{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UMOTYCK7M63RQMWZNB3D73OE4G","short_pith_number":"pith:UMOTYCK7","canonical_record":{"source":{"id":"2407.16261","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-23T08:03:14Z","cross_cats_sorted":[],"title_canon_sha256":"8ddb48fe09b50d9717d07fa59528ebbfc49ab0228fc732201a222feff3b6722f","abstract_canon_sha256":"c6daac804ff6ab936556d4dcaeabeb68fc6e400b23f8d69d00747c40461284f1"},"schema_version":"1.0"},"canonical_sha256":"a31d3c095f67b71832d968763fedc4e18098fa2780adf0b52c837e30d47c4aa0","source":{"kind":"arxiv","id":"2407.16261","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.16261","created_at":"2026-06-02T01:03:29Z"},{"alias_kind":"arxiv_version","alias_value":"2407.16261v3","created_at":"2026-06-02T01:03:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.16261","created_at":"2026-06-02T01:03:29Z"},{"alias_kind":"pith_short_12","alias_value":"UMOTYCK7M63R","created_at":"2026-06-02T01:03:29Z"},{"alias_kind":"pith_short_16","alias_value":"UMOTYCK7M63RQMWZ","created_at":"2026-06-02T01:03:29Z"},{"alias_kind":"pith_short_8","alias_value":"UMOTYCK7","created_at":"2026-06-02T01:03:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UMOTYCK7M63RQMWZNB3D73OE4G","target":"record","payload":{"canonical_record":{"source":{"id":"2407.16261","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-23T08:03:14Z","cross_cats_sorted":[],"title_canon_sha256":"8ddb48fe09b50d9717d07fa59528ebbfc49ab0228fc732201a222feff3b6722f","abstract_canon_sha256":"c6daac804ff6ab936556d4dcaeabeb68fc6e400b23f8d69d00747c40461284f1"},"schema_version":"1.0"},"canonical_sha256":"a31d3c095f67b71832d968763fedc4e18098fa2780adf0b52c837e30d47c4aa0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:03:29.079576Z","signature_b64":"NWWL1ad5uwo9uvdYoiWut6R8YMKOdzteU37ASipbt763/67zIhkRJf4rHho05vvqq3JdsXs2m37AwNHvDpK1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a31d3c095f67b71832d968763fedc4e18098fa2780adf0b52c837e30d47c4aa0","last_reissued_at":"2026-06-02T01:03:29.079099Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:03:29.079099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.16261","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":"2026-06-02T01:03:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RzEsD/0zgYhdOjVWUZZKUu4KAsc8IJSm1//FuRT/LkW/fkl2q07P1EypJ20DJFCpgZhTkLmnDtwdiFWSAgd1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:19:28.363522Z"},"content_sha256":"306c4710ffb4ce247cc36a36df3abe0ff40b4e4d4164eba27499f3c5029b09ef","schema_version":"1.0","event_id":"sha256:306c4710ffb4ce247cc36a36df3abe0ff40b4e4d4164eba27499f3c5029b09ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UMOTYCK7M63RQMWZNB3D73OE4G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A martingale-type characterisation of the Gaussian free field and fractional Gaussian free fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guillaume Woessner, Juhan Aru","submitted_at":"2024-07-23T08:03:14Z","abstract_excerpt":"We establish a martingale-type characterisations for the continuum Gaussian free field (GFF) and for fractional Gaussian free fields (FGFs), using their connection to the stochastic heat equation and to fractional stochastic heat equations. The main theorem on the GFF generalizes previous results of similar flavour and the characterisation theorems on the FGFs are new. The proof strategy is to link the resampling dynamics coming from a martingale-type of decomposition property to the stationary dynamics of the desired field, i.e. to the (fractional) stochastic heat equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.16261","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/2407.16261/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":"2026-06-02T01:03:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ck+C+aQ+ZaYd16U+ftCbZ94HowPlKvEEkC+yYeEQIpoJSHUXETy2qKxszTjEvJArIx20hQmTz+aMwI++A2ZgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:19:28.364172Z"},"content_sha256":"220dfa581adaa4c42e9fffb5fad610989145980c2911b87537bf068e0d29be9f","schema_version":"1.0","event_id":"sha256:220dfa581adaa4c42e9fffb5fad610989145980c2911b87537bf068e0d29be9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UMOTYCK7M63RQMWZNB3D73OE4G/bundle.json","state_url":"https://pith.science