{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RC6LLWICZEV4ZKMBWC3B7TS5YI","short_pith_number":"pith:RC6LLWIC","schema_version":"1.0","canonical_sha256":"88bcb5d902c92bcca981b0b61fce5dc21552c675609ffa8dc9c9008c845a7a95","source":{"kind":"arxiv","id":"1812.02457","version":2},"attestation_state":"computed","paper":{"title":"Lie-Schwinger block-diagonalization and gapped quantum chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alessandro Pizzo, Juerg Froehlich","submitted_at":"2018-12-06T10:58:29Z","abstract_excerpt":"We study quantum chains whose Hamiltonians are perturbations by bounded interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state energy. We prove that, for small values of a coupling constant, the spectral gap of the perturbed Hamiltonian above its ground-state energy is bounded from below by a positive constant uniformly in the length of the chain. In our proof we use a novel method based on local Lie-Schwinger conjugations of the Hamiltonians associated with c"},"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":"1812.02457","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-06T10:58:29Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b0d927d464bf04bdacfeedf4e953639f90ec742451a48f7cd3e31aabbd2f246c","abstract_canon_sha256":"cee8a2631c7cc8f3c62e718fd19fe6753ebbd43da290c838383dc0387d76313f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:31.982958Z","signature_b64":"r/DTdEvM2FjvdoAk/NSKKOA/PH/UsTL6t5g6jzWIwuWPpgA0wdI3SFUtJl5LNF4mjoj9a3YqnPRHxRm9r8QsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88bcb5d902c92bcca981b0b61fce5dc21552c675609ffa8dc9c9008c845a7a95","last_reissued_at":"2026-05-17T23:52:31.982501Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:31.982501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lie-Schwinger block-diagonalization and gapped quantum chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alessandro Pizzo, Juerg Froehlich","submitted_at":"2018-12-06T10:58:29Z","abstract_excerpt":"We study quantum chains whose Hamiltonians are perturbations by bounded interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state energy. We prove that, for small values of a coupling constant, the spectral gap of the perturbed Hamiltonian above its ground-state energy is bounded from below by a positive constant uniformly in the length of the chain. In our proof we use a novel method based on local Lie-Schwinger conjugations of the Hamiltonians associated with c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02457","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1812.02457","created_at":"2026-05-17T23:52:31.982571+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.02457v2","created_at":"2026-05-17T23:52:31.982571+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02457","created_at":"2026-05-17T23:52:31.982571+00:00"},{"alias_kind":"pith_short_12","alias_value":"RC6LLWICZEV4","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RC6LLWICZEV4ZKMB","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RC6LLWIC","created_at":"2026-05-18T12:32:50.500415+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.12184","citing_title":"Local Topological Quantum Order and Spectral Gap Stability for the AKLT Models on the Hexagonal and Lieb Lattices","ref_index":21,"is_internal_anchor":true},{"citing_arxiv_id":"2605.12184","citing_title":"Local Topological Quantum Order and Spectral Gap Stability for the AKLT Models on the Hexagonal and Lieb Lattices","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RC6LLWICZEV4ZKMBWC3B7TS5YI","json":"https://pith.science/pith/RC6LLWICZEV4ZKMBWC3B7TS5YI.json","graph_json":"https://pith.science/api/pith-number/RC6LLWICZEV4ZKMBWC3B7TS5YI/graph.json","events_json":"https://pith.science/api/pith-number/RC6LLWICZEV4ZKMBWC3B7TS5YI/events.json","paper":"https://pith.science/paper/RC6LLWIC"},"agent_actions":{"view_html":"https://pith.science/pith/RC6LLWICZEV4ZKMBWC3B7TS5YI","download_json":"https://pith.science/pith/RC6LLWICZEV4ZKMBWC3B7TS5YI.json","view_paper":"https://pith.science/paper/RC6LLWIC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.02457&json=true","fetch_graph":"https://pith.science/api/pith-number/RC6LLWICZEV4ZKMBWC3B7TS5YI/graph.json","fetch_events":"https://pith.science/api/pith-number/RC6LLWICZEV4ZKMBWC3B7TS5YI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RC6LLWICZEV4ZKMBWC3B7TS5YI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RC6LLWICZEV4ZKMBWC3B7TS5YI/action/storage_attestation","attest_author":"https://pith.science/pith/RC6LLWICZEV4ZKMBWC3B7TS5YI/action/author_attestation","sign_citation":"https://pith.science/pith/RC6LLWICZEV4ZKMBWC3B7TS5YI/action/citation_signature","submit_replication":"https://pith.science/pith/RC6LLWICZEV4ZKMBWC3B7TS5YI/action/replication_record"}},"created_at":"2026-05-17T23:52:31.982571+00:00","updated_at":"2026-05-17T23:52:31.982571+00:00"}