{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:Q4B4WS2QN33LWO5BTXXU542AVS","short_pith_number":"pith:Q4B4WS2Q","canonical_record":{"source":{"id":"math/0001057","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2000-01-11T03:56:25Z","cross_cats_sorted":[],"title_canon_sha256":"aa3d42b8f72fd435cab343ee12590a3549be4de44cefd94896173b2fc90656df","abstract_canon_sha256":"a4b66953cf05c875bfb894af46dc869e3e9f1f2cb51d877c4b5c650733a40a29"},"schema_version":"1.0"},"canonical_sha256":"8703cb4b506ef6bb3ba19def4ef340ac921faf55328a30b4149ac7d35866dc20","source":{"kind":"arxiv","id":"math/0001057","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0001057","created_at":"2026-07-04T14:34:13Z"},{"alias_kind":"arxiv_version","alias_value":"math/0001057v1","created_at":"2026-07-04T14:34:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0001057","created_at":"2026-07-04T14:34:13Z"},{"alias_kind":"pith_short_12","alias_value":"Q4B4WS2QN33L","created_at":"2026-07-04T14:34:13Z"},{"alias_kind":"pith_short_16","alias_value":"Q4B4WS2QN33LWO5B","created_at":"2026-07-04T14:34:13Z"},{"alias_kind":"pith_short_8","alias_value":"Q4B4WS2Q","created_at":"2026-07-04T14:34:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:Q4B4WS2QN33LWO5BTXXU542AVS","target":"record","payload":{"canonical_record":{"source":{"id":"math/0001057","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2000-01-11T03:56:25Z","cross_cats_sorted":[],"title_canon_sha256":"aa3d42b8f72fd435cab343ee12590a3549be4de44cefd94896173b2fc90656df","abstract_canon_sha256":"a4b66953cf05c875bfb894af46dc869e3e9f1f2cb51d877c4b5c650733a40a29"},"schema_version":"1.0"},"canonical_sha256":"8703cb4b506ef6bb3ba19def4ef340ac921faf55328a30b4149ac7d35866dc20","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:34:13.658506Z","signature_b64":"hRot6WnxA1CTKNKDEviw1lUD01h1ZXa7/lopCn7aLQKz3nmeTZDfcLEVWK5rANBEdQ0xCG6IWRasz0QZH07JDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8703cb4b506ef6bb3ba19def4ef340ac921faf55328a30b4149ac7d35866dc20","last_reissued_at":"2026-07-04T14:34:13.658136Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:34:13.658136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0001057","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":"2026-07-04T14:34:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FlEQLgzh4uxJZMr29jYO/HnmIT20ydBqJWggQGko5p1yWa9wN9oPsO9rsX24EnQrswcKk5YlI1Vk2N/89+jGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:42:48.279258Z"},"content_sha256":"16902f574123275d0460b4d9c3ba4751c91cbbbfcb2616d5dcf7dad6173a2ab5","schema_version":"1.0","event_id":"sha256:16902f574123275d0460b4d9c3ba4751c91cbbbfcb2616d5dcf7dad6173a2ab5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:Q4B4WS2QN33LWO5BTXXU542AVS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random Walks and Electric Networks","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"J. Laurie Snell (Dartmouth), Peter G. Doyle (Dartmouth)","submitted_at":"2000-01-11T03:56:25Z","abstract_excerpt":"A popular account of the connection between random walks and electric networks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0001057","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0001057/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":"2026-07-04T14:34:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yTVyN6z5VmlIVre8WDYGRMNw/eGz0qK9jCghQENOS4rGh/p/YUDfsFWKoc2TbFG0Bnhv4ft+KGGldNl8RHYCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:42:48.279779Z"},"content_sha256":"9d55c5f555c3f7804686efb8132960ae6ceb4f9135994cdde4df6a3d7b961d59","schema_version":"1.0","event_id":"sha256:9d55c5f555c3f7804686efb8132960ae6ceb4f9135994cdde4df6a3d7b961d59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q4B4WS2QN33LWO5BTXXU542AVS/bundle.json","state_url":"https://pith.science