{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:T4MELKBGAVIIW5XDKMSYBP2JSY","short_pith_number":"pith:T4MELKBG","schema_version":"1.0","canonical_sha256":"9f1845a82605508b76e3532580bf499617964807b5dbea0fc3f051f8782a7aec","source":{"kind":"arxiv","id":"0906.2745","version":4},"attestation_state":"computed","paper":{"title":"Gel'fand triples and boundaries of infinite networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MG","math.PR"],"primary_cat":"math.FA","authors_text":"Erin P. J. Pearse, Palle E. T. Jorgensen","submitted_at":"2009-06-15T17:18:53Z","abstract_excerpt":"We study the boundary theory of a connected weighted graph $G$ from the viewpoint of stochastic integration. For the Hilbert space \\HE of Dirichlet-finite functions on $G$, we construct a Gel'fand triple $S \\ci {\\mathcal H}_{\\mathcal E} \\ci S'$. This yields a probability measure $\\mathbb{P}$ on $S'$ and an isometric embedding of ${\\mathcal H}_{\\mathcal E}$ into $L^2(S',\\mathbb{P})$, and hence gives a concrete representation of the boundary as a certain class of \"distributions\" in $S'$. In a previous paper, we proved a discrete Gauss-Green identity for infinite networks which produces a boundar"},"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":"0906.2745","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-06-15T17:18:53Z","cross_cats_sorted":["math.DS","math.MG","math.PR"],"title_canon_sha256":"62d7e1ed604096db642fb4e072b52c626694d6d7c212f00871aca0631f70575d","abstract_canon_sha256":"e36efc0c650fe2b5392d7a8ed6328ba32225f47a707bcade5ce6a558993a8d22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:35.751646Z","signature_b64":"cUM9VAXNzhSxtBrQci0+WohPQUC0xWAd7QkSMA69y/gQdbD6Tek5xL1Nrn4yy7rsYRyitjt+I0jW9iXjuJSsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f1845a82605508b76e3532580bf499617964807b5dbea0fc3f051f8782a7aec","last_reissued_at":"2026-05-18T03:48:35.751223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:35.751223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gel'fand triples and boundaries of infinite networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MG","math.PR"],"primary_cat":"math.FA","authors_text":"Erin P. J. Pearse, Palle E. T. Jorgensen","submitted_at":"2009-06-15T17:18:53Z","abstract_excerpt":"We study the boundary theory of a connected weighted graph $G$ from the viewpoint of stochastic integration. For the Hilbert space \\HE of Dirichlet-finite functions on $G$, we construct a Gel'fand triple $S \\ci {\\mathcal H}_{\\mathcal E} \\ci S'$. This yields a probability measure $\\mathbb{P}$ on $S'$ and an isometric embedding of ${\\mathcal H}_{\\mathcal E}$ into $L^2(S',\\mathbb{P})$, and hence gives a concrete representation of the boundary as a certain class of \"distributions\" in $S'$. In a previous paper, we proved a discrete Gauss-Green identity for infinite networks which produces a boundar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2745","kind":"arxiv","version":4},"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":"0906.2745","created_at":"2026-05-18T03:48:35.751286+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.2745v4","created_at":"2026-05-18T03:48:35.751286+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2745","created_at":"2026-05-18T03:48:35.751286+00:00"},{"alias_kind":"pith_short_12","alias_value":"T4MELKBGAVII","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"T4MELKBGAVIIW5XD","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"T4MELKBG","created_at":"2026-05-18T12:26:01.383474+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/T4MELKBGAVIIW5XDKMSYBP2JSY","json":"https://pith.science/pith/T4MELKBGAVIIW5XDKMSYBP2JSY.json","graph_json":"https://pith.science/api/pith-number/T4MELKBGAVIIW5XDKMSYBP2JSY/graph.json","events_json":"https://pith.science/api/pith-number/T4MELKBGAVIIW5XDKMSYBP2JSY/events.json","paper":"https://pith.science/paper/T4MELKBG"},"agent_actions":{"view_html":"https://pith.science/pith/T4MELKBGAVIIW5XDKMSYBP2JSY","download_json":"https://pith.science/pith/T4MELKBGAVIIW5XDKMSYBP2JSY.json","view_paper":"https://pith.science/paper/T4MELKBG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.2745&json=true","fetch_graph":"https://pith.science/api/pith-number/T4MELKBGAVIIW5XDKMSYBP2JSY/graph.json","fetch_events":"https://pith.science/api/pith-number/T4MELKBGAVIIW5XDKMSYBP2JSY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T4MELKBGAVIIW5XDKMSYBP2JSY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T4MELKBGAVIIW5XDKMSYBP2JSY/action/storage_attestation","attest_author":"https://pith.science/pith/T4MELKBGAVIIW5XDKMSYBP2JSY/action/author_attestation","sign_citation":"https://pith.science/pith/T4MELKBGAVIIW5XDKMSYBP2JSY/action/citation_signature","submit_replication":"https://pith.science/pith/T4MELKBGAVIIW5XDKMSYBP2JSY/action/replication_record"}},"created_at":"2026-05-18T03:48:35.751286+00:00","updated_at":"2026-05-18T03:48:35.751286+00:00"}