{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CCELRBBT27AXXYFPPJ3H7YZBFK","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":"f1c957393b5ab243256579d16844f31fae1f3ba6ecb4e984e6aec4371f51fbc0","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2019-12-05T07:35:46Z","title_canon_sha256":"23a83371e2d5b2390e2845947072686cc6b94d9be748f928bfb68561efcf6d75"},"schema_version":"1.0","source":{"id":"1912.02414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.02414","created_at":"2026-07-05T00:24:13Z"},{"alias_kind":"arxiv_version","alias_value":"1912.02414v1","created_at":"2026-07-05T00:24:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.02414","created_at":"2026-07-05T00:24:13Z"},{"alias_kind":"pith_short_12","alias_value":"CCELRBBT27AX","created_at":"2026-07-05T00:24:13Z"},{"alias_kind":"pith_short_16","alias_value":"CCELRBBT27AXXYFP","created_at":"2026-07-05T00:24:13Z"},{"alias_kind":"pith_short_8","alias_value":"CCELRBBT","created_at":"2026-07-05T00:24:13Z"}],"graph_snapshots":[{"event_id":"sha256:1ea4bc595b4d746132203e3791319589621f4753940dbfc2250774aeba8bcb1a","target":"graph","created_at":"2026-07-05T00:24:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1912.02414/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a new renormalization scheme of tensor networks made only of third order tensors. The isometry used for coarse-graining the network can be prepared at an $O(D^6)$ computational cost in any $d$ dimension ($d \\ge 2$), where $D$ is the truncated bond dimension of tensors. Although it is reduced to $O(D^5)$ if a randomized singular value decomposition is employed, the total cost is $O(D^{d+3})$ because the contraction part for creating a renormalized tensor with isometries has $D^{d+3}$ multiplications. We test our method in three dimensional Ising model and find that the numerical resu","authors_text":"Daisuke Kadoh, Katsumasa Nakayama","cross_cats":["cond-mat.stat-mech","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2019-12-05T07:35:46Z","title":"Renormalization group on a triad network"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.02414","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":"sha256:28d661c82a0e1944ac835d4b5363fe217bd47d3a7d3834b87b6bee554951da2e","target":"record","created_at":"2026-07-05T00:24:13Z","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":"f1c957393b5ab243256579d16844f31fae1f3ba6ecb4e984e6aec4371f51fbc0","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2019-12-05T07:35:46Z","title_canon_sha256":"23a83371e2d5b2390e2845947072686cc6b94d9be748f928bfb68561efcf6d75"},"schema_version":"1.0","source":{"id":"1912.02414","kind":"arxiv","version":1}},"canonical_sha256":"1088b88433d7c17be0af7a767fe3212aa94ae2ad6a641d87457d113a29e36ef1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1088b88433d7c17be0af7a767fe3212aa94ae2ad6a641d87457d113a29e36ef1","first_computed_at":"2026-07-05T00:24:13.392695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:24:13.392695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r4ZDIiFDjn8ILuZAQvIZcbswLDndloARN+AcU0bO+ngv5o+V/hTujHHI40XvXz4rZPX8A9fasTrv3wzdD75kDA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:24:13.393190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.02414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28d661c82a0e1944ac835d4b5363fe217bd47d3a7d3834b87b6bee554951da2e","sha256:1ea4bc595b4d746132203e3791319589621f4753940dbfc2250774aeba8bcb1a"],"state_sha256":"98945913c57f0b0373fd99dbf007dc15ff427f1003abdab0bc78f9d59c25f587"}