{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:IZEQN3VDPYNLW6BWMNNOX45SNK","short_pith_number":"pith:IZEQN3VD","schema_version":"1.0","canonical_sha256":"464906eea37e1abb7836635aebf3b26abe32736213b7f252a39a86491a4abe1d","source":{"kind":"arxiv","id":"1112.0762","version":1},"attestation_state":"computed","paper":{"title":"Ground-State Spaces of Frustration-Free Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Bei Zeng, David Kribs, Jianxin Chen, Zhaohui Wei, Zhengfeng Ji","submitted_at":"2011-12-04T15:46:35Z","abstract_excerpt":"We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of `reduced spaces' to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set $\\Theta_k$ of all the $k$-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in $\\Theta_k$, called atoms, are analogs of extreme points. We study the properties of atoms in $\\Theta_k$ and discuss its relationship with groun"},"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":"1112.0762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-12-04T15:46:35Z","cross_cats_sorted":[],"title_canon_sha256":"80f699bdd80391af0451aa96a86f1e44cca13f8d6084830c75fd3215d94ca2dd","abstract_canon_sha256":"214c8ee56d4da5075c955d716db793ad42a4633860d5c41fc33adf6c14fdfa98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:17.340201Z","signature_b64":"HpWaGV+/oSJFqjbQHtF10IkV96yKqCBF8cMWwFdZr/mcTR7mkdUttqBtd0crpZnvJuTi8qQsbxh2gt65rqzgDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"464906eea37e1abb7836635aebf3b26abe32736213b7f252a39a86491a4abe1d","last_reissued_at":"2026-05-18T01:59:17.339500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:17.339500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ground-State Spaces of Frustration-Free Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Bei Zeng, David Kribs, Jianxin Chen, Zhaohui Wei, Zhengfeng Ji","submitted_at":"2011-12-04T15:46:35Z","abstract_excerpt":"We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of `reduced spaces' to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set $\\Theta_k$ of all the $k$-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in $\\Theta_k$, called atoms, are analogs of extreme points. We study the properties of atoms in $\\Theta_k$ and discuss its relationship with groun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0762","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":"1112.0762","created_at":"2026-05-18T01:59:17.339614+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.0762v1","created_at":"2026-05-18T01:59:17.339614+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0762","created_at":"2026-05-18T01:59:17.339614+00:00"},{"alias_kind":"pith_short_12","alias_value":"IZEQN3VDPYNL","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"IZEQN3VDPYNLW6BW","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"IZEQN3VD","created_at":"2026-05-18T12:26:32.869790+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/IZEQN3VDPYNLW6BWMNNOX45SNK","json":"https://pith.science/pith/IZEQN3VDPYNLW6BWMNNOX45SNK.json","graph_json":"https://pith.science/api/pith-number/IZEQN3VDPYNLW6BWMNNOX45SNK/graph.json","events_json":"https://pith.science/api/pith-number/IZEQN3VDPYNLW6BWMNNOX45SNK/events.json","paper":"https://pith.science/paper/IZEQN3VD"},"agent_actions":{"view_html":"https://pith.science/pith/IZEQN3VDPYNLW6BWMNNOX45SNK","download_json":"https://pith.science/pith/IZEQN3VDPYNLW6BWMNNOX45SNK.json","view_paper":"https://pith.science/paper/IZEQN3VD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.0762&json=true","fetch_graph":"https://pith.science/api/pith-number/IZEQN3VDPYNLW6BWMNNOX45SNK/graph.json","fetch_events":"https://pith.science/api/pith-number/IZEQN3VDPYNLW6BWMNNOX45SNK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IZEQN3VDPYNLW6BWMNNOX45SNK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IZEQN3VDPYNLW6BWMNNOX45SNK/action/storage_attestation","attest_author":"https://pith.science/pith/IZEQN3VDPYNLW6BWMNNOX45SNK/action/author_attestation","sign_citation":"https://pith.science/pith/IZEQN3VDPYNLW6BWMNNOX45SNK/action/citation_signature","submit_replication":"https://pith.science/pith/IZEQN3VDPYNLW6BWMNNOX45SNK/action/replication_record"}},"created_at":"2026-05-18T01:59:17.339614+00:00","updated_at":"2026-05-18T01:59:17.339614+00:00"}