{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7S3P776FOATAI46P2PH7MAT3EE","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":"e098f973479373ea1362bd7e162281b20a91058ca6681ac6e11832738c488727","cross_cats_sorted":["math.GT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-03-05T09:27:56Z","title_canon_sha256":"1dec9ea069a79ad5807dc9d409b595e3c457532bf6e60e0af9b2d2fa86e75a01"},"schema_version":"1.0","source":{"id":"1503.01582","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01582","created_at":"2026-05-18T01:16:51Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01582v1","created_at":"2026-05-18T01:16:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01582","created_at":"2026-05-18T01:16:51Z"},{"alias_kind":"pith_short_12","alias_value":"7S3P776FOATA","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7S3P776FOATAI46P","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7S3P776F","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:2ed26f850d4512550512f5397daf629afaa7c79f788b4f71b6e35527566cb80e","target":"graph","created_at":"2026-05-18T01:16:51Z","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 give, as $L$ grows to infinity, an explicit lower bound of order $L^{n/m}$ for the expected Betti numbers of the vanishing locus of a random linear combination of eigenvectors of $P$ with eigenvalues below $L$. Here, $P$ denotes an elliptic self-adjoint pseudo-differential operator of order $m\\textgreater{}0$, bounded from below and acting on the sections of a Riemannian line bundle over a smooth closed $n$-dimensional manifold  $M$ equipped with some Lebesgue measure. In fact, for every closed hypersurface $\\Sigma$ of $\\mathbb R^n$, we prove that there exists a positive constant $p\\_\\Sigma","authors_text":"Damien Gayet (IF), Jean-Yves Welschinger (ICJ)","cross_cats":["math.GT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-03-05T09:27:56Z","title":"Universal components of random nodal sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01582","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":"sha256:036017947b31f031f1504a7d4e397094e563a4c05014b4fb330226d8a247ff85","target":"record","created_at":"2026-05-18T01:16:51Z","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":"e098f973479373ea1362bd7e162281b20a91058ca6681ac6e11832738c488727","cross_cats_sorted":["math.GT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-03-05T09:27:56Z","title_canon_sha256":"1dec9ea069a79ad5807dc9d409b595e3c457532bf6e60e0af9b2d2fa86e75a01"},"schema_version":"1.0","source":{"id":"1503.01582","kind":"arxiv","version":1}},"canonical_sha256":"fcb6ffffc570260473cfd3cff6027b21028262d84ddd71480e95d2c44ec0a216","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcb6ffffc570260473cfd3cff6027b21028262d84ddd71480e95d2c44ec0a216","first_computed_at":"2026-05-18T01:16:51.134429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:51.134429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"325c8ewb2vEUi4SMcZLEBtc0J6OPEEQ0vyb332Mddfo7gOTHPxIbFwxpf3ICXfTR4i7qyUxglIARF64LqZ0SCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:51.135128Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01582","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:036017947b31f031f1504a7d4e397094e563a4c05014b4fb330226d8a247ff85","sha256:2ed26f850d4512550512f5397daf629afaa7c79f788b4f71b6e35527566cb80e"],"state_sha256":"f985fc94e4c999f84132650522cfff0d196a6e49c74c6d8a9d18ecda90d8e1f1"}