{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SCW5XTFFZT7YRJOEUOSAMS3TBJ","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":"653590437c060528c2a61775a9b52f8d04e64514584d152f30410da23df25d20","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-01-15T12:29:09Z","title_canon_sha256":"225a897778ddaf2f97981e2b5263e52b56c87da14359e8588b6846039aff2a7d"},"schema_version":"1.0","source":{"id":"1101.2979","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2979","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2979v1","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2979","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"SCW5XTFFZT7Y","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SCW5XTFFZT7YRJOE","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SCW5XTFF","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:cd87b80c730a4d0f53e2ba1e32e85d9c9c787f3391d9e68c14c01cc18af6c601","target":"graph","created_at":"2026-05-18T04:31:30Z","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":"We discuss Laplacians on graphs in a framework of regular Dirichlet forms. We focus on phenomena related to unboundedness of the Laplacians. This includes (failure of) essential selfadjointness, absence of essential spectrum and stochastic incompleteness.","authors_text":"Daniel Lenz, Matthias Keller","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-01-15T12:29:09Z","title":"Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2979","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":"sha256:2ae6651c8934558c82a35fbadf56fb19823e4eaac527453a89039ce593009020","target":"record","created_at":"2026-05-18T04:31:30Z","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":"653590437c060528c2a61775a9b52f8d04e64514584d152f30410da23df25d20","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-01-15T12:29:09Z","title_canon_sha256":"225a897778ddaf2f97981e2b5263e52b56c87da14359e8588b6846039aff2a7d"},"schema_version":"1.0","source":{"id":"1101.2979","kind":"arxiv","version":1}},"canonical_sha256":"90addbcca5ccff88a5c4a3a4064b730a4fb2f1442f301cb632e3bc13f3485355","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90addbcca5ccff88a5c4a3a4064b730a4fb2f1442f301cb632e3bc13f3485355","first_computed_at":"2026-05-18T04:31:30.639451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:30.639451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2QLTrjhQtimBKPrjrPUsQJYnQ9337BtHJkbYJ+DPNtL9co7aLb7hyri68hsYASQRFdsHoZDjshgXHaMHJFDiAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:30.640084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2979","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ae6651c8934558c82a35fbadf56fb19823e4eaac527453a89039ce593009020","sha256:cd87b80c730a4d0f53e2ba1e32e85d9c9c787f3391d9e68c14c01cc18af6c601"],"state_sha256":"79e932ea7673f980677dea41518dea51eecf0db1ea550fec238c2a87781ab84b"}