{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IPI6RGAK6M3YC6XOAKDICU2R6B","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":"867c384daddf0911917476975184173515495cb6fc16f213bb9f3cdccc0ed09f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-26T20:29:28Z","title_canon_sha256":"2d2e6eca1bdf929dd08975299fe8f9754f1b67c4ec4191c844d2088caec5a76e"},"schema_version":"1.0","source":{"id":"1007.4565","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4565","created_at":"2026-07-04T17:32:16Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4565v1","created_at":"2026-07-04T17:32:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4565","created_at":"2026-07-04T17:32:16Z"},{"alias_kind":"pith_short_12","alias_value":"IPI6RGAK6M3Y","created_at":"2026-07-04T17:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"IPI6RGAK6M3YC6XO","created_at":"2026-07-04T17:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"IPI6RGAK","created_at":"2026-07-04T17:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:141a2f483564d7a4ccf514956f42b4ec940f2290e64a1e688d2e4590520864f1","target":"graph","created_at":"2026-07-04T17:32:16Z","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/1007.4565/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let T be an infinite homogenous tree of homogeneity $q+1$. Attaching to each edge the conductance $1$, the tree will became an electric network. The reversible Markov chain associated to this network is the simple random walk on the homogenous tree. Using results regarding the equivalence between a reversible Markov chain and an electric network, we will express voltages, currents, the Green fuction hitting times, transitions number, probabilities of reaching a set before another, as functions of the distance on the homogenous tree. This connection enables us to give simpler proofs for the pro","authors_text":"Alice Vatamanelu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-26T20:29:28Z","title":"The homogenous tree as an electric network"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4565","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":"sha256:1b1b052b986f44dafe7a46b04e64df7126ed60a6cf2552352e3e0d061940c431","target":"record","created_at":"2026-07-04T17:32:16Z","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":"867c384daddf0911917476975184173515495cb6fc16f213bb9f3cdccc0ed09f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-26T20:29:28Z","title_canon_sha256":"2d2e6eca1bdf929dd08975299fe8f9754f1b67c4ec4191c844d2088caec5a76e"},"schema_version":"1.0","source":{"id":"1007.4565","kind":"arxiv","version":1}},"canonical_sha256":"43d1e8980af337817aee0286815351f05139a79cb70eb410ece884192d6854e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43d1e8980af337817aee0286815351f05139a79cb70eb410ece884192d6854e6","first_computed_at":"2026-07-04T17:32:16.956755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:32:16.956755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YVt0WQ3AT7ynIc/JgEct+HpQauSJre8jlcWyDJbw6jQqtUe4vE1nB5PAkFqy+OKTQnUHf9t8WPZXZFW2tRJKBw==","signature_status":"signed_v1","signed_at":"2026-07-04T17:32:16.957117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.4565","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b1b052b986f44dafe7a46b04e64df7126ed60a6cf2552352e3e0d061940c431","sha256:141a2f483564d7a4ccf514956f42b4ec940f2290e64a1e688d2e4590520864f1"],"state_sha256":"853582e0e88f92c2ea4da0e94f328a9bd27947ad3f7ddc320dda27aea5d00078"}