{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HIHG32HBAJFYEQOTOZTRQYGIEN","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":"208b898ca7af0bcd6c84adafbc965a622940caa6374eeb634d138c2b66c49dd0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2019-06-14T07:49:15Z","title_canon_sha256":"b1659c534d61726e2f97af116ebc7ee7d8e739f6c9227f0862329408aec86612"},"schema_version":"1.0","source":{"id":"1906.06060","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.06060","created_at":"2026-07-05T00:06:09Z"},{"alias_kind":"arxiv_version","alias_value":"1906.06060v2","created_at":"2026-07-05T00:06:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.06060","created_at":"2026-07-05T00:06:09Z"},{"alias_kind":"pith_short_12","alias_value":"HIHG32HBAJFY","created_at":"2026-07-05T00:06:09Z"},{"alias_kind":"pith_short_16","alias_value":"HIHG32HBAJFYEQOT","created_at":"2026-07-05T00:06:09Z"},{"alias_kind":"pith_short_8","alias_value":"HIHG32HB","created_at":"2026-07-05T00:06:09Z"}],"graph_snapshots":[{"event_id":"sha256:b674abbf8fe29b0c98bbe360e29b6d780e35d69c038e9418d3ecedaa5221d773","target":"graph","created_at":"2026-07-05T00:06:09Z","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/1906.06060/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We apply the higher-order tensor renormalization group (HOTRG) to the four-dimensional ferromagnetic Ising model, which has been attracting interests in the context of the triviality of the scalar $\\phi^4_{d=4}$ theory. We investigate the phase transition of this model with HOTRG enlarging the lattice size up to $1024^4$ with parallel computation. The results for the internal energy and the magnetization are consistent with the weak first-order phase transition.","authors_text":"Shinichiro Akiyama, Takumi Yamashita, Yoshinobu Kuramashi, Yusuke Yoshimura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2019-06-14T07:49:15Z","title":"Phase transition of four-dimensional Ising model with higher-order tensor renormalization group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.06060","kind":"arxiv","version":2},"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:ab84cb21c09a94d9c2ba86107d7e659baefe2de43125fd5259a55420feba214c","target":"record","created_at":"2026-07-05T00:06:09Z","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":"208b898ca7af0bcd6c84adafbc965a622940caa6374eeb634d138c2b66c49dd0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2019-06-14T07:49:15Z","title_canon_sha256":"b1659c534d61726e2f97af116ebc7ee7d8e739f6c9227f0862329408aec86612"},"schema_version":"1.0","source":{"id":"1906.06060","kind":"arxiv","version":2}},"canonical_sha256":"3a0e6de8e1024b8241d376671860c823686c5775b9d510a965084e497a519ed6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a0e6de8e1024b8241d376671860c823686c5775b9d510a965084e497a519ed6","first_computed_at":"2026-07-05T00:06:09.123613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:06:09.123613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hun7Q2bhgI5cH6XAPpRtH3YI2fQDazrrAfei34BEnu1KruMM+6gZ0gl1B0+ZxCIkMWX343z7ukqJPJyCsMjmAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:06:09.124107Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.06060","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab84cb21c09a94d9c2ba86107d7e659baefe2de43125fd5259a55420feba214c","sha256:b674abbf8fe29b0c98bbe360e29b6d780e35d69c038e9418d3ecedaa5221d773"],"state_sha256":"e50c5ba7dfa368fee2ff772487a485df72f731d9f963f2d24542ee1067b5759c"}