/pith/Q4B4WS2QN33LWO5BTXXU542AVS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q4B4WS2QN33LWO5BTXXU542AVS/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":"2026-08-13T00:42:48Z","links":{"resolver":"https://pith.science/pith/Q4B4WS2QN33LWO5BTXXU542AVS","bundle":"https://pith.science/pith/Q4B4WS2QN33LWO5BTXXU542AVS/bundle.json","state":"https://pith.science/pith/Q4B4WS2QN33LWO5BTXXU542AVS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q4B4WS2QN33LWO5BTXXU542AVS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:Q4B4WS2QN33LWO5BTXXU542AVS","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":"a4b66953cf05c875bfb894af46dc869e3e9f1f2cb51d877c4b5c650733a40a29","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2000-01-11T03:56:25Z","title_canon_sha256":"aa3d42b8f72fd435cab343ee12590a3549be4de44cefd94896173b2fc90656df"},"schema_version":"1.0","source":{"id":"math/0001057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0001057","created_at":"2026-07-04T14:34:13Z"},{"alias_kind":"arxiv_version","alias_value":"math/0001057v1","created_at":"2026-07-04T14:34:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0001057","created_at":"2026-07-04T14:34:13Z"},{"alias_kind":"pith_short_12","alias_value":"Q4B4WS2QN33L","created_at":"2026-07-04T14:34:13Z"},{"alias_kind":"pith_short_16","alias_value":"Q4B4WS2QN33LWO5B","created_at":"2026-07-04T14:34:13Z"},{"alias_kind":"pith_short_8","alias_value":"Q4B4WS2Q","created_at":"2026-07-04T14:34:13Z"}],"graph_snapshots":[{"event_id":"sha256:9d55c5f555c3f7804686efb8132960ae6ceb4f9135994cdde4df6a3d7b961d59","target":"graph","created_at":"2026-07-04T14:34:13Z","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/math/0001057/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A popular account of the connection between random walks and electric networks.","authors_text":"J. Laurie Snell (Dartmouth), Peter G. Doyle (Dartmouth)","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2000-01-11T03:56:25Z","title":"Random Walks and Electric Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0001057","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":"sha256:16902f574123275d0460b4d9c3ba4751c91cbbbfcb2616d5dcf7dad6173a2ab5","target":"record","created_at":"2026-07-04T14:34:13Z","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":"a4b66953cf05c875bfb894af46dc869e3e9f1f2cb51d877c4b5c650733a40a29","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2000-01-11T03:56:25Z","title_canon_sha256":"aa3d42b8f72fd435cab343ee12590a3549be4de44cefd94896173b2fc90656df"},"schema_version":"1.0","source":{"id":"math/0001057","kind":"arxiv","version":1}},"canonical_sha256":"8703cb4b506ef6bb3ba19def4ef340ac921faf55328a30b4149ac7d35866dc20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8703cb4b506ef6bb3ba19def4ef340ac921faf55328a30b4149ac7d35866dc20","first_computed_at":"2026-07-04T14:34:13.658136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:34:13.658136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hRot6WnxA1CTKNKDEviw1lUD01h1ZXa7/lopCn7aLQKz3nmeTZDfcLEVWK5rANBEdQ0xCG6IWRasz0QZH07JDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:34:13.658506Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0001057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16902f574123275d0460b4d9c3ba4751c91cbbbfcb2616d5dcf7dad6173a2ab5","sha256:9d55c5f555c3f7804686efb8132960ae6ceb4f9135994cdde4df6a3d7b961d59"],"state_sha256":"865965188364d6222bb9d79313a33259b51d867a665f3640141bf9f531294579"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w5EPJMqehg+pDilQA6zZzqFrcUS5p390N8Qu+dyXBPw8xdsVgFM8wcp43lqFGQKVdWoAObCvcbIxPyEFLBPQDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T00:42:48.285492Z","bundle_sha256":"0afbf2048d861472c06c8c43648560d5000169ee7f204c47e085b0ae2552e21e"}}