{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:D273IG3JIBK5VB7L73YLDOBT4P","short_pith_number":"pith:D273IG3J","schema_version":"1.0","canonical_sha256":"1ebfb41b694055da87ebfef0b1b833e3ea081c2d28b486c8397ed0abda1061f1","source":{"kind":"arxiv","id":"2605.29959","version":1},"attestation_state":"computed","paper":{"title":"Quantitative semidefinite certificates for ground-state energies of Pauli Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"quant-ph","authors_text":"Igor Klep, Nando Leijenhorst, Victor Magron","submitted_at":"2026-05-28T14:01:21Z","abstract_excerpt":"The $k$-local Hamiltonian problem is a central model for quantum many-body systems and Hamiltonian complexity. Semidefinite programming and noncommutative sum-of-squares hierarchies provide systematic certificates for ground-state energies, but existing finite-convergence results give no quantitative guarantee on the accuracy of the low hierarchy levels accessible in computation. We prove explicit finite-level convergence rates for these hierarchies in the Pauli setting. For $k$-local Hamiltonians whose Pauli expansion contains only even-weight terms, we show that both the NPA-type lower-bound"},"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":"2605.29959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-05-28T14:01:21Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"430b0d31257d8ab8661290a1d1d51563e9f397201259723a3cda275062ccdd13","abstract_canon_sha256":"c49cdf356dadbb5b70d339e8162bdd782e3f0dd670dfa48ad8822707c4b74331"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:06:03.792679Z","signature_b64":"RnfYHvfw7CfFEf9buHr8fzPyTXPMZXsy1BtxcKd+cd1vsxGWh3XFxVmtmsFUu1/De8ORoSL0lN48jyRONz2PAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ebfb41b694055da87ebfef0b1b833e3ea081c2d28b486c8397ed0abda1061f1","last_reissued_at":"2026-05-29T02:06:03.791933Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:06:03.791933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantitative semidefinite certificates for ground-state energies of Pauli Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"quant-ph","authors_text":"Igor Klep, Nando Leijenhorst, Victor Magron","submitted_at":"2026-05-28T14:01:21Z","abstract_excerpt":"The $k$-local Hamiltonian problem is a central model for quantum many-body systems and Hamiltonian complexity. Semidefinite programming and noncommutative sum-of-squares hierarchies provide systematic certificates for ground-state energies, but existing finite-convergence results give no quantitative guarantee on the accuracy of the low hierarchy levels accessible in computation. We prove explicit finite-level convergence rates for these hierarchies in the Pauli setting. For $k$-local Hamiltonians whose Pauli expansion contains only even-weight terms, we show that both the NPA-type lower-bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29959","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.29959/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.29959","created_at":"2026-05-29T02:06:03.792052+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.29959v1","created_at":"2026-05-29T02:06:03.792052+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29959","created_at":"2026-05-29T02:06:03.792052+00:00"},{"alias_kind":"pith_short_12","alias_value":"D273IG3JIBK5","created_at":"2026-05-29T02:06:03.792052+00:00"},{"alias_kind":"pith_short_16","alias_value":"D273IG3JIBK5VB7L","created_at":"2026-05-29T02:06:03.792052+00:00"},{"alias_kind":"pith_short_8","alias_value":"D273IG3J","created_at":"2026-05-29T02:06:03.792052+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/D273IG3JIBK5VB7L73YLDOBT4P","json":"https://pith.science/pith/D273IG3JIBK5VB7L73YLDOBT4P.json","graph_json":"https://pith.science/api/pith-number/D273IG3JIBK5VB7L73YLDOBT4P/graph.json","events_json":"https://pith.science/api/pith-number/D273IG3JIBK5VB7L73YLDOBT4P/events.json","paper":"https://pith.science/paper/D273IG3J"},"agent_actions":{"view_html":"https://pith.science/pith/D273IG3JIBK5VB7L73YLDOBT4P","download_json":"https://pith.science/pith/D273IG3JIBK5VB7L73YLDOBT4P.json","view_paper":"https://pith.science/paper/D273IG3J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.29959&json=true","fetch_graph":"https://pith.science/api/pith-number/D273IG3JIBK5VB7L73YLDOBT4P/graph.json","fetch_events":"https://pith.science/api/pith-number/D273IG3JIBK5VB7L73YLDOBT4P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D273IG3JIBK5VB7L73YLDOBT4P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D273IG3JIBK5VB7L73YLDOBT4P/action/storage_attestation","attest_author":"https://pith.science/pith/D273IG3JIBK5VB7L73YLDOBT4P/action/author_attestation","sign_citation":"https://pith.science/pith/D273IG3JIBK5VB7L73YLDOBT4P/action/citation_signature","submit_replication":"https://pith.science/pith/D273IG3JIBK5VB7L73YLDOBT4P/action/replication_record"}},"created_at":"2026-05-29T02:06:03.792052+00:00","updated_at":"2026-05-29T02:06:03.792052+00:00"}