{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TR3SGIZ6CUYL2PJUAMPRFCKHSR","short_pith_number":"pith:TR3SGIZ6","canonical_record":{"source":{"id":"2401.13648","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-01-24T18:33:15Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"5feda8c1f547460f495a96d4caa87071ca759b67a81d6d5bfb5dd4a49ed8a754","abstract_canon_sha256":"23689c27f7679d7a4fa3ad8c51ea684df73d710ce204f4fc150889cf72cfd336"},"schema_version":"1.0"},"canonical_sha256":"9c7723233e1530bd3d34031f128947944059198cc4ce5b411ca2e265fb45c7f2","source":{"kind":"arxiv","id":"2401.13648","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.13648","created_at":"2026-06-19T16:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"2401.13648v3","created_at":"2026-06-19T16:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.13648","created_at":"2026-06-19T16:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"TR3SGIZ6CUYL","created_at":"2026-06-19T16:11:08Z"},{"alias_kind":"pith_short_16","alias_value":"TR3SGIZ6CUYL2PJU","created_at":"2026-06-19T16:11:08Z"},{"alias_kind":"pith_short_8","alias_value":"TR3SGIZ6","created_at":"2026-06-19T16:11:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TR3SGIZ6CUYL2PJUAMPRFCKHSR","target":"record","payload":{"canonical_record":{"source":{"id":"2401.13648","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-01-24T18:33:15Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"5feda8c1f547460f495a96d4caa87071ca759b67a81d6d5bfb5dd4a49ed8a754","abstract_canon_sha256":"23689c27f7679d7a4fa3ad8c51ea684df73d710ce204f4fc150889cf72cfd336"},"schema_version":"1.0"},"canonical_sha256":"9c7723233e1530bd3d34031f128947944059198cc4ce5b411ca2e265fb45c7f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:08.001891Z","signature_b64":"oY9rLCCj+XXmSSvutLW7rq2HSrt5ACax+iueW7TAgl31ZiBKR2oAafN4H41k5Gm76CoBL9NYAvlfQL963jP6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c7723233e1530bd3d34031f128947944059198cc4ce5b411ca2e265fb45c7f2","last_reissued_at":"2026-06-19T16:11:08.001549Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:08.001549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.13648","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:11:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rKWr/+U+wg9ArOL1LSZV1Hpaq3AE/Ow4LyQ5g1rtl3//t+VZ4BNUVNFV4J/MAk9ABX/DqCs04M5Qnabdj3rWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:58:03.666853Z"},"content_sha256":"279f48370fdd96007c8650b9ad3911c5a04d4327bca81c427988b38d9fb02c7f","schema_version":"1.0","event_id":"sha256:279f48370fdd96007c8650b9ad3911c5a04d4327bca81c427988b38d9fb02c7f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TR3SGIZ6CUYL2PJUAMPRFCKHSR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The FBSDE approach to sine-Gordon up to $6\\pi$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Massimiliano Gubinelli, Sarah-Jean Meyer","submitted_at":"2024-01-24T18:33:15Z","abstract_excerpt":"We develop a stochastic analysis of the sine-Gordon Euclidean quantum field $(\\cos (\\beta \\varphi))_2$ on the full space up to the second threshold, i.e. for $\\beta^2 < 6 \\pi$. The basis of our method is a forward-backward stochastic differential equation (FBSDE) for a decomposition $(X_t)_{t \\geqslant 0}$ of the interacting Euclidean field $X_{\\infty}$ along a scale parameter $t \\geqslant 0$. This FBSDE describes the optimiser of the stochastic control representation of the Euclidean QFT introduced by Barashkov and one of the authors. We show that the FBSDE provides a description of the inter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.13648","kind":"arxiv","version":3},"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/2401.13648/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":"2026-06-19T16:11:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EzEQPPbIWsEI/baiD+XjC/29pjPz4Jv+8c9VF38Qvpk+UWw5r2NXx66nMnGxlVeXmmeT/EEh8idlmpMRDGv/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:58:03.667354Z"},"content_sha256":"6a068a52dd845c22ba0cefe234bf8fc854726add83257474fd698a68c51e66b0","schema_version":"1.0","event_id":"sha256:6a068a52dd845c22ba0cefe234bf8fc854726add83257474fd698a68c51e66b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TR3SGIZ6CUYL2PJUAMPRFCKHSR/bundle.json","state_url":"https://pith.science/pith/TR3SGIZ6CUYL2PJUAMPRFCKHSR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TR3SGIZ6CUYL2PJUAMPRFCKHSR/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":"2026-08-08T16:58:03Z","links":{"resolver":"https://pith.science/pith/TR3SGIZ6CUYL2PJUAMPRFCKHSR","bundle":"https://pith.science/pith/TR3SGIZ6CUYL2PJUAMPRFCKHSR/bundle.json","state":"https://pith.science/pith/TR3SGIZ6CUYL2PJUAMPRFCKHSR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TR3SGIZ6CUYL2PJUAMPRFCKHSR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TR3SGIZ6CUYL2PJUAMPRFCKHSR","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":"23689c27f7679d7a4fa3ad8c51ea684df73d710ce204f4fc150889cf72cfd336","cross_cats_sorted":["math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-01-24T18:33:15Z","title_canon_sha256":"5feda8c1f547460f495a96d4caa87071ca759b67a81d6d5bfb5dd4a49ed8a754"},"schema_version":"1.0","source":{"id":"2401.13648","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.13648","created_at":"2026-06-19T16:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"2401.13648v3","created_at":"2026-06-19T16:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.13648","created_at":"2026-06-19T16:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"TR3SGIZ6CUYL","created_at":"2026-06-19T16:11:08Z"},{"alias_kind":"pith_short_16","alias_value":"TR3SGIZ6CUYL2PJU","created_at":"2026-06-19T16:11:08Z"},{"alias_kind":"pith_short_8","alias_value":"TR3SGIZ6","created_at":"2026-06-19T16:11:08Z"}],"graph_snapshots":[{"event_id":"sha256:6a068a52dd845c22ba0cefe234bf8fc854726add83257474fd698a68c51e66b0","target":"graph","created_at":"2026-06-19T16:11:08Z","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/2401.13648/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a stochastic analysis of the sine-Gordon Euclidean quantum field $(\\cos (\\beta \\varphi))_2$ on the full space up to the second threshold, i.e. for $\\beta^2 < 6 \\pi$. The basis of our method is a forward-backward stochastic differential equation (FBSDE) for a decomposition $(X_t)_{t \\geqslant 0}$ of the interacting Euclidean field $X_{\\infty}$ along a scale parameter $t \\geqslant 0$. This FBSDE describes the optimiser of the stochastic control representation of the Euclidean QFT introduced by Barashkov and one of the authors. We show that the FBSDE provides a description of the inter","authors_text":"Massimiliano Gubinelli, Sarah-Jean Meyer","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-01-24T18:33:15Z","title":"The FBSDE approach to sine-Gordon up to $6\\pi$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.13648","kind":"arxiv","version":3},"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":"sha256:279f48370fdd96007c8650b9ad3911c5a04d4327bca81c427988b38d9fb02c7f","target":"record","created_at":"2026-06-19T16:11:08Z","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":"23689c27f7679d7a4fa3ad8c51ea684df73d710ce204f4fc150889cf72cfd336","cross_cats_sorted":["math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-01-24T18:33:15Z","title_canon_sha256":"5feda8c1f547460f495a96d4caa87071ca759b67a81d6d5bfb5dd4a49ed8a754"},"schema_version":"1.0","source":{"id":"2401.13648","kind":"arxiv","version":3}},"canonical_sha256":"9c7723233e1530bd3d34031f128947944059198cc4ce5b411ca2e265fb45c7f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c7723233e1530bd3d34031f128947944059198cc4ce5b411ca2e265fb45c7f2","first_computed_at":"2026-06-19T16:11:08.001549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:08.001549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oY9rLCCj+XXmSSvutLW7rq2HSrt5ACax+iueW7TAgl31ZiBKR2oAafN4H41k5Gm76CoBL9NYAvlfQL963jP6CA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:08.001891Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.13648","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:279f48370fdd96007c8650b9ad3911c5a04d4327bca81c427988b38d9fb02c7f","sha256:6a068a52dd845c22ba0cefe234bf8fc854726add83257474fd698a68c51e66b0"],"state_sha256":"7e16cc94a595a7eca54a0a4031b98dbc770ef6d9112d8bc26af587f045e851bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uaXakSFmBd5LLFITsWeE9YyjgRJEbwl7YwziVlya5ImruJWrY0XWmJRPYNSUEhElDMYWH+h7BkyMr5IljCm2BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T16:58:03.671712Z","bundle_sha256":"1c6bcd0166f4f4fcb6fc262c3add5170e7891932cd266902e58a25725cf9a3b4"}}