{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:NAGLSHNBH6S5CBTME37Q3TJVX5","short_pith_number":"pith:NAGLSHNB","canonical_record":{"source":{"id":"0808.1528","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2008-08-11T15:26:24Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0fc37dc0d98756628083e14d053e7af66774a9e71fa884ceb1e9d76179d49287","abstract_canon_sha256":"1ada9639f1db18dbd2a1fa333267decf0de18c862607610a56c2fb2860fee99d"},"schema_version":"1.0"},"canonical_sha256":"680cb91da13fa5d1066c26ff0dcd35bf779bdda3e754ef175ae7038d23c26008","source":{"kind":"arxiv","id":"0808.1528","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.1528","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"0808.1528v3","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.1528","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"NAGLSHNBH6S5","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"NAGLSHNBH6S5CBTM","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"NAGLSHNB","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:NAGLSHNBH6S5CBTME37Q3TJVX5","target":"record","payload":{"canonical_record":{"source":{"id":"0808.1528","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2008-08-11T15:26:24Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0fc37dc0d98756628083e14d053e7af66774a9e71fa884ceb1e9d76179d49287","abstract_canon_sha256":"1ada9639f1db18dbd2a1fa333267decf0de18c862607610a56c2fb2860fee99d"},"schema_version":"1.0"},"canonical_sha256":"680cb91da13fa5d1066c26ff0dcd35bf779bdda3e754ef175ae7038d23c26008","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:02.553895Z","signature_b64":"LeEemYDvbYLTPm5K73CJ12klS+ufN0FQDA6w/KHEFZcBAd3sDfXhHTD1JtI2ry22KSfBi3VC+CkFlvYZV9aoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"680cb91da13fa5d1066c26ff0dcd35bf779bdda3e754ef175ae7038d23c26008","last_reissued_at":"2026-05-18T00:02:02.553264Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:02.553264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0808.1528","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nHzAbX5b9qw3+et9RF9y2uFBClsAcJB1ac7iXIuwlV5wWwtrd3r0/9C+An0UBkfgt3C/2EeHiO0B4zRkgNPCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:59:53.539916Z"},"content_sha256":"5907b1784b30daff8fd0cd756bf51615171350ce14053cd883d131072416a959","schema_version":"1.0","event_id":"sha256:5907b1784b30daff8fd0cd756bf51615171350ce14053cd883d131072416a959"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:NAGLSHNBH6S5CBTME37Q3TJVX5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalue Asymptotics in a Twisted Waveguide","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Eric Soccorsi, Georgi Raikov, Hynek Kovarik, Philippe Briet","submitted_at":"2008-08-11T15:26:24Z","abstract_excerpt":"We consider a twisted quantum wave guide, and are interested in the spectral analysis of the associated Dirichlet Laplacian H. We show that if the derivative of rotation angle decays slowly enough at infinity, then there is an infinite sequence of discrete eigenvalues lying below the infimum of the essential spectrum of H, and obtain the main asymptotic term of this sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1528","kind":"arxiv","version":3},"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":"2026-05-18T00:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xtVayc1LniPJyH1qB4nM3CYaiNaBf+t7OPxwdAk74GtFh1bkov6JSnet82vaGaq7LwGMeqwllz9xBIjzyxpQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:59:53.540257Z"},"content_sha256":"dbccedcbec10793e800cf0fc30499a6330a6ef904bd88a18be544416300befcb","schema_version":"1.0","event_id":"sha256:dbccedcbec10793e800cf0fc30499a6330a6ef904bd88a18be544416300befcb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NAGLSHNBH6S5CBTME37Q3TJVX5/bundle.json","state_url":"https://pith.science/pith/NAGLSHNBH6S5CBTME37Q3TJVX5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NAGLSHNBH6S5CBTME37Q3TJVX5/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":"2026-06-03T00:59:53Z","links":{"resolver":"https://pith.science/pith/NAGLSHNBH6S5CBTME37Q3TJVX5","bundle":"https://pith.science/pith/NAGLSHNBH6S5CBTME37Q3TJVX5/bundle.json","state":"https://pith.science/pith/NAGLSHNBH6S5CBTME37Q3TJVX5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NAGLSHNBH6S5CBTME37Q3TJVX5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:NAGLSHNBH6S5CBTME37Q3TJVX5","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":"1ada9639f1db18dbd2a1fa333267decf0de18c862607610a56c2fb2860fee99d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2008-08-11T15:26:24Z","title_canon_sha256":"0fc37dc0d98756628083e14d053e7af66774a9e71fa884ceb1e9d76179d49287"},"schema_version":"1.0","source":{"id":"0808.1528","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.1528","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"0808.1528v3","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.1528","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"NAGLSHNBH6S5","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"NAGLSHNBH6S5CBTM","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"NAGLSHNB","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:dbccedcbec10793e800cf0fc30499a6330a6ef904bd88a18be544416300befcb","target":"graph","created_at":"2026-05-18T00:02:02Z","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 consider a twisted quantum wave guide, and are interested in the spectral analysis of the associated Dirichlet Laplacian H. We show that if the derivative of rotation angle decays slowly enough at infinity, then there is an infinite sequence of discrete eigenvalues lying below the infimum of the essential spectrum of H, and obtain the main asymptotic term of this sequence.","authors_text":"Eric Soccorsi, Georgi Raikov, Hynek Kovarik, Philippe Briet","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2008-08-11T15:26:24Z","title":"Eigenvalue Asymptotics in a Twisted Waveguide"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1528","kind":"arxiv","version":3},"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":"sha256:5907b1784b30daff8fd0cd756bf51615171350ce14053cd883d131072416a959","target":"record","created_at":"2026-05-18T00:02:02Z","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":"1ada9639f1db18dbd2a1fa333267decf0de18c862607610a56c2fb2860fee99d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2008-08-11T15:26:24Z","title_canon_sha256":"0fc37dc0d98756628083e14d053e7af66774a9e71fa884ceb1e9d76179d49287"},"schema_version":"1.0","source":{"id":"0808.1528","kind":"arxiv","version":3}},"canonical_sha256":"680cb91da13fa5d1066c26ff0dcd35bf779bdda3e754ef175ae7038d23c26008","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"680cb91da13fa5d1066c26ff0dcd35bf779bdda3e754ef175ae7038d23c26008","first_computed_at":"2026-05-18T00:02:02.553264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:02.553264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LeEemYDvbYLTPm5K73CJ12klS+ufN0FQDA6w/KHEFZcBAd3sDfXhHTD1JtI2ry22KSfBi3VC+CkFlvYZV9aoAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:02.553895Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.1528","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5907b1784b30daff8fd0cd756bf51615171350ce14053cd883d131072416a959","sha256:dbccedcbec10793e800cf0fc30499a6330a6ef904bd88a18be544416300befcb"],"state_sha256":"b33b77bc0ef2e6c43f93ed242d1b96c47268886ff8bcecdd70dc538ab78379ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jmCs7GKJUe21FkreGTNOxEWGhQ4Q1CSXPPKKrMuuQidQXfIknxuMS9yFAGSSA6wmjMNe+S/XfE7zIVZ44ppVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:59:53.542231Z","bundle_sha256":"6a6fa873f6a8870faa0b95dd96b20c80366e12c03ed0e3a6a5e2d29246fe0298"}}