{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:HHVK6CEVFA7ZEZW3QI2D7BEBTV","short_pith_number":"pith:HHVK6CEV","canonical_record":{"source":{"id":"1010.5366","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-10-26T11:46:09Z","cross_cats_sorted":[],"title_canon_sha256":"c3835b8c7869d5712c47a9b1f515e652b74e8e1e7204728054d25a71675ed58c","abstract_canon_sha256":"1b959a1b18fe275bb29d47f3dca6cc59374ed64702357fd858b354b83a621283"},"schema_version":"1.0"},"canonical_sha256":"39eaaf0895283f9266db82343f84819d5f5f78613233f4a2d342820ef6c47bed","source":{"kind":"arxiv","id":"1010.5366","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5366","created_at":"2026-05-18T04:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5366v1","created_at":"2026-05-18T04:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5366","created_at":"2026-05-18T04:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"HHVK6CEVFA7Z","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HHVK6CEVFA7ZEZW3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HHVK6CEV","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:HHVK6CEVFA7ZEZW3QI2D7BEBTV","target":"record","payload":{"canonical_record":{"source":{"id":"1010.5366","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-10-26T11:46:09Z","cross_cats_sorted":[],"title_canon_sha256":"c3835b8c7869d5712c47a9b1f515e652b74e8e1e7204728054d25a71675ed58c","abstract_canon_sha256":"1b959a1b18fe275bb29d47f3dca6cc59374ed64702357fd858b354b83a621283"},"schema_version":"1.0"},"canonical_sha256":"39eaaf0895283f9266db82343f84819d5f5f78613233f4a2d342820ef6c47bed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:38.947474Z","signature_b64":"G50c0VVJpO6g7Oo0OE8iykqgjvhGBlCGBohBOLEI/AqzhFi7/rqH44SIFeLt2YHaSxhKnB93EfuoElgfMEHBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39eaaf0895283f9266db82343f84819d5f5f78613233f4a2d342820ef6c47bed","last_reissued_at":"2026-05-18T04:38:38.946700Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:38.946700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.5366","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":"2026-05-18T04:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wndF8s9mwjm14wV/sTpYDvkHzO6MfbHlRSQY0OiT6nVDZKDN5eHJr4WkYYefer98Q8qaQiueg5g7oSwQfVXwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:54:24.019777Z"},"content_sha256":"861aef82a6e0c8889641f2ca3f602cefe37c16df8866de8b57182bae986981d7","schema_version":"1.0","event_id":"sha256:861aef82a6e0c8889641f2ca3f602cefe37c16df8866de8b57182bae986981d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:HHVK6CEVFA7ZEZW3QI2D7BEBTV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some sufficient conditions for infinite collisions of simple random walks on a wedge comb","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dayue Chen, Xinxing Chen","submitted_at":"2010-10-26T11:46:09Z","abstract_excerpt":"In this paper, we give some sufficient conditions for the infinite collisions of independent simple random walks on a wedge comb with profile $\\{f(n), n\\in \\ZZ\\}$. One interesting result is that if $f(n)$ has a growth order as $n\\log n$, then two independent simple random walks on the wedge comb will collide infinitely many times. Another is that if $\\{f(n); n\\in \\ZZ\\}$ are given by i.i.d. non-negative random variables with finite mean, then for almost all wedge comb with such profile, three independent simple random walks on it will collide infinitely many times."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5366","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":"2026-05-18T04:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gs3Z7cEETyfgiLSUIAVJDBTaramu5UdeMwAIsgFbD/krvOdnEYha9i1GOpESpHIF3xsyR1ehFBDUIonwm46oAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:54:24.020484Z"},"content_sha256":"54d8cbf394b58c76cdc77cd39d3cf8a811fa7575e4ece69544c69badf46a8f5b","schema_version":"1.0","event_id":"sha256:54d8cbf394b58c76cdc77cd39d3cf8a811fa7575e4ece69544c69badf46a8f5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HHVK6CEVFA7ZEZW3QI2D7BEBTV/bundle.json","state