{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5Y3BUHCEJDACIQGXAN6O2BAX3C","short_pith_number":"pith:5Y3BUHCE","canonical_record":{"source":{"id":"1402.0382","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-03T13:54:17Z","cross_cats_sorted":["math.AP","math.DG","math.MP"],"title_canon_sha256":"afe901e0134bec5397c4a9827590701aacf32db13e0cc1bdcb48efc2e45f7b84","abstract_canon_sha256":"05089309a9c0ea030876ad2cf724d42bbfcfe8ea08d1f813655593e5d7eb757e"},"schema_version":"1.0"},"canonical_sha256":"ee361a1c4448c02440d7037ced0417d8b5e2f6181661753863c06c0dbc763f03","source":{"kind":"arxiv","id":"1402.0382","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0382","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0382v2","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0382","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"5Y3BUHCEJDAC","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5Y3BUHCEJDACIQGX","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5Y3BUHCE","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5Y3BUHCEJDACIQGXAN6O2BAX3C","target":"record","payload":{"canonical_record":{"source":{"id":"1402.0382","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-03T13:54:17Z","cross_cats_sorted":["math.AP","math.DG","math.MP"],"title_canon_sha256":"afe901e0134bec5397c4a9827590701aacf32db13e0cc1bdcb48efc2e45f7b84","abstract_canon_sha256":"05089309a9c0ea030876ad2cf724d42bbfcfe8ea08d1f813655593e5d7eb757e"},"schema_version":"1.0"},"canonical_sha256":"ee361a1c4448c02440d7037ced0417d8b5e2f6181661753863c06c0dbc763f03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:55.319430Z","signature_b64":"Ej+O0ueQ0Wd9XCexzPw6miBIUEl+XVXOfN/uGt2FBNrENOi2wVRyGs8sL3agFIUwERxf1Ms8J9MgIYYw6zuvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee361a1c4448c02440d7037ced0417d8b5e2f6181661753863c06c0dbc763f03","last_reissued_at":"2026-05-18T00:48:55.318659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:55.318659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.0382","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":"2026-05-18T00:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ghZL3hxEp+i6r+FYQEzJbs8RnowNxKNC8SfoFmnygZfjQABzG1xQpIzsgLlZDhREUcNVIjhbbhAGqODI+NkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:50:51.097539Z"},"content_sha256":"2ef9c6e99a2589cde9323cc81494327b3220656824a01e233415e932f1303871","schema_version":"1.0","event_id":"sha256:2ef9c6e99a2589cde9323cc81494327b3220656824a01e233415e932f1303871"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5Y3BUHCEJDACIQGXAN6O2BAX3C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The adiabatic limit of Schr\\\"odinger operators on fibre bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Jonas Lampart, Stefan Teufel","submitted_at":"2014-02-03T13:54:17Z","abstract_excerpt":"We consider Schr\\\"odinger operators $H=-\\Delta_{g_\\varepsilon} + V$ on a fibre bundle $M\\stackrel{\\pi}{\\to}B$ with compact fibres and a metric $g_\\varepsilon$ that blows up directions perpendicular to the fibres by a factor ${\\varepsilon^{-1}\\gg 1}$. We show that for an eigenvalue $\\lambda$ of the fibre-wise part of $H$, satisfying a local gap condition, and every $N\\in \\mathbb{N}$ there exists a subspace of $L^2(M)$ that is invariant under $H$ up to errors of order $\\varepsilon^{N+1}$. The dynamical and spectral features of $H$ on this subspace can be described by an effective operator on the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0382","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":"2026-05-18T00:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h2VbGK4rTNueooJI5RP2wLMO0Wvwa5yESnNjNsCG7aBiO2MorC56k05YY5tXu0QIlsgEDldIkYyifPBLAo93Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:50:51.097891Z"},"content_sha256":"df777612f7f2af99883cd7cfcc4ea3930f59792c5fa9c51706fe85029e311f89","schema_version":"1.0","event_id":"sha256:df777612f7f2af99883cd7cfcc4ea3930f59792c5fa9c51706fe85029e311f89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5Y3BUHCEJDACIQGXAN6O2BAX3C/bundle.json","state_url":"https://pith.science/pith/5Y3BUHCEJDACIQGXAN6O2BAX3C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5Y3BUHCEJDACIQGXAN6O2BAX3C/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":"2026-06-02T06:50:51Z","links":{"resolver":"https://pith.science/pith/5Y3BUHCEJDACIQGXAN6O2BAX3C","bundle":"https://pith.science/pith/5Y3BUHCEJDACIQGXAN6O2BAX3C/bundle.json","state":"https://pith.science/pith/5Y3BUHCEJDACIQGXAN6O2BAX3C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5Y3BUHCEJDACIQGXAN6O2BAX3C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5Y3BUHCEJDACIQGXAN6O2BAX3C","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":"05089309a9c0ea030876ad2cf724d42bbfcfe8ea08d1f813655593e5d7eb757e","cross_cats_sorted":["math.AP","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-03T13:54:17Z","title_canon_sha256":"afe901e0134bec5397c4a9827590701aacf32db13e0cc1bdcb48efc2e45f7b84"},"schema_version":"1.0","source":{"id":"1402.0382","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0382","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0382v2","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0382","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"5Y3BUHCEJDAC","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5Y3BUHCEJDACIQGX","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5Y3BUHCE","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:df777612f7f2af99883cd7cfcc4ea3930f59792c5fa9c51706fe85029e311f89","target":"graph","created_at":"2026-05-18T00:48:55Z","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 Schr\\\"odinger operators $H=-\\Delta_{g_\\varepsilon} + V$ on a fibre bundle $M\\stackrel{\\pi}{\\to}B$ with compact fibres and a metric $g_\\varepsilon$ that blows up directions perpendicular to the fibres by a factor ${\\varepsilon^{-1}\\gg 1}$. We show that for an eigenvalue $\\lambda$ of the fibre-wise part of $H$, satisfying a local gap condition, and every $N\\in \\mathbb{N}$ there exists a subspace of $L^2(M)$ that is invariant under $H$ up to errors of order $\\varepsilon^{N+1}$. The dynamical and spectral features of $H$ on this subspace can be described by an effective operator on the","authors_text":"Jonas Lampart, Stefan Teufel","cross_cats":["math.AP","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-03T13:54:17Z","title":"The adiabatic limit of Schr\\\"odinger operators on fibre bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0382","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":"sha256:2ef9c6e99a2589cde9323cc81494327b3220656824a01e233415e932f1303871","target":"record","created_at":"2026-05-18T00:48:55Z","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":"05089309a9c0ea030876ad2cf724d42bbfcfe8ea08d1f813655593e5d7eb757e","cross_cats_sorted":["math.AP","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-03T13:54:17Z","title_canon_sha256":"afe901e0134bec5397c4a9827590701aacf32db13e0cc1bdcb48efc2e45f7b84"},"schema_version":"1.0","source":{"id":"1402.0382","kind":"arxiv","version":2}},"canonical_sha256":"ee361a1c4448c02440d7037ced0417d8b5e2f6181661753863c06c0dbc763f03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee361a1c4448c02440d7037ced0417d8b5e2f6181661753863c06c0dbc763f03","first_computed_at":"2026-05-18T00:48:55.318659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:55.318659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ej+O0ueQ0Wd9XCexzPw6miBIUEl+XVXOfN/uGt2FBNrENOi2wVRyGs8sL3agFIUwERxf1Ms8J9MgIYYw6zuvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:55.319430Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0382","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ef9c6e99a2589cde9323cc81494327b3220656824a01e233415e932f1303871","sha256:df777612f7f2af99883cd7cfcc4ea3930f59792c5fa9c51706fe85029e311f89"],"state_sha256":"79d852946844c4d1cb7f856d92d1816c9ad77df002203c3eee62c2a09cd9679b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Td7sgcBlJsh6p1/+zhp63tItQgsO9qthB2KvIZjnUHmASKabwoY9O6aW5vGg4IIxETbXyck6G+oZaXgWgbAJAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:50:51.099911Z","bundle_sha256":"21a940ab3886c8f5de4923e148c3456383ca05b1ed08f8ea989e2a3ab247605b"}}