{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:I3ANSXU3I33MC4PEJJATL74SWL","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":"b545eec041578a22a55274d6295503f2d24432b3d7d406d94d7f2318eed8fe54","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-23T14:56:56Z","title_canon_sha256":"b4118c92ae9c8b506e5a49750e85d0208a0de95328971116b3841eb9c64fa9d6"},"schema_version":"1.0","source":{"id":"1106.4746","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4746","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4746v1","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4746","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"pith_short_12","alias_value":"I3ANSXU3I33M","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"I3ANSXU3I33MC4PE","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"I3ANSXU3","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:dd7bbe51ffc6eb87d7a261a2e0c0cbe48cbd267e0aecd2e1ae22faf2b99224a8","target":"graph","created_at":"2026-05-18T03:06:43Z","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 formulate a systematic elegant perturbative scheme for determining the eigenvalues of the Helmholtz equation (\\bigtriangledown^{2} + k^{2}){\\psi} = 0 in two dimensions when the normal derivative of {\\psi} vanishes on an irregular closed curve. Unique feature of this method, unlike other perturbation schemes, is that it does not require a separate formalism to treat degeneracies. Degenerate states are handled equally elegantly as the non-degenerate ones. A real parameter, extracted from the parameters defining the irregular boundary, serves as a perturbation parameter in this scheme as oppos","authors_text":"S. Chakraborty, S. Panda, S.P. Khastgir","cross_cats":["hep-th","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-23T14:56:56Z","title":"Eigenvalue Problem in Two Dimensions for an Irregular Boundary II: Neumann Condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4746","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":"sha256:2d65e8886fc06f1701f0c45f73829dc7cbd1f0e524108a59a0616104079f9136","target":"record","created_at":"2026-05-18T03:06:43Z","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":"b545eec041578a22a55274d6295503f2d24432b3d7d406d94d7f2318eed8fe54","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-23T14:56:56Z","title_canon_sha256":"b4118c92ae9c8b506e5a49750e85d0208a0de95328971116b3841eb9c64fa9d6"},"schema_version":"1.0","source":{"id":"1106.4746","kind":"arxiv","version":1}},"canonical_sha256":"46c0d95e9b46f6c171e44a4135ff92b2dfe953dcc5fc0b7facbc1eb9437d98df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46c0d95e9b46f6c171e44a4135ff92b2dfe953dcc5fc0b7facbc1eb9437d98df","first_computed_at":"2026-05-18T03:06:43.149775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:43.149775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RcLohXof5PYe79wYRhZZDYecvUCYdvmuT5w4/7yJV0g6+eyR+qmiplEnp8eTQJQnJsms4iEhbFDwiVfT94H3Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:43.150188Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.4746","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d65e8886fc06f1701f0c45f73829dc7cbd1f0e524108a59a0616104079f9136","sha256:dd7bbe51ffc6eb87d7a261a2e0c0cbe48cbd267e0aecd2e1ae22faf2b99224a8"],"state_sha256":"70e60a32d1eab57db5b2608395c48a40fe2b5216dff6a27153e285fee58bd4c8"}