{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QHWLNHKIDGNPQ4JWJWFP2ITYUI","short_pith_number":"pith:QHWLNHKI","canonical_record":{"source":{"id":"2508.15689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-21T16:13:08Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"544366dadbae47dd7ff921aa1950b5d3fc72b14bfe1876c5e101f7785cca2b52","abstract_canon_sha256":"c30637b3a3d0d201ff3a5675426f508ff0851d430f88b5e13461ef938acf0050"},"schema_version":"1.0"},"canonical_sha256":"81ecb69d48199af871364d8afd2278a2338ba43b77b609e730fd23f8ad215262","source":{"kind":"arxiv","id":"2508.15689","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.15689","created_at":"2026-07-05T11:57:17Z"},{"alias_kind":"arxiv_version","alias_value":"2508.15689v1","created_at":"2026-07-05T11:57:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.15689","created_at":"2026-07-05T11:57:17Z"},{"alias_kind":"pith_short_12","alias_value":"QHWLNHKIDGNP","created_at":"2026-07-05T11:57:17Z"},{"alias_kind":"pith_short_16","alias_value":"QHWLNHKIDGNPQ4JW","created_at":"2026-07-05T11:57:17Z"},{"alias_kind":"pith_short_8","alias_value":"QHWLNHKI","created_at":"2026-07-05T11:57:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QHWLNHKIDGNPQ4JWJWFP2ITYUI","target":"record","payload":{"canonical_record":{"source":{"id":"2508.15689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-21T16:13:08Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"544366dadbae47dd7ff921aa1950b5d3fc72b14bfe1876c5e101f7785cca2b52","abstract_canon_sha256":"c30637b3a3d0d201ff3a5675426f508ff0851d430f88b5e13461ef938acf0050"},"schema_version":"1.0"},"canonical_sha256":"81ecb69d48199af871364d8afd2278a2338ba43b77b609e730fd23f8ad215262","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:57:17.110095Z","signature_b64":"trHTHEOh1BzAQqa335ZPaGUhOY0ddhVAaLod/DThptO/7LoJUYYwtnR96dK3yMm05RLnkn8inzNJ+Xh/o2mxDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81ecb69d48199af871364d8afd2278a2338ba43b77b609e730fd23f8ad215262","last_reissued_at":"2026-07-05T11:57:17.109616Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:57:17.109616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.15689","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:57:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YyLkzF3J1zOyD/seXei5RLZ84O82xQd+FZSjqAiOXuTcJiYdfF1NVipx7EkCGM8JH3IisoJaZJrSBpimk9RCBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T04:51:19.802257Z"},"content_sha256":"7f362f88cec68e9958028ab4ffb0bac6ca454be3ca7d7137cac3f64e4d93c5c3","schema_version":"1.0","event_id":"sha256:7f362f88cec68e9958028ab4ffb0bac6ca454be3ca7d7137cac3f64e4d93c5c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QHWLNHKIDGNPQ4JWJWFP2ITYUI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Liouville model in the $L^1$ phase: coupling and extreme values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Michael Hofstetter, Ofer Zeitouni","submitted_at":"2025-08-21T16:13:08Z","abstract_excerpt":"We establish a strong coupling between the Liouville model and the Gaussian free field on the two dimensional torus in the $L^1$ phase $\\beta \\in (0, 8\\pi)$, such that the difference of the two fields is a H\\\"older continuous function. The coupling originates from a Polchinski renormalisation group approach, which was previously used to prove analogous results for other Euclidean field theories in dimension two. Our main observations for the Liouville model are that the Polchinski flow has a definite sign and can be controlled well thanks to an FKG argument.\n  The coupling allows to relate ext"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.15689","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.15689/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:57:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fZy8QvDPmgmwm1FY9is6tQgbnMch/cafHxG4PtWh1sKq6Sz5OjdD9gXsU1cjPNXS3S1ANZnu8EawyC8Ar/r+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T04:51:19.802995Z"},"content_sha256":"51a83a437e3eef150cf77dc6a2f9e4574b65bf7369c84ba243298e108ee6bff2","schema_version":"1.0","event_id":"sha256:51a83a437e3eef150cf77dc6a2f9e4574b65bf7369c84ba243298e108ee6bff2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QHWLNHKIDGNPQ4JWJWFP2ITYUI/bundle.json","state_url":"https://pith.science