/pith/UMOTYCK7M63RQMWZNB3D73OE4G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UMOTYCK7M63RQMWZNB3D73OE4G/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":"2026-06-12T09:19:28Z","links":{"resolver":"https://pith.science/pith/UMOTYCK7M63RQMWZNB3D73OE4G","bundle":"https://pith.science/pith/UMOTYCK7M63RQMWZNB3D73OE4G/bundle.json","state":"https://pith.science/pith/UMOTYCK7M63RQMWZNB3D73OE4G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UMOTYCK7M63RQMWZNB3D73OE4G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UMOTYCK7M63RQMWZNB3D73OE4G","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":"c6daac804ff6ab936556d4dcaeabeb68fc6e400b23f8d69d00747c40461284f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-23T08:03:14Z","title_canon_sha256":"8ddb48fe09b50d9717d07fa59528ebbfc49ab0228fc732201a222feff3b6722f"},"schema_version":"1.0","source":{"id":"2407.16261","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.16261","created_at":"2026-06-02T01:03:29Z"},{"alias_kind":"arxiv_version","alias_value":"2407.16261v3","created_at":"2026-06-02T01:03:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.16261","created_at":"2026-06-02T01:03:29Z"},{"alias_kind":"pith_short_12","alias_value":"UMOTYCK7M63R","created_at":"2026-06-02T01:03:29Z"},{"alias_kind":"pith_short_16","alias_value":"UMOTYCK7M63RQMWZ","created_at":"2026-06-02T01:03:29Z"},{"alias_kind":"pith_short_8","alias_value":"UMOTYCK7","created_at":"2026-06-02T01:03:29Z"}],"graph_snapshots":[{"event_id":"sha256:220dfa581adaa4c42e9fffb5fad610989145980c2911b87537bf068e0d29be9f","target":"graph","created_at":"2026-06-02T01:03:29Z","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/2407.16261/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a martingale-type characterisations for the continuum Gaussian free field (GFF) and for fractional Gaussian free fields (FGFs), using their connection to the stochastic heat equation and to fractional stochastic heat equations. The main theorem on the GFF generalizes previous results of similar flavour and the characterisation theorems on the FGFs are new. The proof strategy is to link the resampling dynamics coming from a martingale-type of decomposition property to the stationary dynamics of the desired field, i.e. to the (fractional) stochastic heat equation.","authors_text":"Guillaume Woessner, Juhan Aru","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-23T08:03:14Z","title":"A martingale-type characterisation of the Gaussian free field and fractional Gaussian free fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.16261","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":"sha256:306c4710ffb4ce247cc36a36df3abe0ff40b4e4d4164eba27499f3c5029b09ef","target":"record","created_at":"2026-06-02T01:03:29Z","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":"c6daac804ff6ab936556d4dcaeabeb68fc6e400b23f8d69d00747c40461284f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-23T08:03:14Z","title_canon_sha256":"8ddb48fe09b50d9717d07fa59528ebbfc49ab0228fc732201a222feff3b6722f"},"schema_version":"1.0","source":{"id":"2407.16261","kind":"arxiv","version":3}},"canonical_sha256":"a31d3c095f67b71832d968763fedc4e18098fa2780adf0b52c837e30d47c4aa0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a31d3c095f67b71832d968763fedc4e18098fa2780adf0b52c837e30d47c4aa0","first_computed_at":"2026-06-02T01:03:29.079099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:03:29.079099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NWWL1ad5uwo9uvdYoiWut6R8YMKOdzteU37ASipbt763/67zIhkRJf4rHho05vvqq3JdsXs2m37AwNHvDpK1AQ==","signature_status":"signed_v1","signed_at":"2026-06-02T01:03:29.079576Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.16261","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:306c4710ffb4ce247cc36a36df3abe0ff40b4e4d4164eba27499f3c5029b09ef","sha256:220dfa581adaa4c42e9fffb5fad610989145980c2911b87537bf068e0d29be9f"],"state_sha256":"ebf70e70338fc27f6d5b8dbe977e3b46c69bb2f11091a5713aca79502661eeaf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Hg3Z+OmpOK3dDjSlTlkiH3LOTfk09VRv0wKW9bZQYocdfxghFzY7MNrVoPnQzX92P4OoAwmZT4rOwnamIAfCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T09:19:28.366662Z","bundle_sha256":"ac22a1a8543566405bd870cc44f9feea7473dbd303fab20e1756fd54b4684d7d"}}