{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FI7IMNW3YRVFC6YQ47XCECKCZD","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":"8fb6f26c8aaac52e427f0cf66f91037118fcdae47941236ab11e9dcd6af64c06","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-12-20T11:02:26Z","title_canon_sha256":"a193168f5264befd3911da65dd9c48a60c48d3f6e450fe5862aae4f2b186e950"},"schema_version":"1.0","source":{"id":"1712.07414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.07414","created_at":"2026-05-18T00:27:34Z"},{"alias_kind":"arxiv_version","alias_value":"1712.07414v1","created_at":"2026-05-18T00:27:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.07414","created_at":"2026-05-18T00:27:34Z"},{"alias_kind":"pith_short_12","alias_value":"FI7IMNW3YRVF","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FI7IMNW3YRVFC6YQ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FI7IMNW3","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:861b1586c6fd038539f7af56c26a8cbb65633eb859e6780d8fde252185bd4e61","target":"graph","created_at":"2026-05-18T00:27:34Z","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 introduce a notion of nodal domains for positivity preserving forms. This notion generalizes the classical ones for Laplacians on domains and on graphs. We prove the Courant nodal domain theorem in this generalized setting using purely analytical methods.","authors_text":"Matthias Keller, Michael Schwarz","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-12-20T11:02:26Z","title":"Courant's Nodal Domain Theorem for Positivity Preserving Forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07414","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":"sha256:434a7234ecea7dc38ac7ab19b8811f2a7c9f9ac01075a4945c478e2cba6ee793","target":"record","created_at":"2026-05-18T00:27:34Z","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":"8fb6f26c8aaac52e427f0cf66f91037118fcdae47941236ab11e9dcd6af64c06","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-12-20T11:02:26Z","title_canon_sha256":"a193168f5264befd3911da65dd9c48a60c48d3f6e450fe5862aae4f2b186e950"},"schema_version":"1.0","source":{"id":"1712.07414","kind":"arxiv","version":1}},"canonical_sha256":"2a3e8636dbc46a517b10e7ee220942c8e40f6ee25d6b4c0b8d95c70544d8ecbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a3e8636dbc46a517b10e7ee220942c8e40f6ee25d6b4c0b8d95c70544d8ecbb","first_computed_at":"2026-05-18T00:27:34.538985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:34.538985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yv69WYF0q5/V8PEqDGJlRAf1Zsdn6zGt+l3zmuyJ8BS8bnBueHr4jR6+YAa8Z5FtRIozdVln3XCmo1J0QkIfCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:34.539660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.07414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:434a7234ecea7dc38ac7ab19b8811f2a7c9f9ac01075a4945c478e2cba6ee793","sha256:861b1586c6fd038539f7af56c26a8cbb65633eb859e6780d8fde252185bd4e61"],"state_sha256":"15e6f3b601587bdc076a329366b9bfc538c5fc412d7a41c79a437aca443f0b40"}