{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SLLIMNPYADF36CTVJRCDVGTU6S","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":"85ff6e45ca8ebd7d171883e270aae1b6e555b818ae0a16595acf50c6a38921d4","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-01-29T14:15:49Z","title_canon_sha256":"dee5120d0d12e38e3842557aeeb6a5b06e851dccc38a1889ce51a0ce018d6531"},"schema_version":"1.0","source":{"id":"2501.17669","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.17669","created_at":"2026-07-05T10:06:56Z"},{"alias_kind":"arxiv_version","alias_value":"2501.17669v1","created_at":"2026-07-05T10:06:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.17669","created_at":"2026-07-05T10:06:56Z"},{"alias_kind":"pith_short_12","alias_value":"SLLIMNPYADF3","created_at":"2026-07-05T10:06:56Z"},{"alias_kind":"pith_short_16","alias_value":"SLLIMNPYADF36CTV","created_at":"2026-07-05T10:06:56Z"},{"alias_kind":"pith_short_8","alias_value":"SLLIMNPY","created_at":"2026-07-05T10:06:56Z"}],"graph_snapshots":[{"event_id":"sha256:ccfbaacaf732298160fedb2fafcea96b74191fe4ad4c606193846c1c040d5694","target":"graph","created_at":"2026-07-05T10:06:56Z","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/2501.17669/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the fractional $\\Phi^3_d$-measure on the $d$-dimensional torus, with Gaussian free field having inverse covariance $(1-\\Delta)^\\alpha$, and show a phase transition at $d=3\\alpha$. More precisely, in a regular regime $d<3\\alpha$, one can construct and normalise this measure, and obtain a measure which is absolutely continuous with respect to the Gaussian free field $\\mu$. At $d=3\\alpha$, the behaviour depends on the size $|\\sigma|$ of the nonlinearity: for $|\\sigma|\\ll1$, the measure exists, but is singular with respect to $\\mu$, whereas for $|\\sigma|\\gg1$, the measure is not normal","authors_text":"Niko Nikov","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-01-29T14:15:49Z","title":"Phase transitions for fractional $\\Phi^3_d$ on the torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.17669","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":"sha256:62a2959f9367f705e36509b6d342dfe21bfa02ed2dc90ddef22f74b6be0be1e2","target":"record","created_at":"2026-07-05T10:06:56Z","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":"85ff6e45ca8ebd7d171883e270aae1b6e555b818ae0a16595acf50c6a38921d4","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-01-29T14:15:49Z","title_canon_sha256":"dee5120d0d12e38e3842557aeeb6a5b06e851dccc38a1889ce51a0ce018d6531"},"schema_version":"1.0","source":{"id":"2501.17669","kind":"arxiv","version":1}},"canonical_sha256":"92d68635f800cbbf0a754c443a9a74f49bae720310121fc467e2c38f827faae3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92d68635f800cbbf0a754c443a9a74f49bae720310121fc467e2c38f827faae3","first_computed_at":"2026-07-05T10:06:56.459706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:06:56.459706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ihxTGGdyCnluvwo4g3GHNritb+6SWkNVZLHmUwrwwq5tAKBghKpDNsOL7hqc5CqrdLEVxVZFuxLJarnfcs2IDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:06:56.460111Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.17669","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62a2959f9367f705e36509b6d342dfe21bfa02ed2dc90ddef22f74b6be0be1e2","sha256:ccfbaacaf732298160fedb2fafcea96b74191fe4ad4c606193846c1c040d5694"],"state_sha256":"14b7f0484e29a59f5bb2b7ec548d5afe2bd401dabd3bc0804d6d82fe74336d32"}