{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:IUT5TKFPO5N6AT54UZNTZMJZOZ","short_pith_number":"pith:IUT5TKFP","schema_version":"1.0","canonical_sha256":"4527d9a8af775be04fbca65b3cb139767a023b6fb71a3518e8c2b740040d6780","source":{"kind":"arxiv","id":"0909.1518","version":2},"attestation_state":"computed","paper":{"title":"Resistance boundaries of infinite networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.PR"],"primary_cat":"math.FA","authors_text":"Erin P. J. Pearse, Palle E. T. Jorgensen","submitted_at":"2009-09-08T17:03:09Z","abstract_excerpt":"A resistance network is a connected graph $(G,c)$. The conductance function $c_{xy}$ weights the edges, which are then interpreted as conductors of possibly varying strengths. The Dirichlet energy form $\\mathcal E$ produces a Hilbert space structure ${\\mathcal H}_{\\mathcal E}$ on the space of functions of finite energy.\n  The relationship between the natural Dirichlet form $\\mathcal E$ and the discrete Laplace operator $\\Delta$ on a finite network is given by $\\mathcal E(u,v) = \\la u, \\Lap v\\ra_2$, where the latter is the usual $\\ell^2$ inner product. We describe a reproducing kernel $\\{v_x\\}$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0909.1518","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-09-08T17:03:09Z","cross_cats_sorted":["math.MG","math.PR"],"title_canon_sha256":"56e9eb26f25de7aff8cf25c15d0f030bf8cb986578d2bf053cf96f9818ae8c80","abstract_canon_sha256":"47e7e71035c1ad93b0483d47b2da8099ea501201633cebf0daf9f039b4a5533b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:26.544005Z","signature_b64":"LoPoIKTegliYUZ75SX/4OBRUjEoAv9TCRiF5kKOTHVzrxi1bLD9f4HWeGj1qKw4buCaM7pGKdxd634LOAUhxCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4527d9a8af775be04fbca65b3cb139767a023b6fb71a3518e8c2b740040d6780","last_reissued_at":"2026-05-18T04:30:26.543553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:26.543553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resistance boundaries of infinite networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.PR"],"primary_cat":"math.FA","authors_text":"Erin P. J. Pearse, Palle E. T. Jorgensen","submitted_at":"2009-09-08T17:03:09Z","abstract_excerpt":"A resistance network is a connected graph $(G,c)$. The conductance function $c_{xy}$ weights the edges, which are then interpreted as conductors of possibly varying strengths. The Dirichlet energy form $\\mathcal E$ produces a Hilbert space structure ${\\mathcal H}_{\\mathcal E}$ on the space of functions of finite energy.\n  The relationship between the natural Dirichlet form $\\mathcal E$ and the discrete Laplace operator $\\Delta$ on a finite network is given by $\\mathcal E(u,v) = \\la u, \\Lap v\\ra_2$, where the latter is the usual $\\ell^2$ inner product. We describe a reproducing kernel $\\{v_x\\}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1518","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0909.1518","created_at":"2026-05-18T04:30:26.543625+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.1518v2","created_at":"2026-05-18T04:30:26.543625+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1518","created_at":"2026-05-18T04:30:26.543625+00:00"},{"alias_kind":"pith_short_12","alias_value":"IUT5TKFPO5N6","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"IUT5TKFPO5N6AT54","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"IUT5TKFP","created_at":"2026-05-18T12:26:00.592388+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IUT5TKFPO5N6AT54UZNTZMJZOZ","json":"https://pith.science/pith/IUT5TKFPO5N6AT54UZNTZMJZOZ.json","graph_json":"https://pith.science/api/pith-number/IUT5TKFPO5N6AT54UZNTZMJZOZ/graph.json","events_json":"https://pith.science/api/pith-number/IUT5TKFPO5N6AT54UZNTZMJZOZ/events.json","paper":"https://pith.science/paper/IUT5TKFP"},"agent_actions":{"view_html":"https://pith.science/pith/IUT5TKFPO5N6AT54UZNTZMJZOZ","download_json":"https://pith.science/pith/IUT5TKFPO5N6AT54UZNTZMJZOZ.json","view_paper":"https://pith.science/paper/IUT5TKFP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.1518&json=true","fetch_graph":"https://pith.science/api/pith-number/IUT5TKFPO5N6AT54UZNTZMJZOZ/graph.json","fetch_events":"https://pith.science/api/pith-number/IUT5TKFPO5N6AT54UZNTZMJZOZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IUT5TKFPO5N6AT54UZNTZMJZOZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IUT5TKFPO5N6AT54UZNTZMJZOZ/action/storage_attestation","attest_author":"https://pith.science/pith/IUT5TKFPO5N6AT54UZNTZMJZOZ/action/author_attestation","sign_citation":"https://pith.science/pith/IUT5TKFPO5N6AT54UZNTZMJZOZ/action/citation_signature","submit_replication":"https://pith.science/pith/IUT5TKFPO5N6AT54UZNTZMJZOZ/action/replication_record"}},"created_at":"2026-05-18T04:30:26.543625+00:00","updated_at":"2026-05-18T04:30:26.543625+00:00"}