{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:52J2DQX2CNMCZ563CJINOWFZ3M","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":"c4ac94376ef2f9e2f7a9ca136f1331159301742e3026011e900a302a5f406d5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2009-01-02T04:36:23Z","title_canon_sha256":"3f9255944dbf2fca13ee442a6b51f65d54aa001379a06a482ec3ece109c61dc4"},"schema_version":"1.0","source":{"id":"0901.0214","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.0214","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"0901.0214v3","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0214","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"52J2DQX2CNMC","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"52J2DQX2CNMCZ563","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"52J2DQX2","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:d913fb1b209de90202b1bf0d46066b39a8bde2e2554cac86d48e2086dc08c8b8","target":"graph","created_at":"2026-05-18T04:22:40Z","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":"We present a method for contracting a square-lattice tensor network in two dimensions, based on auxiliary tensors accomplishing successive truncations (renormalization) of 8-index tensors for 2 by 2 plaquettes into 4-index tensors. The scheme is variational, and thus the tensors can be optimized by minimizing the energy. Test results for the quantum phase transition of the transverse-field Ising model confirm that even the smallest possible tensors (two values for each tensor index at each renormalization level) produce much better results than the simple product (mean-field) state.","authors_text":"Anders W. Sandvik, Ling Wang, Ying-Jer Kao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2009-01-02T04:36:23Z","title":"Plaquette Renormalization Scheme for Tensor Network States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0214","kind":"arxiv","version":3},"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:fec7b434c7aee1f3e03640c840ec16f7c81247eb05020fa6c31fbfa17d2e7db7","target":"record","created_at":"2026-05-18T04:22:40Z","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":"c4ac94376ef2f9e2f7a9ca136f1331159301742e3026011e900a302a5f406d5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2009-01-02T04:36:23Z","title_canon_sha256":"3f9255944dbf2fca13ee442a6b51f65d54aa001379a06a482ec3ece109c61dc4"},"schema_version":"1.0","source":{"id":"0901.0214","kind":"arxiv","version":3}},"canonical_sha256":"ee93a1c2fa13582cf7db1250d758b9db0f51bc7088fdd710f7751b69cfc8eabb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee93a1c2fa13582cf7db1250d758b9db0f51bc7088fdd710f7751b69cfc8eabb","first_computed_at":"2026-05-18T04:22:40.567511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:40.567511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fSNNDnqAko/sczdLB6lql03Sx8nQxaetRr91qd0tFEuc2e1BThHf6X3xwAi+TFbaLmW8/XsaYkwK//SxXTZVDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:40.567911Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.0214","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fec7b434c7aee1f3e03640c840ec16f7c81247eb05020fa6c31fbfa17d2e7db7","sha256:d913fb1b209de90202b1bf0d46066b39a8bde2e2554cac86d48e2086dc08c8b8"],"state_sha256":"127cf2f149b2922efe29ad58d034fd18b91e922a85818ae734839e544fb87f21"}