{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:UNMERU3TD5O4GV6AFG73SAUMJB","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":"092e3c4f96681a8767c5c92b2646233ca1d853b73877ad393c287a9c1d93521b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-09-21T15:08:22Z","title_canon_sha256":"037139d172221b96d474c61c71b1fff49099f213ca0a498f68293d50ecbf59a5"},"schema_version":"1.0","source":{"id":"0909.3797","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.3797","created_at":"2026-05-18T02:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"0909.3797v2","created_at":"2026-05-18T02:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.3797","created_at":"2026-05-18T02:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"UNMERU3TD5O4","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"UNMERU3TD5O4GV6A","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"UNMERU3T","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:c7790aa7d8354077f699878e7ac8293d69b89a8471fec92ffc552dc1cf6ef84d","target":"graph","created_at":"2026-05-18T02:11:45Z","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 describe some new families of quasimodes for the Laplacian perturbed by the addition of a potential formally described by a Dirac delta function. As an application we find, under some additional hypotheses on the spectrum, subsequences of eigenfunctions of Seba billiards that localise around a pair of unperturbed eigenfunctions.","authors_text":"B. Winn, J. Marklof, J. P. Keating","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-09-21T15:08:22Z","title":"Localised eigenfunctions in Seba billiards"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3797","kind":"arxiv","version":2},"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":"sha256:839e5f1cf6582f83d0a327c075dad2b934c88e58090df90ef232c0febbb6050a","target":"record","created_at":"2026-05-18T02:11:45Z","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":"092e3c4f96681a8767c5c92b2646233ca1d853b73877ad393c287a9c1d93521b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-09-21T15:08:22Z","title_canon_sha256":"037139d172221b96d474c61c71b1fff49099f213ca0a498f68293d50ecbf59a5"},"schema_version":"1.0","source":{"id":"0909.3797","kind":"arxiv","version":2}},"canonical_sha256":"a35848d3731f5dc357c029bfb9028c484d91e0f170a7e5a3c69c0290c24443bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a35848d3731f5dc357c029bfb9028c484d91e0f170a7e5a3c69c0290c24443bc","first_computed_at":"2026-05-18T02:11:45.735052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:11:45.735052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ijsMNcIBuUkj6JHLPVxlRdt8ygxcp8I0xeMJfBWynI1mush3RlD4tYvr0S2jypWTtuNWxUTnUgnqtWEOulhXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:11:45.735751Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.3797","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:839e5f1cf6582f83d0a327c075dad2b934c88e58090df90ef232c0febbb6050a","sha256:c7790aa7d8354077f699878e7ac8293d69b89a8471fec92ffc552dc1cf6ef84d"],"state_sha256":"2e958ac432491069f7d88bc274652b5179729a221410f043f538735c61e1e8c2"}