{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TUPSVNFAQRISJA7FNJXETGCZ6L","short_pith_number":"pith:TUPSVNFA","canonical_record":{"source":{"id":"1412.5406","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T14:25:37Z","cross_cats_sorted":["math.CO","math.SP"],"title_canon_sha256":"b383909bde9f5b319fdc684fa8430f412808c0ca885a54f504ca2690e71bc264","abstract_canon_sha256":"4281e7fa0a1c32e7855606e5215c8e6a2d1b6daffaf8dd7256a6d829c34248d2"},"schema_version":"1.0"},"canonical_sha256":"9d1f2ab4a084512483e56a6e499859f2e8df4b70c929299a023431ab687afafa","source":{"kind":"arxiv","id":"1412.5406","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5406","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5406v1","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5406","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"TUPSVNFAQRIS","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TUPSVNFAQRISJA7F","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TUPSVNFA","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TUPSVNFAQRISJA7FNJXETGCZ6L","target":"record","payload":{"canonical_record":{"source":{"id":"1412.5406","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T14:25:37Z","cross_cats_sorted":["math.CO","math.SP"],"title_canon_sha256":"b383909bde9f5b319fdc684fa8430f412808c0ca885a54f504ca2690e71bc264","abstract_canon_sha256":"4281e7fa0a1c32e7855606e5215c8e6a2d1b6daffaf8dd7256a6d829c34248d2"},"schema_version":"1.0"},"canonical_sha256":"9d1f2ab4a084512483e56a6e499859f2e8df4b70c929299a023431ab687afafa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:03.058557Z","signature_b64":"MAPiQ6/wdwRW+wFQkiK9cGQSRbmsx5dhwd673BO26v2OTjFE0zb+zZOmQoHv7dgNqHeNMJTXkG856yMVarFVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d1f2ab4a084512483e56a6e499859f2e8df4b70c929299a023431ab687afafa","last_reissued_at":"2026-05-18T02:31:03.058158Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:03.058158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.5406","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":"2026-05-18T02:31:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DSMpPhFsnbM/skSHwc7VuFc0R6KklIfXfzNYCN86Z2NbEYSjpNx3iH+MXdEz9l8xWxj+0KQJNBDBMr/ahGHwBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T21:52:45.876300Z"},"content_sha256":"2f1ca93d5a1d0b121366eddbe7322c2ee0c4b0ba3e75f9655ee59c25de513721","schema_version":"1.0","event_id":"sha256:2f1ca93d5a1d0b121366eddbe7322c2ee0c4b0ba3e75f9655ee59c25de513721"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TUPSVNFAQRISJA7FNJXETGCZ6L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simplicial branching random walks and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.SP"],"primary_cat":"math.PR","authors_text":"Ron Rosenthal","submitted_at":"2014-12-17T14:25:37Z","abstract_excerpt":"We define a new stochastic process on general simplicial complexes which allows to study their spectral and homological properties. Some results for random walks on graphs are shown to hold in this general setting. As an application, the process is used to calculate the spectral measure of high-dimensional analogues of regular trees and to construct solutions to the high-dimensional Dirichlet problem for forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5406","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":"2026-05-18T02:31:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3He7xj1++WVr94jABESO1lOp2OT3MxAUer3sO3+2xMrnXLxw7sgSwho4iel5iRUGpNT3ZFdiNB+y2qKiAOkVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T21:52:45.876875Z"},"content_sha256":"c7480418fa8df9c825eab120f6bb27368486c2eb55bfaea8e9279209b1cc94a5","schema_version":"1.0","event_id":"sha256:c7480418fa8df9c825eab120f6bb27368486c2eb55bfaea8e9279209b1cc94a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TUPSVNFAQRISJA7FNJXETGCZ6L/bundle.json","state_url":"https://pith.science/pith/TUPSVNFAQRISJA7FNJXETGCZ6L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TUPSVNFAQRISJA7FNJXETGCZ6L/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":"2026-05-18T21:52:45Z","links":{"resolver":"https://pith.science/pith/TUPSVNFAQRISJA7FNJXETGCZ6L","bundle":"https://pith.science/pith/TUPSVNFAQRISJA7FNJXETGCZ6L/bundle.json","state":"https://pith.science/pith/TUPSVNFAQRISJA7FNJXETGCZ6L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TUPSVNFAQRISJA7FNJXETGCZ6L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TUPSVNFAQRISJA7FNJXETGCZ6L","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":"4281e7fa0a1c32e7855606e5215c8e6a2d1b6daffaf8dd7256a6d829c34248d2","cross_cats_sorted":["math.CO","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T14:25:37Z","title_canon_sha256":"b383909bde9f5b319fdc684fa8430f412808c0ca885a54f504ca2690e71bc264"},"schema_version":"1.0","source":{"id":"1412.5406","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5406","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5406v1","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5406","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"TUPSVNFAQRIS","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TUPSVNFAQRISJA7F","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TUPSVNFA","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:c7480418fa8df9c825eab120f6bb27368486c2eb55bfaea8e9279209b1cc94a5","target":"graph","created_at":"2026-05-18T02:31:03Z","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 a new stochastic process on general simplicial complexes which allows to study their spectral and homological properties. Some results for random walks on graphs are shown to hold in this general setting. As an application, the process is used to calculate the spectral measure of high-dimensional analogues of regular trees and to construct solutions to the high-dimensional Dirichlet problem for forms.","authors_text":"Ron Rosenthal","cross_cats":["math.CO","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T14:25:37Z","title":"Simplicial branching random walks and their applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5406","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":"sha256:2f1ca93d5a1d0b121366eddbe7322c2ee0c4b0ba3e75f9655ee59c25de513721","target":"record","created_at":"2026-05-18T02:31:03Z","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":"4281e7fa0a1c32e7855606e5215c8e6a2d1b6daffaf8dd7256a6d829c34248d2","cross_cats_sorted":["math.CO","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T14:25:37Z","title_canon_sha256":"b383909bde9f5b319fdc684fa8430f412808c0ca885a54f504ca2690e71bc264"},"schema_version":"1.0","source":{"id":"1412.5406","kind":"arxiv","version":1}},"canonical_sha256":"9d1f2ab4a084512483e56a6e499859f2e8df4b70c929299a023431ab687afafa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d1f2ab4a084512483e56a6e499859f2e8df4b70c929299a023431ab687afafa","first_computed_at":"2026-05-18T02:31:03.058158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:03.058158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MAPiQ6/wdwRW+wFQkiK9cGQSRbmsx5dhwd673BO26v2OTjFE0zb+zZOmQoHv7dgNqHeNMJTXkG856yMVarFVCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:03.058557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5406","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f1ca93d5a1d0b121366eddbe7322c2ee0c4b0ba3e75f9655ee59c25de513721","sha256:c7480418fa8df9c825eab120f6bb27368486c2eb55bfaea8e9279209b1cc94a5"],"state_sha256":"a5c5abfd12c905cd42f432321df6ffc9176aca14ae15c2a328ac9c19eefde5df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kc+CDDCM6oENsPbtt2VaQDUVuTij7mvQHr28H457lKbk0v7/e+Rr4F9phsuDAlxuVfWi7vae3L3r1FAGapZFDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T21:52:45.878643Z","bundle_sha256":"58edba5f3a544f279da49e06743cf865769875c36d261c4b5727670aeeb620e2"}}