{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3FEKRP326HTFMLNOVN2HCVGLL5","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":"2cb7ec668ac089461604623d85209da3a69fdb18dd7cb6f642d24fcd909f0f94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-08-10T12:13:32Z","title_canon_sha256":"2b310dfe49228afe97110e64186f350e4282704520e0720403a4e240828ec726"},"schema_version":"1.0","source":{"id":"1508.02214","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02214","created_at":"2026-05-18T01:23:55Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02214v2","created_at":"2026-05-18T01:23:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02214","created_at":"2026-05-18T01:23:55Z"},{"alias_kind":"pith_short_12","alias_value":"3FEKRP326HTF","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3FEKRP326HTFMLNO","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3FEKRP32","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:721ae5a052077334273ff51eac3c65c331b4098659d98989c7241abbbc1f0bdd","target":"graph","created_at":"2026-05-18T01:23:55Z","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 study phase transitions and the nature of order in a class of classical generalized $O(N)$ nonlinear $\\sigma$-models (NLS) constructed by minimally coupling pure NLS with additional degrees of freedom in the form of (i) Ising ferromagnetic spins, (ii) an advective Stokesian velocity and (iii) multiplicative noises. In examples (i) and (ii), and also (iii) with the associated multiplicative noise being not sufficiently long-ranged, we show that the models may display a class of unusual phase transitions between {\\em stiff} and {\\em soft phases}, where the effective spin stiffness, respective","authors_text":"Abhik Basu, Niladri Sarkar, Tirthankar Banerjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-08-10T12:13:32Z","title":"Phase transitions and order in two-dimensional generalized nonlinear $\\sigma$-models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02214","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":"sha256:99e1a84c5866fc87808487c2021f18859fdb067f429dd7bd9fd389401852824c","target":"record","created_at":"2026-05-18T01:23:55Z","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":"2cb7ec668ac089461604623d85209da3a69fdb18dd7cb6f642d24fcd909f0f94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-08-10T12:13:32Z","title_canon_sha256":"2b310dfe49228afe97110e64186f350e4282704520e0720403a4e240828ec726"},"schema_version":"1.0","source":{"id":"1508.02214","kind":"arxiv","version":2}},"canonical_sha256":"d948a8bf7af1e6562daeab747154cb5f41183b82ea44ac1d03d60bb3e01124e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d948a8bf7af1e6562daeab747154cb5f41183b82ea44ac1d03d60bb3e01124e1","first_computed_at":"2026-05-18T01:23:55.835977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:55.835977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/UFmTkUlzujbL7rDPC+zSFH+E8bp7GigesyxS1Yad3CdzRyZDsx/BJK+a+NrB/L+5bN45BgczU9Zr0zyCWB3Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:55.836589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02214","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99e1a84c5866fc87808487c2021f18859fdb067f429dd7bd9fd389401852824c","sha256:721ae5a052077334273ff51eac3c65c331b4098659d98989c7241abbbc1f0bdd"],"state_sha256":"4aaaf72646b52e8e8f4753d6457b56e43edfc0a266010219ee405e4c2c3c1438"}