{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:52T4JVSIVWSIY2HYDPJE3N6OWY","short_pith_number":"pith:52T4JVSI","canonical_record":{"source":{"id":"1902.09078","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-25T03:47:49Z","cross_cats_sorted":[],"title_canon_sha256":"3f2fe1c33abe3db0146b00710cc020e173b96306abcb9d2651c9d274e90f7f49","abstract_canon_sha256":"9f8dc07640d93cba6ff894934b46d7c3575db1c070a242e8fb6901869817ad04"},"schema_version":"1.0"},"canonical_sha256":"eea7c4d648ada48c68f81bd24db7ceb61aa7629835419b72fe6446c626256277","source":{"kind":"arxiv","id":"1902.09078","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09078","created_at":"2026-05-17T23:52:14Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09078v1","created_at":"2026-05-17T23:52:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09078","created_at":"2026-05-17T23:52:14Z"},{"alias_kind":"pith_short_12","alias_value":"52T4JVSIVWSI","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"52T4JVSIVWSIY2HY","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"52T4JVSI","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:52T4JVSIVWSIY2HYDPJE3N6OWY","target":"record","payload":{"canonical_record":{"source":{"id":"1902.09078","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-25T03:47:49Z","cross_cats_sorted":[],"title_canon_sha256":"3f2fe1c33abe3db0146b00710cc020e173b96306abcb9d2651c9d274e90f7f49","abstract_canon_sha256":"9f8dc07640d93cba6ff894934b46d7c3575db1c070a242e8fb6901869817ad04"},"schema_version":"1.0"},"canonical_sha256":"eea7c4d648ada48c68f81bd24db7ceb61aa7629835419b72fe6446c626256277","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:14.574225Z","signature_b64":"6PklQEUGOMUrQmupqI1Xvk4SD/TCBPTXqMrHvo06H6QUZtKZYeOrRtwQCQ3S1MHtWsGkZR0tbEVXIE0vHl+EBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eea7c4d648ada48c68f81bd24db7ceb61aa7629835419b72fe6446c626256277","last_reissued_at":"2026-05-17T23:52:14.573616Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:14.573616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.09078","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":"2026-05-17T23:52:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPMVW1Hdq+Xw+gkXpeYD+21e8ufXi4PtnFH63sxckwMmLkrEBN4eaAiNDD/KTMSDL0Ne+6111H8xDnEEavqeAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:57:08.944587Z"},"content_sha256":"c6288cf526636e1fa566b8bb1e248e7a83b4439f2bdf8c5e8915916b0696234e","schema_version":"1.0","event_id":"sha256:c6288cf526636e1fa566b8bb1e248e7a83b4439f2bdf8c5e8915916b0696234e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:52T4JVSIVWSIY2HYDPJE3N6OWY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On resistance distance of Markov chain and its sum rules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michael C.H. Choi","submitted_at":"2019-02-25T03:47:49Z","abstract_excerpt":"Motivated by the notion of resistance distance on graph, we define a new resistance distance between two states on a given finite ergodic Markov chain based on its fundamental matrix. We prove a few equivalent formulations and discuss its relation with other parameters of the Markov chain such as its group inverse, stationary distribution, eigenvalues or hitting time. In addition, building upon existing sum rules for the hitting time of Markov chain, we give sum rules of this new resistance distance of Markov chains that resembles the sum rules of the resistance distance on graph. This yields "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09078","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":"2026-05-17T23:52:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NGEIQWLb272T3O3X/thdcWW9zLwIJa22TjG6CEpbAqFonN/JEYyzCPoE+1VrklZl+09Lp6JsInxwPk438U0KBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:57:08.944934Z"},"content_sha256":"09d9d1fb46d0fc6658b373b5dd5443a32ebf29bc533b7ab86a0c96d201862505","schema_version":"1.0","event_id":"sha256:09d9d1fb46d0fc6658b373b5dd5443a32ebf29bc533b7ab86a0c96d201862505"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/52T4JVSIVWSIY2HYDPJE3N6OWY/bundle.json","state_url":"https://pith