{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:PCUGW2C2ETSGFUUGP6753VX32P","short_pith_number":"pith:PCUGW2C2","canonical_record":{"source":{"id":"2006.15071","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.SP","submitted_at":"2020-06-26T16:04:53Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"558ec33fc68428c410b34d9e0919aa520bd4be6e0b4d7005eb31ab0ec79106a7","abstract_canon_sha256":"318e1ed38a855ae5ddf93cc05ce61079d2d7a266c15e1b9f8d27884017fb01e0"},"schema_version":"1.0"},"canonical_sha256":"78a86b685a24e462d2867fbfddd6fbd3c635521e01093c1e51305864a8b2756e","source":{"kind":"arxiv","id":"2006.15071","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.15071","created_at":"2026-07-05T03:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"2006.15071v3","created_at":"2026-07-05T03:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.15071","created_at":"2026-07-05T03:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"PCUGW2C2ETSG","created_at":"2026-07-05T03:09:56Z"},{"alias_kind":"pith_short_16","alias_value":"PCUGW2C2ETSGFUUG","created_at":"2026-07-05T03:09:56Z"},{"alias_kind":"pith_short_8","alias_value":"PCUGW2C2","created_at":"2026-07-05T03:09:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:PCUGW2C2ETSGFUUGP6753VX32P","target":"record","payload":{"canonical_record":{"source":{"id":"2006.15071","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.SP","submitted_at":"2020-06-26T16:04:53Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"558ec33fc68428c410b34d9e0919aa520bd4be6e0b4d7005eb31ab0ec79106a7","abstract_canon_sha256":"318e1ed38a855ae5ddf93cc05ce61079d2d7a266c15e1b9f8d27884017fb01e0"},"schema_version":"1.0"},"canonical_sha256":"78a86b685a24e462d2867fbfddd6fbd3c635521e01093c1e51305864a8b2756e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:09:56.030562Z","signature_b64":"qKN2altSekWn1WHgqNHB9N1sWiB0BE5TjvEToV56p4iTLKq9QQQmtSd08jUC/JdWkd2TYwIq14FV2lpCFE96CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78a86b685a24e462d2867fbfddd6fbd3c635521e01093c1e51305864a8b2756e","last_reissued_at":"2026-07-05T03:09:56.030067Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:09:56.030067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.15071","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":"2026-07-05T03:09:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GJCulwbLYn4azc+jr5lzU/ctsRtQn7cbhf11muFm7NGOPN30npP9FZfK9U/OjRDegKyFYlMARsE4qf2sHsRgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:57:22.630687Z"},"content_sha256":"ba79f1cd3d1a0bd8d204f071f5b93f643c36b4373ceb19c923460c5a79550c3d","schema_version":"1.0","event_id":"sha256:ba79f1cd3d1a0bd8d204f071f5b93f643c36b4373ceb19c923460c5a79550c3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:PCUGW2C2ETSGFUUGP6753VX32P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral properties of soft quantum waveguides","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"math.SP","authors_text":"Pavel Exner","submitted_at":"2020-06-26T16:04:53Z","abstract_excerpt":"We consider a soft quantum waveguide described by a two-dimensional Schr\\\"odinger operators with an attractive potential in the form of a channel of a fixed profile built along an infinite smooth curve which is not straight but it is asymptotically straight in a suitable sense. Using Birman-Schwinger principle we show that the discrete spectrum of such an operator is nonempty if the potential well defining the channel profile is deep and narrow enough. Some related problems are also mentioned."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.15071","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.15071/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:09:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fuxLx+QLODqnATdMjO9yg8hdBJb9uh6FOx6fvrohkyZNQhXD4K4wFzJeH3RCLM/LxHPMbnUTgA7oTZxxt92EAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:57:22.631225Z"},"content_sha256":"61fbe25191267ccef15d377053a157329d64e516b69c804f6ad96b6133defe60","schema_version":"1.0","event_id":"sha256:61fbe25191267ccef15d377053a157329d64e516b69c804f6ad96b6133defe60"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCUGW2C2ETSGFUUGP6753VX32P/bundle.json","state_url":"https://pith.science