{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:GI7YNWTIKQBOL3J5NF2A2EH7EK","short_pith_number":"pith:GI7YNWTI","canonical_record":{"source":{"id":"2303.09499","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-03-16T17:19:42Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"2c4ac3812cfe8f8a00c3ad590e64dec413b92ee64ac82a777bcccf40c00413e7","abstract_canon_sha256":"35635b4d361ca484d02ae127e493348aefbab5788614e7b56ce3ec722ad52e22"},"schema_version":"1.0"},"canonical_sha256":"323f86da685402e5ed3d69740d10ff22838e255942d7047eb61e01f099b68e75","source":{"kind":"arxiv","id":"2303.09499","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.09499","created_at":"2026-07-05T07:33:11Z"},{"alias_kind":"arxiv_version","alias_value":"2303.09499v3","created_at":"2026-07-05T07:33:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.09499","created_at":"2026-07-05T07:33:11Z"},{"alias_kind":"pith_short_12","alias_value":"GI7YNWTIKQBO","created_at":"2026-07-05T07:33:11Z"},{"alias_kind":"pith_short_16","alias_value":"GI7YNWTIKQBOL3J5","created_at":"2026-07-05T07:33:11Z"},{"alias_kind":"pith_short_8","alias_value":"GI7YNWTI","created_at":"2026-07-05T07:33:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:GI7YNWTIKQBOL3J5NF2A2EH7EK","target":"record","payload":{"canonical_record":{"source":{"id":"2303.09499","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-03-16T17:19:42Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"2c4ac3812cfe8f8a00c3ad590e64dec413b92ee64ac82a777bcccf40c00413e7","abstract_canon_sha256":"35635b4d361ca484d02ae127e493348aefbab5788614e7b56ce3ec722ad52e22"},"schema_version":"1.0"},"canonical_sha256":"323f86da685402e5ed3d69740d10ff22838e255942d7047eb61e01f099b68e75","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:33:11.366790Z","signature_b64":"Fy3Pq63U4HIKiXaEuS+bHCxmdX0RNcRabt29JQnaaWQA0RalaV6608+BX+RLZz0i6h7km8LgikjQ/STgMrhBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"323f86da685402e5ed3d69740d10ff22838e255942d7047eb61e01f099b68e75","last_reissued_at":"2026-07-05T07:33:11.366357Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:33:11.366357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.09499","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":"2026-07-05T07:33:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fUWNQJzjkp3ROUJfSciQKkxbW88kfB20HmfQL8Mcg3/Zuc066I5ocfDwbHHKTmXvIZkISiwpkyRKGU3wrMuACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:35:18.973012Z"},"content_sha256":"635ab27abd032caae639d90246181fd42b1b660caf20f7efc84e134823afd988","schema_version":"1.0","event_id":"sha256:635ab27abd032caae639d90246181fd42b1b660caf20f7efc84e134823afd988"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:GI7YNWTIKQBOL3J5NF2A2EH7EK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effective density of non-degenerate random walks on homogeneous spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.PR","authors_text":"Constantin Kogler, Wooyeon Kim","submitted_at":"2023-03-16T17:19:42Z","abstract_excerpt":"We prove effective density of random walks on homogeneous spaces, assuming that the underlying measure is supported on matrices generating a dense subgroup and having algebraic entries. The main novelty is an argument passing from high dimension to effective equidistribution in the setting of random walks on homogeneous spaces, exploiting spectral gap of the associated convolution operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.09499","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/2303.09499/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":"2026-07-05T07:33:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"65EQoaQdJCjmoVHKk6qP2s/VlVRlXaqu7/IMH6N2P/aNN0rRhCiLdisCWhI2dradnjcwkNHPXRAYpifg81doCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:35:18.973956Z"},"content_sha256":"1d4a4d5ed0a34763dcd34134b8aa0f69badbf46b8ad62bd7036ecbace19166ef","schema_version":"1.0","event_id":"sha256:1d4a4d5ed0a34763dcd34134b8aa0f69badbf46b8ad62bd7036ecbace19166ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GI7YNWTIKQBOL3J5NF2A2EH7EK/bundle.json","state_url":"https://pith.science/pith/GI7YNWTIKQBOL3J5NF2A2EH