{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:Z6FA3KSFEPEOQAHWLTNDKXGOQH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fcf085f278cf3349b1019999f39ee47a6c168aa334fff6875b0184df2c1bf838","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-08-24T14:34:48Z","title_canon_sha256":"68d41267baaf230beeb36499b118dd1db54db862742e81867cde91a24ca4ed8d"},"schema_version":"1.0","source":{"id":"1008.4055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4055","created_at":"2026-05-18T02:05:43Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4055v1","created_at":"2026-05-18T02:05:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4055","created_at":"2026-05-18T02:05:43Z"},{"alias_kind":"pith_short_12","alias_value":"Z6FA3KSFEPEO","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"Z6FA3KSFEPEOQAHW","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"Z6FA3KSF","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:f00a43045f366f3665ff3b972e747696fa81d09798f1f51c087a81672b43268c","target":"graph","created_at":"2026-05-18T02:05:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Following the recent approach of using order domains to construct Grobner bases from general projective varieties, we examine the parity and time-reversal arguments relating de Witt and Lyman's assertion that all path weights associated with homotopy in dimensions d <= 2 form a faithful representation of the fundamental group of a quantum system. We then show how the most general polynomial ring obtained for a fermionic quantum system does not, in fact, admit a faithful representation, and so give a general prescription for calcluating Grobner bases for finite temperature many-body quantum sys","authors_text":"P.R. Crompton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-08-24T14:34:48Z","title":"Grobner Bases for Finite-temperature Quantum Computing and their Complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4055","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cfbc61f13ed354032c8058b14f8c4e8ca267b82a243835e886a0a64f1849a67b","target":"record","created_at":"2026-05-18T02:05:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fcf085f278cf3349b1019999f39ee47a6c168aa334fff6875b0184df2c1bf838","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-08-24T14:34:48Z","title_canon_sha256":"68d41267baaf230beeb36499b118dd1db54db862742e81867cde91a24ca4ed8d"},"schema_version":"1.0","source":{"id":"1008.4055","kind":"arxiv","version":1}},"canonical_sha256":"cf8a0daa4523c8e800f65cda355cce81c64ffedda2598e626bac3a742f6625b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf8a0daa4523c8e800f65cda355cce81c64ffedda2598e626bac3a742f6625b4","first_computed_at":"2026-05-18T02:05:43.292183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:43.292183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qdvFOpp5Ki1/bkcUhyu+GAjs3btvmNQCT1sediFMWX+dsd6oD2mf3RnzC4lAaonbK246xUpiRsSycZ5+RAn+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:43.292843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.4055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfbc61f13ed354032c8058b14f8c4e8ca267b82a243835e886a0a64f1849a67b","sha256:f00a43045f366f3665ff3b972e747696fa81d09798f1f51c087a81672b43268c"],"state_sha256":"36fc87041877e3f4ed608a468e3a366c4a2608656af964814b577799713ab734"}