{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:U6YQNCROGAH2QHAHJB636K56KV","short_pith_number":"pith:U6YQNCRO","canonical_record":{"source":{"id":"1412.6420","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-19T16:31:11Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"80c35296a809af86107c4ac67dfdd0de5e3c7f34064ed8232eb27465e5805148","abstract_canon_sha256":"761ff9d7a7615db535a6c30db4664e2804385814731222e1a586f07af1a426cc"},"schema_version":"1.0"},"canonical_sha256":"a7b1068a2e300fa81c07487dbf2bbe5577b7aa013e53f0c45b50b71125163a1c","source":{"kind":"arxiv","id":"1412.6420","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6420","created_at":"2026-05-18T01:35:35Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6420v2","created_at":"2026-05-18T01:35:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6420","created_at":"2026-05-18T01:35:35Z"},{"alias_kind":"pith_short_12","alias_value":"U6YQNCROGAH2","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"U6YQNCROGAH2QHAH","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"U6YQNCRO","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:U6YQNCROGAH2QHAHJB636K56KV","target":"record","payload":{"canonical_record":{"source":{"id":"1412.6420","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-19T16:31:11Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"80c35296a809af86107c4ac67dfdd0de5e3c7f34064ed8232eb27465e5805148","abstract_canon_sha256":"761ff9d7a7615db535a6c30db4664e2804385814731222e1a586f07af1a426cc"},"schema_version":"1.0"},"canonical_sha256":"a7b1068a2e300fa81c07487dbf2bbe5577b7aa013e53f0c45b50b71125163a1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:35.131648Z","signature_b64":"8zOO5aPjylUMl7/84PYU/qMtjvblkdsYtVVsUij8hZ0RGD4B1eDBalTWiP+lrz7863ZuMpaaPMnlPSWVWV+iCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7b1068a2e300fa81c07487dbf2bbe5577b7aa013e53f0c45b50b71125163a1c","last_reissued_at":"2026-05-18T01:35:35.131035Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:35.131035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.6420","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:35:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tuTmW5dLNfiF2wiDPf243FQpU790pVBHg6qDzxlJ2bMAu0zPTRJH7wUu/oLUlAXqsn82OnmNohcGAYffzBoSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:28:45.666117Z"},"content_sha256":"8e4afe4529fdcf04f7163df2aa2e7e5ddf9a039b9a70e0ee5659bb71b8935e90","schema_version":"1.0","event_id":"sha256:8e4afe4529fdcf04f7163df2aa2e7e5ddf9a039b9a70e0ee5659bb71b8935e90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:U6YQNCROGAH2QHAHJB636K56KV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bound States for Nano-Tubes with a Dislocation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"J\\\"urgen Voigt, Marko Stautz, Martin Kohlmann, Rainer Hempel","submitted_at":"2014-12-19T16:31:11Z","abstract_excerpt":"As a model for an interface in solid state physics, we consider two real-valued potentials $V^{(1)}$ and $V^{(2)}$ on the cylinder or tube $S=\\mathbb R \\times (\\mathbb R/\\mathbb Z)$ where we assume that there exists an interval $(a_0,b_0)$ which is free of spectrum of $-\\Delta+V^{(k)}$ for $k=1,2$. We are then interested in the spectrum of $H_t = -\\Delta + V_t$, for $t \\in \\mathbb R$, where $V_t(x,y) = V^{(1)}(x,y)$, for $x > 0$, and $V_t(x,y) = V^{(2)}(x+t,y)$, for $x < 0$. While the essential spectrum of $H_t$ is independent of $t$, we show that discrete spectrum, related to the interface at"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6420","kind":"arxiv","version":2},"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":"2026-05-18T01:35:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tpY9jeT1hWiwepbK3+WT5N7J0e8cvSoMgaFhBF4+w8zbyTl7FqIddl0EgAaorN3M4UIdMIBMLYtIgfrb9ymECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:28:45.666523Z"},"content_sha256":"4d14d5506035f6acfa610619933e9a5efa851c1e4ccb4355699d6eb192ca3059","schema_version":"1.0","event_id":"sha256:4d14d5506035f6acfa610619933e9a5efa851c1e4ccb4355699d6eb192ca3059"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U6YQNCROGAH2QHAHJB636K56KV/bundle.json","state_url":"https://pith.science