{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FFFDEHCUL5DY3YFKWWQXR3TV5M","short_pith_number":"pith:FFFDEHCU","canonical_record":{"source":{"id":"1412.1705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-04T15:39:22Z","cross_cats_sorted":[],"title_canon_sha256":"0b7d705a01c1598d363ea22db23e494ed55384eeb38284088fc5dff0a57fa39e","abstract_canon_sha256":"c2bc24646bb0c7d82668a2cb533a8f1b7419457e248ac2746e749025329737a1"},"schema_version":"1.0"},"canonical_sha256":"294a321c545f478de0aab5a178ee75eb3824211967ebe0360a1e6307fb6f2b67","source":{"kind":"arxiv","id":"1412.1705","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1705","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1705v1","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1705","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"pith_short_12","alias_value":"FFFDEHCUL5DY","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FFFDEHCUL5DY3YFK","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FFFDEHCU","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FFFDEHCUL5DY3YFKWWQXR3TV5M","target":"record","payload":{"canonical_record":{"source":{"id":"1412.1705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-04T15:39:22Z","cross_cats_sorted":[],"title_canon_sha256":"0b7d705a01c1598d363ea22db23e494ed55384eeb38284088fc5dff0a57fa39e","abstract_canon_sha256":"c2bc24646bb0c7d82668a2cb533a8f1b7419457e248ac2746e749025329737a1"},"schema_version":"1.0"},"canonical_sha256":"294a321c545f478de0aab5a178ee75eb3824211967ebe0360a1e6307fb6f2b67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:06.669583Z","signature_b64":"fMfPbKkdcuByhTzqhMkcG1mvlZyv5+DPKk95bZLX1c7fj1kIEzjZRL+GshIRTO0jHLLkoatwuPS6fV7oYvPRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"294a321c545f478de0aab5a178ee75eb3824211967ebe0360a1e6307fb6f2b67","last_reissued_at":"2026-05-18T02:32:06.669199Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:06.669199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.1705","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":"2026-05-18T02:32:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hmn8avGkTZ7OR3W/WATYyft3cG4iJu/dHkGylqFvj2KZpRjgOscGyjAFTW5l31KIhgGnfStPldilr7E2FgdBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:06:54.287765Z"},"content_sha256":"fe7c67cac1f9e17d17f557d9b08bc51c47e8d5c78fa6674e1b3b7e752477a81a","schema_version":"1.0","event_id":"sha256:fe7c67cac1f9e17d17f557d9b08bc51c47e8d5c78fa6674e1b3b7e752477a81a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FFFDEHCUL5DY3YFKWWQXR3TV5M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Liouville Brownian Motion and Thick Points of the Gaussian Free Field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Henry Jackson","submitted_at":"2014-12-04T15:39:22Z","abstract_excerpt":"We find a lower bound for the Hausdorff dimension that a Liouville Brownian motion spends in $\\alpha$-thick points of the Gaussian Free Field, where $\\alpha$ is not necessarily equal to the parameter used in the construction of the geometry. This completes a conjecture in \\cite{berestycki2013diffusion}, where the corresponding upper bound was shown.\n  In the course of the proof, we obtain estimates on the (Euclidean) diffusivity exponent, which depends strongly on the nature of the starting point. For a Liouville typical point, it is $1/(2 - \\frac{\\gamma^2}{2})$. In particular, for $\\gamma > \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1705","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":""},"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":"2026-05-18T02:32:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V3UZ+o0uV16YJQ3o8KSZvjLJQiwqs1CL2oxdYpFVHKAys2L4ogQxgGCoAdIT2tFq9utv4XJvVE24Bij3NcMJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:06:54.288113Z"},"content_sha256":"fc968be412108aba742582d566ce47ae1ece56ddbc28e28ba75f1bf9822916ae","schema_version":"1.0","event_id":"sha256:fc968be412108aba742582d566ce47ae1ece56ddbc28e28ba75f1bf9822916ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FFFDEHCUL5DY3YFKWWQXR3TV5M