/pith/QHWLNHKIDGNPQ4JWJWFP2ITYUI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QHWLNHKIDGNPQ4JWJWFP2ITYUI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T04:51:19Z","links":{"resolver":"https://pith.science/pith/QHWLNHKIDGNPQ4JWJWFP2ITYUI","bundle":"https://pith.science/pith/QHWLNHKIDGNPQ4JWJWFP2ITYUI/bundle.json","state":"https://pith.science/pith/QHWLNHKIDGNPQ4JWJWFP2ITYUI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QHWLNHKIDGNPQ4JWJWFP2ITYUI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QHWLNHKIDGNPQ4JWJWFP2ITYUI","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":"c30637b3a3d0d201ff3a5675426f508ff0851d430f88b5e13461ef938acf0050","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-21T16:13:08Z","title_canon_sha256":"544366dadbae47dd7ff921aa1950b5d3fc72b14bfe1876c5e101f7785cca2b52"},"schema_version":"1.0","source":{"id":"2508.15689","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.15689","created_at":"2026-07-05T11:57:17Z"},{"alias_kind":"arxiv_version","alias_value":"2508.15689v1","created_at":"2026-07-05T11:57:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.15689","created_at":"2026-07-05T11:57:17Z"},{"alias_kind":"pith_short_12","alias_value":"QHWLNHKIDGNP","created_at":"2026-07-05T11:57:17Z"},{"alias_kind":"pith_short_16","alias_value":"QHWLNHKIDGNPQ4JW","created_at":"2026-07-05T11:57:17Z"},{"alias_kind":"pith_short_8","alias_value":"QHWLNHKI","created_at":"2026-07-05T11:57:17Z"}],"graph_snapshots":[{"event_id":"sha256:51a83a437e3eef150cf77dc6a2f9e4574b65bf7369c84ba243298e108ee6bff2","target":"graph","created_at":"2026-07-05T11:57:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.15689/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a strong coupling between the Liouville model and the Gaussian free field on the two dimensional torus in the $L^1$ phase $\\beta \\in (0, 8\\pi)$, such that the difference of the two fields is a H\\\"older continuous function. The coupling originates from a Polchinski renormalisation group approach, which was previously used to prove analogous results for other Euclidean field theories in dimension two. Our main observations for the Liouville model are that the Polchinski flow has a definite sign and can be controlled well thanks to an FKG argument.\n  The coupling allows to relate ext","authors_text":"Michael Hofstetter, Ofer Zeitouni","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-21T16:13:08Z","title":"The Liouville model in the $L^1$ phase: coupling and extreme values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.15689","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":"sha256:7f362f88cec68e9958028ab4ffb0bac6ca454be3ca7d7137cac3f64e4d93c5c3","target":"record","created_at":"2026-07-05T11:57:17Z","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":"c30637b3a3d0d201ff3a5675426f508ff0851d430f88b5e13461ef938acf0050","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-21T16:13:08Z","title_canon_sha256":"544366dadbae47dd7ff921aa1950b5d3fc72b14bfe1876c5e101f7785cca2b52"},"schema_version":"1.0","source":{"id":"2508.15689","kind":"arxiv","version":1}},"canonical_sha256":"81ecb69d48199af871364d8afd2278a2338ba43b77b609e730fd23f8ad215262","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81ecb69d48199af871364d8afd2278a2338ba43b77b609e730fd23f8ad215262","first_computed_at":"2026-07-05T11:57:17.109616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:57:17.109616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"trHTHEOh1BzAQqa335ZPaGUhOY0ddhVAaLod/DThptO/7LoJUYYwtnR96dK3yMm05RLnkn8inzNJ+Xh/o2mxDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:57:17.110095Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.15689","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f362f88cec68e9958028ab4ffb0bac6ca454be3ca7d7137cac3f64e4d93c5c3","sha256:51a83a437e3eef150cf77dc6a2f9e4574b65bf7369c84ba243298e108ee6bff2"],"state_sha256":"ee1256565c0c06750f704c8cabf3f2da062f3510261ab82c3a75a079ad174685"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/MOKts/01C0Csj4lkBJyPvA6eCFET7f70Ma5/lBzeGEojuh34BYEUKICGVQqJtE7ghHfGO+AtPmgT/G3RscACw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T04:51:19.809687Z","bundle_sha256":"63ac2ccdeef7bc403dbe5bb07fb1000888cf2e2d0da24e9e507eb1f6bd7c2cc8"}}