{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SJDIBL26OCHUPCDZELX332GLJI","short_pith_number":"pith:SJDIBL26","canonical_record":{"source":{"id":"2501.15936","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-27T10:34:26Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"24de91181a3954299be31b3e774078751a81a681895164f0c9c21780ce5db565","abstract_canon_sha256":"d7f3d5be996dbed3c4771e9d1904f3a1508ea6860d53a6ccc11ec239750cea1e"},"schema_version":"1.0"},"canonical_sha256":"924680af5e708f47887922efbde8cb4a2f349f9d0fdbb490e90d8ab2db41b552","source":{"kind":"arxiv","id":"2501.15936","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.15936","created_at":"2026-07-05T10:13:46Z"},{"alias_kind":"arxiv_version","alias_value":"2501.15936v2","created_at":"2026-07-05T10:13:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.15936","created_at":"2026-07-05T10:13:46Z"},{"alias_kind":"pith_short_12","alias_value":"SJDIBL26OCHU","created_at":"2026-07-05T10:13:46Z"},{"alias_kind":"pith_short_16","alias_value":"SJDIBL26OCHUPCDZ","created_at":"2026-07-05T10:13:46Z"},{"alias_kind":"pith_short_8","alias_value":"SJDIBL26","created_at":"2026-07-05T10:13:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SJDIBL26OCHUPCDZELX332GLJI","target":"record","payload":{"canonical_record":{"source":{"id":"2501.15936","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-27T10:34:26Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"24de91181a3954299be31b3e774078751a81a681895164f0c9c21780ce5db565","abstract_canon_sha256":"d7f3d5be996dbed3c4771e9d1904f3a1508ea6860d53a6ccc11ec239750cea1e"},"schema_version":"1.0"},"canonical_sha256":"924680af5e708f47887922efbde8cb4a2f349f9d0fdbb490e90d8ab2db41b552","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:13:46.958404Z","signature_b64":"XMpq4JDxN1Z5JzZ7u/JNfZlE3bJrtKyZhFk47PFDpg8xcqCe3FVkDBLt8oIf127/YjgJiJSqNVEEHx0H95spCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"924680af5e708f47887922efbde8cb4a2f349f9d0fdbb490e90d8ab2db41b552","last_reissued_at":"2026-07-05T10:13:46.957905Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:13:46.957905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.15936","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:13:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0zwiA1b+97A6lKsBSwEkqlOuhMkG+wZzVhPMf6Cqv6RklG+wZsU86fukAkkMgLt9jobS4l2IAM7HKnr+z1TdBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:56:32.381139Z"},"content_sha256":"eb85793da17b02b469f21338430c522db8696920ab950cb1f3f3e1b10e4e844c","schema_version":"1.0","event_id":"sha256:eb85793da17b02b469f21338430c522db8696920ab950cb1f3f3e1b10e4e844c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SJDIBL26OCHUPCDZELX332GLJI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Liouville Brownian motion and quantum cones in dimension $d > 2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ewain Gwynne, Federico Bertacco","submitted_at":"2025-01-27T10:34:26Z","abstract_excerpt":"For $d > 2$ and $\\gamma \\in (0, \\sqrt{2d})$, we study the Liouville Brownian motion associated with the whole-space log-correlated Gaussian field in $\\mathbb{R}^d$. We compute its spectral dimension, i.e., the short-time asymptotics of the heat kernel along the diagonal, which, in contrast to the two-dimensional case, depends on both $\\gamma$ and on the thickness of the starting point. Furthermore, for even dimensions $d > 2$, we show that the spherical average process of the whole-space log-correlated Gaussian field in $\\mathbb{R}^d$ can be identified with the integral of a stationary Gaussia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15936","kind":"arxiv","version":2},"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/2501.15936/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":"2026-07-05T10:13:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J+xSWFyHNCpLxksj4zUcaZ9wSckiKbcTbMkrmiwBTXSFZjH9CtpQEXmKjgFARLtOBJuuGi8xPvVVOcIcZk4zDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:56:32.382074Z"},"content_sha256":"ebe03c689f3b101e2dbecda11f00457fa93a9712c9cdade558979dde90b37b69","schema_version":"1.0","event_id":"sha256:ebe03c689f3b101e2dbecda11f00457fa93a9712c9cdade558979dde90b37b69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SJDIBL26OCHUPCDZELX332GLJI/bundle.json","state_url":"