/pith/U6YQNCROGAH2QHAHJB636K56KV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U6YQNCROGAH2QHAHJB636K56KV/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":"2026-05-31T02:28:45Z","links":{"resolver":"https://pith.science/pith/U6YQNCROGAH2QHAHJB636K56KV","bundle":"https://pith.science/pith/U6YQNCROGAH2QHAHJB636K56KV/bundle.json","state":"https://pith.science/pith/U6YQNCROGAH2QHAHJB636K56KV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U6YQNCROGAH2QHAHJB636K56KV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:U6YQNCROGAH2QHAHJB636K56KV","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":"761ff9d7a7615db535a6c30db4664e2804385814731222e1a586f07af1a426cc","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-19T16:31:11Z","title_canon_sha256":"80c35296a809af86107c4ac67dfdd0de5e3c7f34064ed8232eb27465e5805148"},"schema_version":"1.0","source":{"id":"1412.6420","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6420","created_at":"2026-05-18T01:35:35Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6420v2","created_at":"2026-05-18T01:35:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6420","created_at":"2026-05-18T01:35:35Z"},{"alias_kind":"pith_short_12","alias_value":"U6YQNCROGAH2","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"U6YQNCROGAH2QHAH","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"U6YQNCRO","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:4d14d5506035f6acfa610619933e9a5efa851c1e4ccb4355699d6eb192ca3059","target":"graph","created_at":"2026-05-18T01:35:35Z","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":"As a model for an interface in solid state physics, we consider two real-valued potentials $V^{(1)}$ and $V^{(2)}$ on the cylinder or tube $S=\\mathbb R \\times (\\mathbb R/\\mathbb Z)$ where we assume that there exists an interval $(a_0,b_0)$ which is free of spectrum of $-\\Delta+V^{(k)}$ for $k=1,2$. We are then interested in the spectrum of $H_t = -\\Delta + V_t$, for $t \\in \\mathbb R$, where $V_t(x,y) = V^{(1)}(x,y)$, for $x > 0$, and $V_t(x,y) = V^{(2)}(x+t,y)$, for $x < 0$. While the essential spectrum of $H_t$ is independent of $t$, we show that discrete spectrum, related to the interface at","authors_text":"J\\\"urgen Voigt, Marko Stautz, Martin Kohlmann, Rainer Hempel","cross_cats":["math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-19T16:31:11Z","title":"Bound States for Nano-Tubes with a Dislocation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6420","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":"sha256:8e4afe4529fdcf04f7163df2aa2e7e5ddf9a039b9a70e0ee5659bb71b8935e90","target":"record","created_at":"2026-05-18T01:35:35Z","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":"761ff9d7a7615db535a6c30db4664e2804385814731222e1a586f07af1a426cc","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-19T16:31:11Z","title_canon_sha256":"80c35296a809af86107c4ac67dfdd0de5e3c7f34064ed8232eb27465e5805148"},"schema_version":"1.0","source":{"id":"1412.6420","kind":"arxiv","version":2}},"canonical_sha256":"a7b1068a2e300fa81c07487dbf2bbe5577b7aa013e53f0c45b50b71125163a1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7b1068a2e300fa81c07487dbf2bbe5577b7aa013e53f0c45b50b71125163a1c","first_computed_at":"2026-05-18T01:35:35.131035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:35.131035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8zOO5aPjylUMl7/84PYU/qMtjvblkdsYtVVsUij8hZ0RGD4B1eDBalTWiP+lrz7863ZuMpaaPMnlPSWVWV+iCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:35.131648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.6420","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e4afe4529fdcf04f7163df2aa2e7e5ddf9a039b9a70e0ee5659bb71b8935e90","sha256:4d14d5506035f6acfa610619933e9a5efa851c1e4ccb4355699d6eb192ca3059"],"state_sha256":"3cdce4a03c8ed2a7ad681feb5476650f71887566803e108ce29e7dde20c1e1d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ap1ZB1vxByXhdaH2OG4ekNiYW4KPSWP3V+VwS7qgCePx9U2mc10lA55zCB01P/2DuG2+M8pVT9LMC7cZkdh1Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:28:45.669965Z","bundle_sha256":"911070cd4eb4bef4ed6ac945b036edd9d002d3fcf1a963e9d493827a6db6d45d"}}