-18T03:55:11Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4930v1","created_at":"2026-05-18T03:55:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4930","created_at":"2026-05-18T03:55:11Z"},{"alias_kind":"pith_short_12","alias_value":"CIL4KVIDDAFM","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CIL4KVIDDAFMH5HD","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CIL4KVID","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:59f9685f69f418bd75dec740489acac6a4b2e7f04b9df8b556c0db890d5d3815","target":"graph","created_at":"2026-05-18T03:55:11Z","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 investigate asymptotic behaviour of averaging operators for actions of simple rank-one Lie groups. It was previously known that these averaging operators converge almost everywhere, and we establish a more precise asymptotic formula that describes their deviations from the limit.","authors_text":"Alexander Gorodnik, Felipe A. Ramirez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-22T14:40:49Z","title":"Limit theorems for rank-one Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4930","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:b62cdca94408e24ad85c9fc033ab08707d513a007606b0c75ce01f41124db5c6","target":"record","created_at":"2026-05-18T03:55:11Z","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":"fe5575d3fede5fbd8ef831b5a9fb97b2f23b85b086ebcd1402dbc3afd4ed4ebc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-22T14:40:49Z","title_canon_sha256":"1a114cb1beed8e53990742747ca143d63a5afa8ce2cf5bbd0dbbd85838dea329"},"schema_version":"1.0","source":{"id":"1205.4930","kind":"arxiv","version":1}},"canonical_sha256":"1217c55503180ac3f4e3df02f439bab7bb5cea83cfb81d5555bcc2704c62e1a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1217c55503180ac3f4e3df02f439bab7bb5cea83cfb81d5555bcc2704c62e1a4","first_computed_at":"2026-05-18T03:55:11.277969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:11.277969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x2ufWKrN5+5nNPhH16CDxy8/tHxcp5mQvKgfOoYvpw5LnWkgtOr/abSuG0p+PrA7Qhz+f6QjeZa3LzQpZcTDBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:11.278698Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4930","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b62cdca94408e24ad85c9fc033ab08707d513a007606b0c75ce01f41124db5c6","sha256:59f9685f69f418bd75dec740489acac6a4b2e7f04b9df8b556c0db890d5d3815"],"state_sha256":"627d46700aef3b24eceeaaea539340d887e357d5ac348522b594869af5e84cb9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IGOOgbjjFP5s8SjztrIuRTfLpPoODz6b3OL2w1BuOgzFhNprVxjMTLQn7bsD5Kol2o5xelSlTHG5fLl9ajN7Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:33:14.179682Z","bundle_sha256":"efb2386010f39bdc221cc7485567f0e58ca6527f42d713ee9faab0ff9b94bb03"}}