{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:E5TQH2J2O6SHU5NAV2X75HCDO7","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":"d77737f3a0296f2accb4e7dc42199d92f204260a21cb1ef0cd13e52611459e96","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-12-19T08:30:10Z","title_canon_sha256":"acf43220f50890720f5c4b0a7e09a57b77e09b6fe8678d599df3c01e3cc16b41"},"schema_version":"1.0","source":{"id":"1112.4263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4263","created_at":"2026-06-03T23:07:06Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4263v2","created_at":"2026-06-03T23:07:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4263","created_at":"2026-06-03T23:07:06Z"},{"alias_kind":"pith_short_12","alias_value":"E5TQH2J2O6SH","created_at":"2026-06-03T23:07:06Z"},{"alias_kind":"pith_short_16","alias_value":"E5TQH2J2O6SHU5NA","created_at":"2026-06-03T23:07:06Z"},{"alias_kind":"pith_short_8","alias_value":"E5TQH2J2","created_at":"2026-06-03T23:07:06Z"}],"graph_snapshots":[{"event_id":"sha256:989c347ef9a71eadeedad93f811c55debb9536589d24e7b2c49ac620a2b2b77a","target":"graph","created_at":"2026-06-03T23:07:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1112.4263/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The simplest modeling of planar quantum waveguides is the Dirichlet eigenproblem for the Laplace operator in unbounded open sets which are uniformly thin in one direction. Here we consider V-shaped guides. Their spectral properties depend essentially on a sole parameter, the opening of the V. The free energy band is a semi-infinite interval bounded from below. As soon as the V is not flat, there are bound states below the free energy band. There are a finite number of them, depending on the opening. This number tends to infinity as the opening tends to 0 (sharply bent V). In this situation, th","authors_text":"Monique Dauge (IRMAR), Nicolas Raymond (IRMAR), Yvon Lafranche (IRMAR)","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-12-19T08:30:10Z","title":"Quantum waveguides with corners"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4263","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":"sha256:1beec4c9e606f8d717fd23459f60ec1e5b56a7db7439d13388b9634c6acda641","target":"record","created_at":"2026-06-03T23:07:06Z","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":"d77737f3a0296f2accb4e7dc42199d92f204260a21cb1ef0cd13e52611459e96","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-12-19T08:30:10Z","title_canon_sha256":"acf43220f50890720f5c4b0a7e09a57b77e09b6fe8678d599df3c01e3cc16b41"},"schema_version":"1.0","source":{"id":"1112.4263","kind":"arxiv","version":2}},"canonical_sha256":"276703e93a77a47a75a0aeaffe9c4377c55ebc5a025374ee815a45f1a6914d9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"276703e93a77a47a75a0aeaffe9c4377c55ebc5a025374ee815a45f1a6914d9e","first_computed_at":"2026-06-03T23:07:06.411033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:07:06.411033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"53EwHC9RjKVEJUYCKq4knitAi1c7/Q1Ia7r4IuswZWmPfKs3Bm2V8e1WvIfQh3DClY4jOlgPI155urwgcFBpBg==","signature_status":"signed_v1","signed_at":"2026-06-03T23:07:06.411607Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1beec4c9e606f8d717fd23459f60ec1e5b56a7db7439d13388b9634c6acda641","sha256:989c347ef9a71eadeedad93f811c55debb9536589d24e7b2c49ac620a2b2b77a"],"state_sha256":"5ee559176448feadeaf1c26e9074b1499c7b2f66ba7965b7b43802c8e0f732be"}