{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:GXKC7HU6IGHMXOUAITEPYNLDVQ","short_pith_number":"pith:GXKC7HU6","canonical_record":{"source":{"id":"math/0510371","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.SP","submitted_at":"2005-10-18T09:18:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"37b8ac6cd454cb4078eb04d015145746dff59ce04e96d130e06ca1ccd741def9","abstract_canon_sha256":"10225286b876361f986da423c76c3b9d305e78115807a6c7e31962b42fabe74a"},"schema_version":"1.0"},"canonical_sha256":"35d42f9e9e418ecbba8044c8fc3563ac08d10393364b0b8ccff59b965a4de946","source":{"kind":"arxiv","id":"math/0510371","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0510371","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0510371v1","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510371","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"GXKC7HU6IGHM","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"GXKC7HU6IGHMXOUA","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"GXKC7HU6","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:GXKC7HU6IGHMXOUAITEPYNLDVQ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0510371","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.SP","submitted_at":"2005-10-18T09:18:15Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"37b8ac6cd454cb4078eb04d015145746dff59ce04e96d130e06ca1ccd741def9","abstract_canon_sha256":"10225286b876361f986da423c76c3b9d305e78115807a6c7e31962b42fabe74a"},"schema_version":"1.0"},"canonical_sha256":"35d42f9e9e418ecbba8044c8fc3563ac08d10393364b0b8ccff59b965a4de946","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:22.959147Z","signature_b64":"4sSepLb7hrBcVNps9CIcF6IQ0RFq3FI3vHRkxk/6TuwuFiud8lThXnOuqUhHPWZjvAAQazYiB9iGHnNkEBBzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35d42f9e9e418ecbba8044c8fc3563ac08d10393364b0b8ccff59b965a4de946","last_reissued_at":"2026-05-18T01:05:22.958524Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:22.958524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0510371","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"60LmZHL32CVR49F3ghYwk0PKEavHp+57Lz+ijCi9zmu79khDh/jU03L6HstcWQnmg+ILFcy25JOXFR58/1koDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:08:52.297177Z"},"content_sha256":"411db48ee44bc0b78291b2e8a550ac65c644843aec7c9f9ebc21badac037bd7e","schema_version":"1.0","event_id":"sha256:411db48ee44bc0b78291b2e8a550ac65c644843aec7c9f9ebc21badac037bd7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:GXKC7HU6IGHMXOUAITEPYNLDVQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a family of differential operators with the coupling parameter in the boundary condition","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"G. Rozenblum, M. Solomyak","submitted_at":"2005-10-18T09:18:15Z","abstract_excerpt":"We study a family of differential operators $L_\\alpha$ in two variables, depending on the coupling parameter $\\alpha\\ge0$ that appears only in the boundary conditions. Our main concern is the spectral properties of $L_\\alpha$, which turn out to be quite different for $\\alpha\\le 1$ and for $\\alpha>1$. In particular,\n $L_\\alpha$ has a unique self-adjoint realization for $\\alpha\\le 1$ and many such realizations for $\\alpha>1$. In the more difficult case $\\alpha>1$ an analysis of non-elliptic pseudodifferential operators in dimension one is involved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510371","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QIyBoFu40mA9aAGE8+nHpkJpf4Cy2FsUEYMnRxXl3L2qwMUPKjwQoIB7aYPMPi4jocfZdtHwdlmxcYfKNY7ECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T10:08:52.297540Z"},"content_sha256":"d02de3383a1933c6df3291a07cad07b35d7d8fd2acba1dc0d860a33934b1a979","schema_version":"1.0","event_id":"sha256:d02de3383a1933c6df3291a07cad07b35d7d8fd2acba1dc0d860a33934b1a979"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GXKC7HU6IGHMXOUAITEPYNLDVQ/bundle.json","state_url":"https://pith.science/pith/GXKC7HU6IGHMXOUAITEPYNLDVQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GXKC7HU6IGHMXOUAITEPYNLDVQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T10:08:52Z","links":{"resolver":"https://pith.science/pith/GXKC7HU6IGHMXOUAITEPYNLDVQ","bundle":"https://pith.science/pith/GXKC7HU6IGHMXOUAITEPYNLDVQ/bundle.json","state":"https://pith.science/pith/GXKC7HU6IGHMXOUAITEPYNLDVQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GXKC7HU6IGHMXOUAITEPYNLDVQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:GXKC7HU6IGHMXOUAITEPYNLDVQ","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":"10225286b876361f986da423c76c3b9d305e78115807a6c7e31962b42fabe74a","cross_cats_sorted":["math.AP"],"license":"","primary_cat":"math.SP","submitted_at":"2005-10-18T09:18:15Z","title_canon_sha256":"37b8ac6cd454cb4078eb04d015145746dff59ce04e96d130e06ca1ccd741def9"},"schema_version":"1.0","source":{"id":"math/0510371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0510371","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0510371v1","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510371","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"GXKC7HU6IGHM","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"GXKC7HU6IGHMXOUA","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"GXKC7HU6","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:d02de3383a1933c6df3291a07cad07b35d7d8fd2acba1dc0d860a33934b1a979","target":"graph","created_at":"2026-05-18T01:05:22Z","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 study a family of differential operators $L_\\alpha$ in two variables, depending on the coupling parameter $\\alpha\\ge0$ that appears only in the boundary conditions. Our main concern is the spectral properties of $L_\\alpha$, which turn out to be quite different for $\\alpha\\le 1$ and for $\\alpha>1$. In particular,\n $L_\\alpha$ has a unique self-adjoint realization for $\\alpha\\le 1$ and many such realizations for $\\alpha>1$. In the more difficult case $\\alpha>1$ an analysis of non-elliptic pseudodifferential operators in dimension one is involved.","authors_text":"G. Rozenblum, M. Solomyak","cross_cats":["math.AP"],"headline":"","license":"","primary_cat":"math.SP","submitted_at":"2005-10-18T09:18:15Z","title":"On a family of differential operators with the coupling parameter in the boundary condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510371","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":"sha256:411db48ee44bc0b78291b2e8a550ac65c644843aec7c9f9ebc21badac037bd7e","target":"record","created_at":"2026-05-18T01:05:22Z","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":"10225286b876361f986da423c76c3b9d305e78115807a6c7e31962b42fabe74a","cross_cats_sorted":["math.AP"],"license":"","primary_cat":"math.SP","submitted_at":"2005-10-18T09:18:15Z","title_canon_sha256":"37b8ac6cd454cb4078eb04d015145746dff59ce04e96d130e06ca1ccd741def9"},"schema_version":"1.0","source":{"id":"math/0510371","kind":"arxiv","version":1}},"canonical_sha256":"35d42f9e9e418ecbba8044c8fc3563ac08d10393364b0b8ccff59b965a4de946","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35d42f9e9e418ecbba8044c8fc3563ac08d10393364b0b8ccff59b965a4de946","first_computed_at":"2026-05-18T01:05:22.958524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:22.958524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4sSepLb7hrBcVNps9CIcF6IQ0RFq3FI3vHRkxk/6TuwuFiud8lThXnOuqUhHPWZjvAAQazYiB9iGHnNkEBBzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:22.959147Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0510371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:411db48ee44bc0b78291b2e8a550ac65c644843aec7c9f9ebc21badac037bd7e","sha256:d02de3383a1933c6df3291a07cad07b35d7d8fd2acba1dc0d860a33934b1a979"],"state_sha256":"cf9b0ba98cb88b07ae1f876f959bc196c8149aa983e5d5f71baaa4bd234974c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O03FI0CzhnOBrxHw3CRWxHX1e7X9WTAceNxzufAJTQIIg5pQyGQgUCFiSHwXsjHudVR4wpBohj3Ac7IEqBTeCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T10:08:52.299530Z","bundle_sha256":"4c0e0110fc62f90a173d0ff989738fe8a442e2c3d2e23fff5378ec6f2e165b5d"}}