{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7SA47SJ3KFT5SW3GIFM66LHWIL","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":"27f42cd2f5e3bfc3b4c12602a06a16da7a37735bc2a829614bb6cfbfd5339442","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-01-30T08:21:35Z","title_canon_sha256":"411c1a3571920214d8b301b135a1d7676bb64b840c5d266a21912fe6857c5db0"},"schema_version":"1.0","source":{"id":"1602.00088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00088","created_at":"2026-05-18T01:17:17Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00088v1","created_at":"2026-05-18T01:17:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00088","created_at":"2026-05-18T01:17:17Z"},{"alias_kind":"pith_short_12","alias_value":"7SA47SJ3KFT5","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7SA47SJ3KFT5SW3G","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7SA47SJ3","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:444a1ef5abbc629c7e1040748a222970cada2c19dee49fb2d62b873b91924ea7","target":"graph","created_at":"2026-05-18T01:17:17Z","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 investigate the O($n$) nonintersecting loop model on the square lattice under the constraint that the loops consist of ninety-degree bends only. The model is governed by the loop weight $n$, a weight $x$ for each vertex of the lattice visited once by a loop, and a weight $z$ for each vertex visited twice by a loop. We explore the $(x,z)$ phase diagram for some values of $n$. For $0<n<1$, the diagram has the same topology as the generic O($n$) phase diagram with $n<2$, with a first-order line when $z$ starts to dominate, and an O($n$)-like transition when $x$ starts to dominate. Both lines m","authors_text":"Henk W. J. Bl\\\"ote, Wenan Guo, Zhe Fu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-01-30T08:21:35Z","title":"Special transitions in an O($n$) loop model with an Ising-like constraint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00088","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:ed2e09037f9fa97d5306244cd9dfa7112df69a032c66577f1775188468cd760f","target":"record","created_at":"2026-05-18T01:17:17Z","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":"27f42cd2f5e3bfc3b4c12602a06a16da7a37735bc2a829614bb6cfbfd5339442","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-01-30T08:21:35Z","title_canon_sha256":"411c1a3571920214d8b301b135a1d7676bb64b840c5d266a21912fe6857c5db0"},"schema_version":"1.0","source":{"id":"1602.00088","kind":"arxiv","version":1}},"canonical_sha256":"fc81cfc93b5167d95b664159ef2cf642c604a322185752ffd18a6aaf11fdb7df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc81cfc93b5167d95b664159ef2cf642c604a322185752ffd18a6aaf11fdb7df","first_computed_at":"2026-05-18T01:17:17.587712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:17.587712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mTwc+IefBVM9laOvaUxSkcFLDVLfU6ayoJtUmV+FZjNMGFTV9LmV7cMAMw7R1+R7DtTXeRjn8ITNxPNYIRMjDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:17.588216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.00088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed2e09037f9fa97d5306244cd9dfa7112df69a032c66577f1775188468cd760f","sha256:444a1ef5abbc629c7e1040748a222970cada2c19dee49fb2d62b873b91924ea7"],"state_sha256":"ec828d1ce71b7f31fddb011cfdcef6eaa60779362608109d6907fc246669c113"}