{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:HJCAMWSZPVHB3IF4MDJWKAUPQE","short_pith_number":"pith:HJCAMWSZ","schema_version":"1.0","canonical_sha256":"3a44065a597d4e1da0bc60d365028f81145b017611fdcfdc29d93f35ca2441c3","source":{"kind":"arxiv","id":"0907.0351","version":3},"attestation_state":"computed","paper":{"title":"Effective Hamiltonians for Constrained Quantum Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jakob Wachsmuth, Stefan Teufel","submitted_at":"2009-07-02T11:55:48Z","abstract_excerpt":"We consider the time-dependent Schr\\\"odinger equation on a Riemannian manifold $\\mathcal{A}$ with a potential that localizes a certain class of states close to a fixed submanifold $\\mathcal{C}$. When we scale the potential in the directions normal to $\\mathcal{C}$ by a parameter $\\varepsilon\\ll 1$, the solutions concentrate in an $\\veps$-neighborhood of $\\mathcal{C}$. We derive an effective Schr\\\"odinger equation on the submanifold $\\mathcal{C}$ and show that its solutions, suitably lifted to $\\mathcal{A}$, approximate the solutions of the original equation on $\\mathcal{A}$ up to errors of ord"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0907.0351","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-07-02T11:55:48Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"e5c1c7652a2ec13c12f2ec754cd73bc7ddb784ed6d318f636f3f50a5bd5b0dc0","abstract_canon_sha256":"68fbb1b527b2eeffc7f1a08e5657a6e9c55f363f04743cdad97e1f0cfac62cd2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:57.635622Z","signature_b64":"y0yT4RaW5I+uWdrgJBEkU69qaFhc9uXlCNUNDA3XkOfc3mdAN0bIPvbXTlAwsaUe6jz3Tl0Kzb2sowBGsHYeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a44065a597d4e1da0bc60d365028f81145b017611fdcfdc29d93f35ca2441c3","last_reissued_at":"2026-05-18T03:02:57.635078Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:57.635078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Effective Hamiltonians for Constrained Quantum Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jakob Wachsmuth, Stefan Teufel","submitted_at":"2009-07-02T11:55:48Z","abstract_excerpt":"We consider the time-dependent Schr\\\"odinger equation on a Riemannian manifold $\\mathcal{A}$ with a potential that localizes a certain class of states close to a fixed submanifold $\\mathcal{C}$. When we scale the potential in the directions normal to $\\mathcal{C}$ by a parameter $\\varepsilon\\ll 1$, the solutions concentrate in an $\\veps$-neighborhood of $\\mathcal{C}$. We derive an effective Schr\\\"odinger equation on the submanifold $\\mathcal{C}$ and show that its solutions, suitably lifted to $\\mathcal{A}$, approximate the solutions of the original equation on $\\mathcal{A}$ up to errors of ord"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0351","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0907.0351","created_at":"2026-05-18T03:02:57.635158+00:00"},{"alias_kind":"arxiv_version","alias_value":"0907.0351v3","created_at":"2026-05-18T03:02:57.635158+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0351","created_at":"2026-05-18T03:02:57.635158+00:00"},{"alias_kind":"pith_short_12","alias_value":"HJCAMWSZPVHB","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"HJCAMWSZPVHB3IF4","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"HJCAMWSZ","created_at":"2026-05-18T12:25:59.703012+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HJCAMWSZPVHB3IF4MDJWKAUPQE","json":"https://pith.science/pith/HJCAMWSZPVHB3IF4MDJWKAUPQE.json","graph_json":"https://pith.science/api/pith-number/HJCAMWSZPVHB3IF4MDJWKAUPQE/graph.json","events_json":"https://pith.science/api/pith-number/HJCAMWSZPVHB3IF4MDJWKAUPQE/events.json","paper":"https://pith.science/paper/HJCAMWSZ"},"agent_actions":{"view_html":"https://pith.science/pith/HJCAMWSZPVHB3IF4MDJWKAUPQE","download_json":"https://pith.science/pith/HJCAMWSZPVHB3IF4MDJWKAUPQE.json","view_paper":"https://pith.science/paper/HJCAMWSZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0907.0351&json=true","fetch_graph":"https://pith.science/api/pith-number/HJCAMWSZPVHB3IF4MDJWKAUPQE/graph.json","fetch_events":"https://pith.science/api/pith-number/HJCAMWSZPVHB3IF4MDJWKAUPQE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HJCAMWSZPVHB3IF4MDJWKAUPQE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HJCAMWSZPVHB3IF4MDJWKAUPQE/action/storage_attestation","attest_author":"https://pith.science/pith/HJCAMWSZPVHB3IF4MDJWKAUPQE/action/author_attestation","sign_citation":"https://pith.science/pith/HJCAMWSZPVHB3IF4MDJWKAUPQE/action/citation_signature","submit_replication":"https://pith.science/pith/HJCAMWSZPVHB3IF4MDJWKAUPQE/action/replication_record"}},"created_at":"2026-05-18T03:02:57.635158+00:00","updated_at":"2026-05-18T03:02:57.635158+00:00"}