/pith/PCUGW2C2ETSGFUUGP6753VX32P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCUGW2C2ETSGFUUGP6753VX32P/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":"2026-08-04T05:57:22Z","links":{"resolver":"https://pith.science/pith/PCUGW2C2ETSGFUUGP6753VX32P","bundle":"https://pith.science/pith/PCUGW2C2ETSGFUUGP6753VX32P/bundle.json","state":"https://pith.science/pith/PCUGW2C2ETSGFUUGP6753VX32P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCUGW2C2ETSGFUUGP6753VX32P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:PCUGW2C2ETSGFUUGP6753VX32P","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":"318e1ed38a855ae5ddf93cc05ce61079d2d7a266c15e1b9f8d27884017fb01e0","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.SP","submitted_at":"2020-06-26T16:04:53Z","title_canon_sha256":"558ec33fc68428c410b34d9e0919aa520bd4be6e0b4d7005eb31ab0ec79106a7"},"schema_version":"1.0","source":{"id":"2006.15071","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.15071","created_at":"2026-07-05T03:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"2006.15071v3","created_at":"2026-07-05T03:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.15071","created_at":"2026-07-05T03:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"PCUGW2C2ETSG","created_at":"2026-07-05T03:09:56Z"},{"alias_kind":"pith_short_16","alias_value":"PCUGW2C2ETSGFUUG","created_at":"2026-07-05T03:09:56Z"},{"alias_kind":"pith_short_8","alias_value":"PCUGW2C2","created_at":"2026-07-05T03:09:56Z"}],"graph_snapshots":[{"event_id":"sha256:61fbe25191267ccef15d377053a157329d64e516b69c804f6ad96b6133defe60","target":"graph","created_at":"2026-07-05T03:09:56Z","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/2006.15071/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a soft quantum waveguide described by a two-dimensional Schr\\\"odinger operators with an attractive potential in the form of a channel of a fixed profile built along an infinite smooth curve which is not straight but it is asymptotically straight in a suitable sense. Using Birman-Schwinger principle we show that the discrete spectrum of such an operator is nonempty if the potential well defining the channel profile is deep and narrow enough. Some related problems are also mentioned.","authors_text":"Pavel Exner","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.SP","submitted_at":"2020-06-26T16:04:53Z","title":"Spectral properties of soft quantum waveguides"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.15071","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:ba79f1cd3d1a0bd8d204f071f5b93f643c36b4373ceb19c923460c5a79550c3d","target":"record","created_at":"2026-07-05T03:09:56Z","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":"318e1ed38a855ae5ddf93cc05ce61079d2d7a266c15e1b9f8d27884017fb01e0","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.SP","submitted_at":"2020-06-26T16:04:53Z","title_canon_sha256":"558ec33fc68428c410b34d9e0919aa520bd4be6e0b4d7005eb31ab0ec79106a7"},"schema_version":"1.0","source":{"id":"2006.15071","kind":"arxiv","version":3}},"canonical_sha256":"78a86b685a24e462d2867fbfddd6fbd3c635521e01093c1e51305864a8b2756e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78a86b685a24e462d2867fbfddd6fbd3c635521e01093c1e51305864a8b2756e","first_computed_at":"2026-07-05T03:09:56.030067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:09:56.030067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qKN2altSekWn1WHgqNHB9N1sWiB0BE5TjvEToV56p4iTLKq9QQQmtSd08jUC/JdWkd2TYwIq14FV2lpCFE96CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:09:56.030562Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.15071","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba79f1cd3d1a0bd8d204f071f5b93f643c36b4373ceb19c923460c5a79550c3d","sha256:61fbe25191267ccef15d377053a157329d64e516b69c804f6ad96b6133defe60"],"state_sha256":"9176b22fb4e06e3d8f79a6f64f8f532f2efac87c972a7ed62b36d3727f29a65b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/mjjndgJKf++CCHQN05u/c+14QRltRdeNLytQ/GkyEkcqqA7wkfpHfHnM3aX1Lx+WjYoMmN3Njt9gqibS+qOAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T05:57:22.636133Z","bundle_sha256":"984191882bfa3f7da4f0b3a163a121082aad67d043367bd27be5e66696f4bcd1"}}