{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3N4EPDST6U3DSPPK3GP2PY7Z2A","short_pith_number":"pith:3N4EPDST","schema_version":"1.0","canonical_sha256":"db78478e53f536393dead99fa7e3f9d00308ea6e3623de05a9748f3cfd2df5ee","source":{"kind":"arxiv","id":"1512.00088","version":1},"attestation_state":"computed","paper":{"title":"Local gap threshold for frustration-free spin systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"David Gosset, Evgeny Mozgunov","submitted_at":"2015-11-30T23:18:32Z","abstract_excerpt":"We improve Knabe's spectral gap bound for frustration-free translation-invariant local Hamiltonians in 1D. The bound is based on a relationship between global and local gaps. The global gap is the spectral gap of a size-$m$ chain with periodic boundary conditions, while the local gap is that of a subchain of size $n<m$ with open boundary conditions. Knabe proved that if the local gap is larger than the threshold value $1/(n-1)$ for some $n>2$, then the global gap is lower bounded by a positive constant in the thermodynamic limit $m\\rightarrow \\infty$. Here we improve the threshold to $\\frac{6}"},"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":"1512.00088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-30T23:18:32Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"title_canon_sha256":"679d36c781f31cea9769924a40cafe36148b974b87eda20b823d642c1d88f071","abstract_canon_sha256":"bc33981689eefb5bb563699ccc5539bb7f305221f7da330c9f069b01d6b1b7d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:45.438404Z","signature_b64":"QxNMzUHnjfaRjlUG5W1bBsFZab4w9S272Grly1JbUqei0Sn03VSvUhbWMVhcMEjlJs21K3rLOG/IlalV1+6SBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db78478e53f536393dead99fa7e3f9d00308ea6e3623de05a9748f3cfd2df5ee","last_reissued_at":"2026-05-18T01:02:45.437954Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:45.437954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local gap threshold for frustration-free spin systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"David Gosset, Evgeny Mozgunov","submitted_at":"2015-11-30T23:18:32Z","abstract_excerpt":"We improve Knabe's spectral gap bound for frustration-free translation-invariant local Hamiltonians in 1D. The bound is based on a relationship between global and local gaps. The global gap is the spectral gap of a size-$m$ chain with periodic boundary conditions, while the local gap is that of a subchain of size $n<m$ with open boundary conditions. Knabe proved that if the local gap is larger than the threshold value $1/(n-1)$ for some $n>2$, then the global gap is lower bounded by a positive constant in the thermodynamic limit $m\\rightarrow \\infty$. Here we improve the threshold to $\\frac{6}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00088","kind":"arxiv","version":1},"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":"1512.00088","created_at":"2026-05-18T01:02:45.438009+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.00088v1","created_at":"2026-05-18T01:02:45.438009+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00088","created_at":"2026-05-18T01:02:45.438009+00:00"},{"alias_kind":"pith_short_12","alias_value":"3N4EPDST6U3D","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3N4EPDST6U3DSPPK","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3N4EPDST","created_at":"2026-05-18T12:29:02.477457+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.03680","citing_title":"A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems","ref_index":21,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3N4EPDST6U3DSPPK3GP2PY7Z2A","json":"https://pith.science/pith/3N4EPDST6U3DSPPK3GP2PY7Z2A.json","graph_json":"https://pith.science/api/pith-number/3N4EPDST6U3DSPPK3GP2PY7Z2A/graph.json","events_json":"https://pith.science/api/pith-number/3N4EPDST6U3DSPPK3GP2PY7Z2A/events.json","paper":"https://pith.science/paper/3N4EPDST"},"agent_actions":{"view_html":"https://pith.science/pith/3N4EPDST6U3DSPPK3GP2PY7Z2A","download_json":"https://pith.science/pith/3N4EPDST6U3DSPPK3GP2PY7Z2A.json","view_paper":"https://pith.science/paper/3N4EPDST","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.00088&json=true","fetch_graph":"https://pith.science/api/pith-number/3N4EPDST6U3DSPPK3GP2PY7Z2A/graph.json","fetch_events":"https://pith.science/api/pith-number/3N4EPDST6U3DSPPK3GP2PY7Z2A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3N4EPDST6U3DSPPK3GP2PY7Z2A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3N4EPDST6U3DSPPK3GP2PY7Z2A/action/storage_attestation","attest_author":"https://pith.science/pith/3N4EPDST6U3DSPPK3GP2PY7Z2A/action/author_attestation","sign_citation":"https://pith.science/pith/3N4EPDST6U3DSPPK3GP2PY7Z2A/action/citation_signature","submit_replication":"https://pith.science/pith/3N4EPDST6U3DSPPK3GP2PY7Z2A/action/replication_record"}},"created_at":"2026-05-18T01:02:45.438009+00:00","updated_at":"2026-05-18T01:02:45.438009+00:00"}