7EK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GI7YNWTIKQBOL3J5NF2A2EH7EK/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":"2026-08-12T22:35:18Z","links":{"resolver":"https://pith.science/pith/GI7YNWTIKQBOL3J5NF2A2EH7EK","bundle":"https://pith.science/pith/GI7YNWTIKQBOL3J5NF2A2EH7EK/bundle.json","state":"https://pith.science/pith/GI7YNWTIKQBOL3J5NF2A2EH7EK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GI7YNWTIKQBOL3J5NF2A2EH7EK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:GI7YNWTIKQBOL3J5NF2A2EH7EK","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":"35635b4d361ca484d02ae127e493348aefbab5788614e7b56ce3ec722ad52e22","cross_cats_sorted":["math.DS","math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-03-16T17:19:42Z","title_canon_sha256":"2c4ac3812cfe8f8a00c3ad590e64dec413b92ee64ac82a777bcccf40c00413e7"},"schema_version":"1.0","source":{"id":"2303.09499","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.09499","created_at":"2026-07-05T07:33:11Z"},{"alias_kind":"arxiv_version","alias_value":"2303.09499v3","created_at":"2026-07-05T07:33:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.09499","created_at":"2026-07-05T07:33:11Z"},{"alias_kind":"pith_short_12","alias_value":"GI7YNWTIKQBO","created_at":"2026-07-05T07:33:11Z"},{"alias_kind":"pith_short_16","alias_value":"GI7YNWTIKQBOL3J5","created_at":"2026-07-05T07:33:11Z"},{"alias_kind":"pith_short_8","alias_value":"GI7YNWTI","created_at":"2026-07-05T07:33:11Z"}],"graph_snapshots":[{"event_id":"sha256:1d4a4d5ed0a34763dcd34134b8aa0f69badbf46b8ad62bd7036ecbace19166ef","target":"graph","created_at":"2026-07-05T07:33:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2303.09499/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove effective density of random walks on homogeneous spaces, assuming that the underlying measure is supported on matrices generating a dense subgroup and having algebraic entries. The main novelty is an argument passing from high dimension to effective equidistribution in the setting of random walks on homogeneous spaces, exploiting spectral gap of the associated convolution operator.","authors_text":"Constantin Kogler, Wooyeon Kim","cross_cats":["math.DS","math.GR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-03-16T17:19:42Z","title":"Effective density of non-degenerate random walks on homogeneous spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.09499","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":"sha256:635ab27abd032caae639d90246181fd42b1b660caf20f7efc84e134823afd988","target":"record","created_at":"2026-07-05T07:33:11Z","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":"35635b4d361ca484d02ae127e493348aefbab5788614e7b56ce3ec722ad52e22","cross_cats_sorted":["math.DS","math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-03-16T17:19:42Z","title_canon_sha256":"2c4ac3812cfe8f8a00c3ad590e64dec413b92ee64ac82a777bcccf40c00413e7"},"schema_version":"1.0","source":{"id":"2303.09499","kind":"arxiv","version":3}},"canonical_sha256":"323f86da685402e5ed3d69740d10ff22838e255942d7047eb61e01f099b68e75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"323f86da685402e5ed3d69740d10ff22838e255942d7047eb61e01f099b68e75","first_computed_at":"2026-07-05T07:33:11.366357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:33:11.366357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fy3Pq63U4HIKiXaEuS+bHCxmdX0RNcRabt29JQnaaWQA0RalaV6608+BX+RLZz0i6h7km8LgikjQ/STgMrhBAA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:33:11.366790Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.09499","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:635ab27abd032caae639d90246181fd42b1b660caf20f7efc84e134823afd988","sha256:1d4a4d5ed0a34763dcd34134b8aa0f69badbf46b8ad62bd7036ecbace19166ef"],"state_sha256":"1eb0f90f6ca87ceb7258393d7d50301db041397710ae3c372fd80eac04d0cdf8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7FUJcDuNq6o07NEfk7DrJuTmTWHzyinwyncHbkztdtgB9Q+SQ/GBygufjYhnRUAbCWCknfBABQkzDl5z6cJOAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:35:18.982555Z","bundle_sha256":"34cedbc2caacdcd59f909060c8f18499ca7a19c4d8d17f5625e7d781f9046f39"}}