{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:S25VYWABGQ5PJXM5LQDPXKMAW6","short_pith_number":"pith:S25VYWAB","canonical_record":{"source":{"id":"1308.5120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-23T13:06:38Z","cross_cats_sorted":[],"title_canon_sha256":"9c2e3deb7e03a3b9259a8d8f892f8f3a90ca18b3331571e0f55ed77140acc41b","abstract_canon_sha256":"dc0bed104c4890eb878718f1218dbba1fdc090cb652ff355c9d6e65342b22889"},"schema_version":"1.0"},"canonical_sha256":"96bb5c5801343af4dd9d5c06fba980b793ebff9747f132e6e95a573377765324","source":{"kind":"arxiv","id":"1308.5120","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5120","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5120v2","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5120","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"pith_short_12","alias_value":"S25VYWABGQ5P","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S25VYWABGQ5PJXM5","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S25VYWAB","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:S25VYWABGQ5PJXM5LQDPXKMAW6","target":"record","payload":{"canonical_record":{"source":{"id":"1308.5120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-23T13:06:38Z","cross_cats_sorted":[],"title_canon_sha256":"9c2e3deb7e03a3b9259a8d8f892f8f3a90ca18b3331571e0f55ed77140acc41b","abstract_canon_sha256":"dc0bed104c4890eb878718f1218dbba1fdc090cb652ff355c9d6e65342b22889"},"schema_version":"1.0"},"canonical_sha256":"96bb5c5801343af4dd9d5c06fba980b793ebff9747f132e6e95a573377765324","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:26.308705Z","signature_b64":"mn33vACpporvpe++E9o3q82ALrFfztE6DeF7vn9lzNznqM0c07/iyw+FZhNrIW/c5tS3/rAJboZ1w4gZu9C/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96bb5c5801343af4dd9d5c06fba980b793ebff9747f132e6e95a573377765324","last_reissued_at":"2026-05-18T02:43:26.307990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:26.307990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.5120","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6m6gtwgCh+cseoX/2hMZ4zwp1rCG/JJyRP9hQRzb8PBxfv0v691VB8KqMJ41DrLmqFcVQzUXHGRy0QjAPIAjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:23:05.918546Z"},"content_sha256":"1758c76d4312effd0beee64c8b2ce5e473dfa96caa5d94d03c8ee479c7108713","schema_version":"1.0","event_id":"sha256:1758c76d4312effd0beee64c8b2ce5e473dfa96caa5d94d03c8ee479c7108713"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:S25VYWABGQ5PJXM5LQDPXKMAW6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regular sequences and random walks in affine buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"James Parkinson, Wolfgang Woess","submitted_at":"2013-08-23T13:06:38Z","abstract_excerpt":"We define and characterise regular sequences in affine buildings, thereby giving the \"$p$-adic analogue\" of the fundamental work of Kaimanovich. As applications we prove limit theorems for random walks on affine buildings and their automorphism groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5120","kind":"arxiv","version":2},"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":"2026-05-18T02:43:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tLiftMsNG0oT/M9xfZdqtIG+kaoGE0PmdjYXluxR+LeL7sz+iYQnaQh1m3hdvBTW04cRBb8sgYtY/S7DEQhDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:23:05.919237Z"},"content_sha256":"b8d9004c6b41da56f7455635c4b23872ead30d2f2603adb7be015184b918671a","schema_version":"1.0","event_id":"sha256:b8d9004c6b41da56f7455635c4b23872ead30d2f2603adb7be015184b918671a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S25VYWABGQ5PJXM5LQDPXKMAW6/bundle.json","state_url":"https://pith.science/pith/S25VYWABGQ5PJXM5LQDPXKMAW6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S25VYWABGQ5PJXM5LQDPXKMAW6/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":"2026-05-27T12:23:05Z","links":{"resolver":"https://pith.science/pith/S25VYWABGQ5PJXM5LQDPXKMAW6","bundle":"https://pith.science/pith/S25VYWABGQ5PJXM5LQDPXKMAW6/bundle.json","state":"https://pith.science/pith/S25VYWABGQ5PJXM5LQDPXKMAW6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S25VYWABGQ5PJXM5LQDPXKMAW6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:S25VYWABGQ5PJXM5LQDPXKMAW6","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":"dc0bed104c4890eb878718f1218dbba1fdc090cb652ff355c9d6e65342b22889","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-23T13:06:38Z","title_canon_sha256":"9c2e3deb7e03a3b9259a8d8f892f8f3a90ca18b3331571e0f55ed77140acc41b"},"schema_version":"1.0","source":{"id":"1308.5120","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5120","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5120v2","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5120","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"pith_short_12","alias_value":"S25VYWABGQ5P","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S25VYWABGQ5PJXM5","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S25VYWAB","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:b8d9004c6b41da56f7455635c4b23872ead30d2f2603adb7be015184b918671a","target":"graph","created_at":"2026-05-18T02:43:26Z","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 define and characterise regular sequences in affine buildings, thereby giving the \"$p$-adic analogue\" of the fundamental work of Kaimanovich. As applications we prove limit theorems for random walks on affine buildings and their automorphism groups.","authors_text":"James Parkinson, Wolfgang Woess","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-23T13:06:38Z","title":"Regular sequences and random walks in affine buildings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5120","kind":"arxiv","version":2},"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":"sha256:1758c76d4312effd0beee64c8b2ce5e473dfa96caa5d94d03c8ee479c7108713","target":"record","created_at":"2026-05-18T02:43:26Z","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":"dc0bed104c4890eb878718f1218dbba1fdc090cb652ff355c9d6e65342b22889","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-23T13:06:38Z","title_canon_sha256":"9c2e3deb7e03a3b9259a8d8f892f8f3a90ca18b3331571e0f55ed77140acc41b"},"schema_version":"1.0","source":{"id":"1308.5120","kind":"arxiv","version":2}},"canonical_sha256":"96bb5c5801343af4dd9d5c06fba980b793ebff9747f132e6e95a573377765324","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96bb5c5801343af4dd9d5c06fba980b793ebff9747f132e6e95a573377765324","first_computed_at":"2026-05-18T02:43:26.307990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:26.307990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mn33vACpporvpe++E9o3q82ALrFfztE6DeF7vn9lzNznqM0c07/iyw+FZhNrIW/c5tS3/rAJboZ1w4gZu9C/Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:26.308705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5120","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1758c76d4312effd0beee64c8b2ce5e473dfa96caa5d94d03c8ee479c7108713","sha256:b8d9004c6b41da56f7455635c4b23872ead30d2f2603adb7be015184b918671a"],"state_sha256":"7a21392a1b6186f3028b08187261dc7db1cfa71816d0d3e4edf9755553dbe11a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/54wGMt7EDE/+fdhmWec30zs4uCw5njTETJlFjElWDsNwZ5sFZythY4OKLVc1/ZuLgNmP744443JHhnKVJGvAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:23:05.922814Z","bundle_sha256":"d36a4b7251e17149a3befd2046e56f3ec25c2bd24f7b8ba00faa886f15070a24"}}