https://pith.science/pith/SJDIBL26OCHUPCDZELX332GLJI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SJDIBL26OCHUPCDZELX332GLJI/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":"2026-08-16T10:56:32Z","links":{"resolver":"https://pith.science/pith/SJDIBL26OCHUPCDZELX332GLJI","bundle":"https://pith.science/pith/SJDIBL26OCHUPCDZELX332GLJI/bundle.json","state":"https://pith.science/pith/SJDIBL26OCHUPCDZELX332GLJI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SJDIBL26OCHUPCDZELX332GLJI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SJDIBL26OCHUPCDZELX332GLJI","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":"d7f3d5be996dbed3c4771e9d1904f3a1508ea6860d53a6ccc11ec239750cea1e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-27T10:34:26Z","title_canon_sha256":"24de91181a3954299be31b3e774078751a81a681895164f0c9c21780ce5db565"},"schema_version":"1.0","source":{"id":"2501.15936","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.15936","created_at":"2026-07-05T10:13:46Z"},{"alias_kind":"arxiv_version","alias_value":"2501.15936v2","created_at":"2026-07-05T10:13:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.15936","created_at":"2026-07-05T10:13:46Z"},{"alias_kind":"pith_short_12","alias_value":"SJDIBL26OCHU","created_at":"2026-07-05T10:13:46Z"},{"alias_kind":"pith_short_16","alias_value":"SJDIBL26OCHUPCDZ","created_at":"2026-07-05T10:13:46Z"},{"alias_kind":"pith_short_8","alias_value":"SJDIBL26","created_at":"2026-07-05T10:13:46Z"}],"graph_snapshots":[{"event_id":"sha256:ebe03c689f3b101e2dbecda11f00457fa93a9712c9cdade558979dde90b37b69","target":"graph","created_at":"2026-07-05T10:13:46Z","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/2501.15936/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For $d > 2$ and $\\gamma \\in (0, \\sqrt{2d})$, we study the Liouville Brownian motion associated with the whole-space log-correlated Gaussian field in $\\mathbb{R}^d$. We compute its spectral dimension, i.e., the short-time asymptotics of the heat kernel along the diagonal, which, in contrast to the two-dimensional case, depends on both $\\gamma$ and on the thickness of the starting point. Furthermore, for even dimensions $d > 2$, we show that the spherical average process of the whole-space log-correlated Gaussian field in $\\mathbb{R}^d$ can be identified with the integral of a stationary Gaussia","authors_text":"Ewain Gwynne, Federico Bertacco","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-27T10:34:26Z","title":"Liouville Brownian motion and quantum cones in dimension $d > 2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15936","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:eb85793da17b02b469f21338430c522db8696920ab950cb1f3f3e1b10e4e844c","target":"record","created_at":"2026-07-05T10:13:46Z","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":"d7f3d5be996dbed3c4771e9d1904f3a1508ea6860d53a6ccc11ec239750cea1e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-27T10:34:26Z","title_canon_sha256":"24de91181a3954299be31b3e774078751a81a681895164f0c9c21780ce5db565"},"schema_version":"1.0","source":{"id":"2501.15936","kind":"arxiv","version":2}},"canonical_sha256":"924680af5e708f47887922efbde8cb4a2f349f9d0fdbb490e90d8ab2db41b552","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"924680af5e708f47887922efbde8cb4a2f349f9d0fdbb490e90d8ab2db41b552","first_computed_at":"2026-07-05T10:13:46.957905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:13:46.957905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XMpq4JDxN1Z5JzZ7u/JNfZlE3bJrtKyZhFk47PFDpg8xcqCe3FVkDBLt8oIf127/YjgJiJSqNVEEHx0H95spCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:13:46.958404Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.15936","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb85793da17b02b469f21338430c522db8696920ab950cb1f3f3e1b10e4e844c","sha256:ebe03c689f3b101e2dbecda11f00457fa93a9712c9cdade558979dde90b37b69"],"state_sha256":"865ab0139760aa9304a6019147feb1a781899396e2a26cdbc75c60a78e8fb468"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TJyENhwVc1oMTXO3maXSIst6gUmHdxN0o326PNwiRskftrT1T9TMERG1EuMskFEa/IoeGQeUHVzp0fgF5KtxDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T10:56:32.388533Z","bundle_sha256":"5fdea57314b5f95669bdb8404cd7c78e963a703476fc9bb62f5ea91b200d8254"}}