_url":"https://pith.science/pith/HHVK6CEVFA7ZEZW3QI2D7BEBTV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HHVK6CEVFA7ZEZW3QI2D7BEBTV/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":"2026-06-07T18:54:24Z","links":{"resolver":"https://pith.science/pith/HHVK6CEVFA7ZEZW3QI2D7BEBTV","bundle":"https://pith.science/pith/HHVK6CEVFA7ZEZW3QI2D7BEBTV/bundle.json","state":"https://pith.science/pith/HHVK6CEVFA7ZEZW3QI2D7BEBTV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HHVK6CEVFA7ZEZW3QI2D7BEBTV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HHVK6CEVFA7ZEZW3QI2D7BEBTV","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":"1b959a1b18fe275bb29d47f3dca6cc59374ed64702357fd858b354b83a621283","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-10-26T11:46:09Z","title_canon_sha256":"c3835b8c7869d5712c47a9b1f515e652b74e8e1e7204728054d25a71675ed58c"},"schema_version":"1.0","source":{"id":"1010.5366","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5366","created_at":"2026-05-18T04:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5366v1","created_at":"2026-05-18T04:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5366","created_at":"2026-05-18T04:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"HHVK6CEVFA7Z","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HHVK6CEVFA7ZEZW3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HHVK6CEV","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:54d8cbf394b58c76cdc77cd39d3cf8a811fa7575e4ece69544c69badf46a8f5b","target":"graph","created_at":"2026-05-18T04:38:38Z","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":"In this paper, we give some sufficient conditions for the infinite collisions of independent simple random walks on a wedge comb with profile $\\{f(n), n\\in \\ZZ\\}$. One interesting result is that if $f(n)$ has a growth order as $n\\log n$, then two independent simple random walks on the wedge comb will collide infinitely many times. Another is that if $\\{f(n); n\\in \\ZZ\\}$ are given by i.i.d. non-negative random variables with finite mean, then for almost all wedge comb with such profile, three independent simple random walks on it will collide infinitely many times.","authors_text":"Dayue Chen, Xinxing Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-10-26T11:46:09Z","title":"Some sufficient conditions for infinite collisions of simple random walks on a wedge comb"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5366","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":"sha256:861aef82a6e0c8889641f2ca3f602cefe37c16df8866de8b57182bae986981d7","target":"record","created_at":"2026-05-18T04:38:38Z","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":"1b959a1b18fe275bb29d47f3dca6cc59374ed64702357fd858b354b83a621283","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-10-26T11:46:09Z","title_canon_sha256":"c3835b8c7869d5712c47a9b1f515e652b74e8e1e7204728054d25a71675ed58c"},"schema_version":"1.0","source":{"id":"1010.5366","kind":"arxiv","version":1}},"canonical_sha256":"39eaaf0895283f9266db82343f84819d5f5f78613233f4a2d342820ef6c47bed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39eaaf0895283f9266db82343f84819d5f5f78613233f4a2d342820ef6c47bed","first_computed_at":"2026-05-18T04:38:38.946700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:38.946700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G50c0VVJpO6g7Oo0OE8iykqgjvhGBlCGBohBOLEI/AqzhFi7/rqH44SIFeLt2YHaSxhKnB93EfuoElgfMEHBBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:38.947474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:861aef82a6e0c8889641f2ca3f602cefe37c16df8866de8b57182bae986981d7","sha256:54d8cbf394b58c76cdc77cd39d3cf8a811fa7575e4ece69544c69badf46a8f5b"],"state_sha256":"f4939c8ea656d258b9b5e9ab9ae309b577c44356052de2d38ef4ea0c985e5f25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZQmARDDS8aJVSjZIbzq3mBcAQX2kaOmCbBOLo07FO+dldHWU32lGgWCkx7s1Ac/k0WBvm35oe05fl8aiDjkpBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:54:24.024096Z","bundle_sha256":"b2a83ea9c293ba9a3a31029972561dfd61ef208a29f3dd28497a5cc4a86f8ad6"}}