{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LX2LQHOVKPZFDP6MRA4SXJU32K","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":"fccd7ef03ca4fcda8738240bd65bece4091edc8be79789edfda1cd42d4028426","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2016-11-03T08:58:46Z","title_canon_sha256":"14028c60c5dcf9c72b16d822a3a9a89d58311a67f9a0b56d58fd7f2312c1368f"},"schema_version":"1.0","source":{"id":"1611.00921","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00921","created_at":"2026-05-18T01:00:18Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00921v1","created_at":"2026-05-18T01:00:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00921","created_at":"2026-05-18T01:00:18Z"},{"alias_kind":"pith_short_12","alias_value":"LX2LQHOVKPZF","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LX2LQHOVKPZFDP6M","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LX2LQHOV","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:2281eda1e034d244269d022ccc901942f1df9d8a193d394077bd8d39529f44db","target":"graph","created_at":"2026-05-18T01:00:18Z","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":"The phase structure of the lattice CP($N-1$) model in two dimensions is analyzed by the tensor renormalization group (TRG) method. We focus on the case $N=2$ and compare the numerical result of the TRG method with that of the strong-coupling analysis in the presence of the $\\theta$ term and investigate the nature of the phase transition at $\\theta=\\pi$.","authors_text":"Hikaru Kawauchi, Shinji Takeda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2016-11-03T08:58:46Z","title":"Phase structure analysis of CP(N-1) model using Tensor renormalization group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00921","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:c8b399dad45a84ef311c616161bca38813ee6ce2873bddd1b3c5c74338dabcb1","target":"record","created_at":"2026-05-18T01:00:18Z","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":"fccd7ef03ca4fcda8738240bd65bece4091edc8be79789edfda1cd42d4028426","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2016-11-03T08:58:46Z","title_canon_sha256":"14028c60c5dcf9c72b16d822a3a9a89d58311a67f9a0b56d58fd7f2312c1368f"},"schema_version":"1.0","source":{"id":"1611.00921","kind":"arxiv","version":1}},"canonical_sha256":"5df4b81dd553f251bfcc88392ba69bd2b9a9c99aa49da5850000829733527010","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5df4b81dd553f251bfcc88392ba69bd2b9a9c99aa49da5850000829733527010","first_computed_at":"2026-05-18T01:00:18.250908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:18.250908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5gpaVyo+IjVV7CHhgbVAN29RYaDm0MeExsVunfLUOBTM0UcQrSCryljOyl6LPcI4RN3xwifI+w53c1pXIxvUCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:18.251683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.00921","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8b399dad45a84ef311c616161bca38813ee6ce2873bddd1b3c5c74338dabcb1","sha256:2281eda1e034d244269d022ccc901942f1df9d8a193d394077bd8d39529f44db"],"state_sha256":"c554b2c3e46ff32e2f43950f58ddda65919632b5a57d8c18413fe6cc30a48dab"}