{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:LG7XUWY3NSUBLTI2P4GZ642DH5","short_pith_number":"pith:LG7XUWY3","schema_version":"1.0","canonical_sha256":"59bf7a5b1b6ca815cd1a7f0d9f73433f5cfc37703121da73c3f10f7f257ebb43","source":{"kind":"arxiv","id":"1103.5792","version":3},"attestation_state":"computed","paper":{"title":"Self-adjoint extensions of network Laplacians and applications to resistance metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Erin P. J. Pearse, Palle E. T. Jorgensen","submitted_at":"2011-03-29T23:17:48Z","abstract_excerpt":"Let $(G,c)$ be an infinite network, and let $\\mathcal{E}$ be the canonical energy form. Let $\\Delta_2$ be the Laplace operator with dense domain in $\\ell^2(G)$ and let $\\Delta_{\\mathcal{E}}$ be the Laplace operator with dense domain in the Hilbert space $\\mathcal{H}_\\mathcal{E}$ of finite energy functions on $G$. It is known that $\\Delta_2$ is essentially self-adjoint, but that $\\Delta_{\\mathcal{E}}$ is \\emph{not}. In this paper, we characterize the Friedrichs extension of $\\Delta_{\\mathcal{E}}$ in terms of $\\Delta_2$ and show that the spectral measures of the two operators are mutually absolu"},"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":"1103.5792","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-03-29T23:17:48Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"21a3e5d247993d87f1cbcda6c3cea82c8a2d55caadd6a136816eabd976969e85","abstract_canon_sha256":"2870679ceedd5c0b45ccfecd2f6ce015db67d391da6687f652ba36a8d9243168"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:49.491427Z","signature_b64":"GMpEDEJhX4OXaAgwg6GTQXTg0Dh1e8/sPxd07vfhZgUdvjHgQm/AVuJfqpmgMB1pgb6yO0D/zaBIaE8OYuR6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59bf7a5b1b6ca815cd1a7f0d9f73433f5cfc37703121da73c3f10f7f257ebb43","last_reissued_at":"2026-05-18T04:00:49.490781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:49.490781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-adjoint extensions of network Laplacians and applications to resistance metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Erin P. J. Pearse, Palle E. T. Jorgensen","submitted_at":"2011-03-29T23:17:48Z","abstract_excerpt":"Let $(G,c)$ be an infinite network, and let $\\mathcal{E}$ be the canonical energy form. Let $\\Delta_2$ be the Laplace operator with dense domain in $\\ell^2(G)$ and let $\\Delta_{\\mathcal{E}}$ be the Laplace operator with dense domain in the Hilbert space $\\mathcal{H}_\\mathcal{E}$ of finite energy functions on $G$. It is known that $\\Delta_2$ is essentially self-adjoint, but that $\\Delta_{\\mathcal{E}}$ is \\emph{not}. In this paper, we characterize the Friedrichs extension of $\\Delta_{\\mathcal{E}}$ in terms of $\\Delta_2$ and show that the spectral measures of the two operators are mutually absolu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5792","kind":"arxiv","version":3},"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":"1103.5792","created_at":"2026-05-18T04:00:49.490878+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.5792v3","created_at":"2026-05-18T04:00:49.490878+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5792","created_at":"2026-05-18T04:00:49.490878+00:00"},{"alias_kind":"pith_short_12","alias_value":"LG7XUWY3NSUB","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"LG7XUWY3NSUBLTI2","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"LG7XUWY3","created_at":"2026-05-18T12:26:34.985390+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/LG7XUWY3NSUBLTI2P4GZ642DH5","json":"https://pith.science/pith/LG7XUWY3NSUBLTI2P4GZ642DH5.json","graph_json":"https://pith.science/api/pith-number/LG7XUWY3NSUBLTI2P4GZ642DH5/graph.json","events_json":"https://pith.science/api/pith-number/LG7XUWY3NSUBLTI2P4GZ642DH5/events.json","paper":"https://pith.science/paper/LG7XUWY3"},"agent_actions":{"view_html":"https://pith.science/pith/LG7XUWY3NSUBLTI2P4GZ642DH5","download_json":"https://pith.science/pith/LG7XUWY3NSUBLTI2P4GZ642DH5.json","view_paper":"https://pith.science/paper/LG7XUWY3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.5792&json=true","fetch_graph":"https://pith.science/api/pith-number/LG7XUWY3NSUBLTI2P4GZ642DH5/graph.json","fetch_events":"https://pith.science/api/pith-number/LG7XUWY3NSUBLTI2P4GZ642DH5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LG7XUWY3NSUBLTI2P4GZ642DH5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LG7XUWY3NSUBLTI2P4GZ642DH5/action/storage_attestation","attest_author":"https://pith.science/pith/LG7XUWY3NSUBLTI2P4GZ642DH5/action/author_attestation","sign_citation":"https://pith.science/pith/LG7XUWY3NSUBLTI2P4GZ642DH5/action/citation_signature","submit_replication":"https://pith.science/pith/LG7XUWY3NSUBLTI2P4GZ642DH5/action/replication_record"}},"created_at":"2026-05-18T04:00:49.490878+00:00","updated_at":"2026-05-18T04:00:49.490878+00:00"}