/bundle.json","state_url":"https://pith.science/pith/FFFDEHCUL5DY3YFKWWQXR3TV5M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FFFDEHCUL5DY3YFKWWQXR3TV5M/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":"2026-06-02T11:06:54Z","links":{"resolver":"https://pith.science/pith/FFFDEHCUL5DY3YFKWWQXR3TV5M","bundle":"https://pith.science/pith/FFFDEHCUL5DY3YFKWWQXR3TV5M/bundle.json","state":"https://pith.science/pith/FFFDEHCUL5DY3YFKWWQXR3TV5M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FFFDEHCUL5DY3YFKWWQXR3TV5M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FFFDEHCUL5DY3YFKWWQXR3TV5M","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":"c2bc24646bb0c7d82668a2cb533a8f1b7419457e248ac2746e749025329737a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-04T15:39:22Z","title_canon_sha256":"0b7d705a01c1598d363ea22db23e494ed55384eeb38284088fc5dff0a57fa39e"},"schema_version":"1.0","source":{"id":"1412.1705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1705","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1705v1","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1705","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"pith_short_12","alias_value":"FFFDEHCUL5DY","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FFFDEHCUL5DY3YFK","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FFFDEHCU","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:fc968be412108aba742582d566ce47ae1ece56ddbc28e28ba75f1bf9822916ae","target":"graph","created_at":"2026-05-18T02:32:06Z","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"},"paper":{"abstract_excerpt":"We find a lower bound for the Hausdorff dimension that a Liouville Brownian motion spends in $\\alpha$-thick points of the Gaussian Free Field, where $\\alpha$ is not necessarily equal to the parameter used in the construction of the geometry. This completes a conjecture in \\cite{berestycki2013diffusion}, where the corresponding upper bound was shown.\n  In the course of the proof, we obtain estimates on the (Euclidean) diffusivity exponent, which depends strongly on the nature of the starting point. For a Liouville typical point, it is $1/(2 - \\frac{\\gamma^2}{2})$. In particular, for $\\gamma > \\","authors_text":"Henry Jackson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-04T15:39:22Z","title":"Liouville Brownian Motion and Thick Points of the Gaussian Free Field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1705","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:fe7c67cac1f9e17d17f557d9b08bc51c47e8d5c78fa6674e1b3b7e752477a81a","target":"record","created_at":"2026-05-18T02:32:06Z","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":"c2bc24646bb0c7d82668a2cb533a8f1b7419457e248ac2746e749025329737a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-04T15:39:22Z","title_canon_sha256":"0b7d705a01c1598d363ea22db23e494ed55384eeb38284088fc5dff0a57fa39e"},"schema_version":"1.0","source":{"id":"1412.1705","kind":"arxiv","version":1}},"canonical_sha256":"294a321c545f478de0aab5a178ee75eb3824211967ebe0360a1e6307fb6f2b67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"294a321c545f478de0aab5a178ee75eb3824211967ebe0360a1e6307fb6f2b67","first_computed_at":"2026-05-18T02:32:06.669199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:06.669199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fMfPbKkdcuByhTzqhMkcG1mvlZyv5+DPKk95bZLX1c7fj1kIEzjZRL+GshIRTO0jHLLkoatwuPS6fV7oYvPRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:06.669583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe7c67cac1f9e17d17f557d9b08bc51c47e8d5c78fa6674e1b3b7e752477a81a","sha256:fc968be412108aba742582d566ce47ae1ece56ddbc28e28ba75f1bf9822916ae"],"state_sha256":"3633d80ac867176b4a92b56fe3b13364dbb454354a3970b8d5fbc2c0fd9bbf98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VWE1LOyV/6UttwjtadEGsrMLBquJx6FJcarPXtJq4L0yrMk2QIz8dbhItv11wrI6Fhuf/s4MnBxYf74CwSF6Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T11:06:54.290097Z","bundle_sha256":"f1d154177a4e4502c3768380da901ee7113a87b1eb31cc757f00a4b621a2df73"}}