.science/pith/52T4JVSIVWSIY2HYDPJE3N6OWY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/52T4JVSIVWSIY2HYDPJE3N6OWY/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":"2026-06-01T05:57:08Z","links":{"resolver":"https://pith.science/pith/52T4JVSIVWSIY2HYDPJE3N6OWY","bundle":"https://pith.science/pith/52T4JVSIVWSIY2HYDPJE3N6OWY/bundle.json","state":"https://pith.science/pith/52T4JVSIVWSIY2HYDPJE3N6OWY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/52T4JVSIVWSIY2HYDPJE3N6OWY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:52T4JVSIVWSIY2HYDPJE3N6OWY","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":"9f8dc07640d93cba6ff894934b46d7c3575db1c070a242e8fb6901869817ad04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-25T03:47:49Z","title_canon_sha256":"3f2fe1c33abe3db0146b00710cc020e173b96306abcb9d2651c9d274e90f7f49"},"schema_version":"1.0","source":{"id":"1902.09078","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09078","created_at":"2026-05-17T23:52:14Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09078v1","created_at":"2026-05-17T23:52:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09078","created_at":"2026-05-17T23:52:14Z"},{"alias_kind":"pith_short_12","alias_value":"52T4JVSIVWSI","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"52T4JVSIVWSIY2HY","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"52T4JVSI","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:09d9d1fb46d0fc6658b373b5dd5443a32ebf29bc533b7ab86a0c96d201862505","target":"graph","created_at":"2026-05-17T23:52:14Z","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":"Motivated by the notion of resistance distance on graph, we define a new resistance distance between two states on a given finite ergodic Markov chain based on its fundamental matrix. We prove a few equivalent formulations and discuss its relation with other parameters of the Markov chain such as its group inverse, stationary distribution, eigenvalues or hitting time. In addition, building upon existing sum rules for the hitting time of Markov chain, we give sum rules of this new resistance distance of Markov chains that resembles the sum rules of the resistance distance on graph. This yields ","authors_text":"Michael C.H. Choi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-25T03:47:49Z","title":"On resistance distance of Markov chain and its sum rules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09078","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:c6288cf526636e1fa566b8bb1e248e7a83b4439f2bdf8c5e8915916b0696234e","target":"record","created_at":"2026-05-17T23:52:14Z","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":"9f8dc07640d93cba6ff894934b46d7c3575db1c070a242e8fb6901869817ad04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-25T03:47:49Z","title_canon_sha256":"3f2fe1c33abe3db0146b00710cc020e173b96306abcb9d2651c9d274e90f7f49"},"schema_version":"1.0","source":{"id":"1902.09078","kind":"arxiv","version":1}},"canonical_sha256":"eea7c4d648ada48c68f81bd24db7ceb61aa7629835419b72fe6446c626256277","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eea7c4d648ada48c68f81bd24db7ceb61aa7629835419b72fe6446c626256277","first_computed_at":"2026-05-17T23:52:14.573616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:14.573616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6PklQEUGOMUrQmupqI1Xvk4SD/TCBPTXqMrHvo06H6QUZtKZYeOrRtwQCQ3S1MHtWsGkZR0tbEVXIE0vHl+EBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:14.574225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.09078","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6288cf526636e1fa566b8bb1e248e7a83b4439f2bdf8c5e8915916b0696234e","sha256:09d9d1fb46d0fc6658b373b5dd5443a32ebf29bc533b7ab86a0c96d201862505"],"state_sha256":"caf90c15c6ed834c87f2fad6c1432fe979703973066f1eb93a5ee305876cd6b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MKz7OVcrP0otfP87wY+8K/y5oIECyd24ubVB/Vz1kaM3cm/Uh4/zQFdeEjK3ZGnLTEaVQgTpVvPEzVCHtgCTCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:57:08.946894Z","bundle_sha256":"77a80fbc937788e82146c14f75fadc6e8418db28f002888b283c3c5005f7f881"}}