{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QMFASGSVOKRAHAZHWN4X23QZ5V","short_pith_number":"pith:QMFASGSV","canonical_record":{"source":{"id":"1301.2876","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-14T07:46:22Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"20a2ccb8fe1f823e7105dc1500c96051d7fe42b4e36f4ac7d0bc50d30f0d028c","abstract_canon_sha256":"8a81ad79c67afe3793fd927f1c526fb78a1ca5dbdb3c6f65bf59541519fd180e"},"schema_version":"1.0"},"canonical_sha256":"830a091a5572a2038327b3797d6e19ed781e2fd1c56d08aefd283017278848d9","source":{"kind":"arxiv","id":"1301.2876","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2876","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2876v4","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2876","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"pith_short_12","alias_value":"QMFASGSVOKRA","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QMFASGSVOKRAHAZH","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QMFASGSV","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QMFASGSVOKRAHAZHWN4X23QZ5V","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2876","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-14T07:46:22Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"20a2ccb8fe1f823e7105dc1500c96051d7fe42b4e36f4ac7d0bc50d30f0d028c","abstract_canon_sha256":"8a81ad79c67afe3793fd927f1c526fb78a1ca5dbdb3c6f65bf59541519fd180e"},"schema_version":"1.0"},"canonical_sha256":"830a091a5572a2038327b3797d6e19ed781e2fd1c56d08aefd283017278848d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:24.879773Z","signature_b64":"ekZ6FPEuD829NlLSPnyba7g8fofUOFTyg0owbMBbTGJuM4b6tbCmCcqnvvtBg8mzDhQj1PKDBbjO1IVF7NuwAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"830a091a5572a2038327b3797d6e19ed781e2fd1c56d08aefd283017278848d9","last_reissued_at":"2026-05-18T01:06:24.879381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:24.879381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2876","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2FEeuHwGxNVQPJ+wDy8rxKLnde64LKSbywazGt44MsPrD/dyV3p53u+KSYlOhr3DQm66m/iZRinK3sxU/ExkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:51:19.345897Z"},"content_sha256":"e323b959f4e0c9553756e4b9ffb81b86750838ba5e9f1ae119878a698176c090","schema_version":"1.0","event_id":"sha256:e323b959f4e0c9553756e4b9ffb81b86750838ba5e9f1ae119878a698176c090"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QMFASGSVOKRAHAZHWN4X23QZ5V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Liouville Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Christophe Garban, R\\'emi Rhodes, Vincent Vargas","submitted_at":"2013-01-14T07:46:22Z","abstract_excerpt":"We construct a stochastic process, called the Liouville Brownian motion, which is the Brownian motion associated to the metric $e^{\\gamma X(z)}\\,dz^2$, $\\gamma<\\gamma_c=2$ and $X$ is a Gaussian Free Field. Such a process is conjectured to be related to the scaling limit of random walks on large planar maps eventually weighted by a model of statistical physics which are embedded in the Euclidean plane or in the sphere in a conformal manner. The construction amounts to changing the speed of a standard two-dimensional Brownian motion $B_t$ depending on the local behavior of the Liouville measure "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2876","kind":"arxiv","version":4},"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":"2026-05-18T01:06:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fQCyH26RWbKktRdxqeweBrfUVi0MurekURlDnH4pkvUNsBWi5NfG0gLBlbZy+/IfrS++/Xyw2O5ypKTkebnKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:51:19.346243Z"},"content_sha256":"d83609b437bb251867b1e6b5a9173797f3753dc8285625485747f90b9a3c59eb","schema_version":"1.0","event_id":"sha256:d83609b437bb251867b1e6b5a9173797f3753dc8285625485747f90b9a3c59eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QMFASGSVOKRAHAZHWN4X23QZ5V/bundle.json","state_url":"https://pith.science/pith/QMFASGSVOKRAHAZHWN4X23QZ5V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QMFASGSVOKRAHAZHWN4X23QZ5V/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":"2026-05-30T03:51:19Z","links":{"resolver":"https://pith.science/pith/QMFASGSVOKRAHAZHWN4X23QZ5V","bundle":"https://pith.science/pith/QMFASGSVOKRAHAZHWN4X23QZ5V/bundle.json","state":"https://pith.science/pith/QMFASGSVOKRAHAZHWN4X23QZ5V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QMFASGSVOKRAHAZHWN4X23QZ5V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QMFASGSVOKRAHAZHWN4X23QZ5V","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":"8a81ad79c67afe3793fd927f1c526fb78a1ca5dbdb3c6f65bf59541519fd180e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-14T07:46:22Z","title_canon_sha256":"20a2ccb8fe1f823e7105dc1500c96051d7fe42b4e36f4ac7d0bc50d30f0d028c"},"schema_version":"1.0","source":{"id":"1301.2876","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2876","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2876v4","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2876","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"pith_short_12","alias_value":"QMFASGSVOKRA","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QMFASGSVOKRAHAZH","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QMFASGSV","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:d83609b437bb251867b1e6b5a9173797f3753dc8285625485747f90b9a3c59eb","target":"graph","created_at":"2026-05-18T01:06:24Z","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 construct a stochastic process, called the Liouville Brownian motion, which is the Brownian motion associated to the metric $e^{\\gamma X(z)}\\,dz^2$, $\\gamma<\\gamma_c=2$ and $X$ is a Gaussian Free Field. Such a process is conjectured to be related to the scaling limit of random walks on large planar maps eventually weighted by a model of statistical physics which are embedded in the Euclidean plane or in the sphere in a conformal manner. The construction amounts to changing the speed of a standard two-dimensional Brownian motion $B_t$ depending on the local behavior of the Liouville measure ","authors_text":"Christophe Garban, R\\'emi Rhodes, Vincent Vargas","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-14T07:46:22Z","title":"Liouville Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2876","kind":"arxiv","version":4},"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:e323b959f4e0c9553756e4b9ffb81b86750838ba5e9f1ae119878a698176c090","target":"record","created_at":"2026-05-18T01:06:24Z","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":"8a81ad79c67afe3793fd927f1c526fb78a1ca5dbdb3c6f65bf59541519fd180e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-14T07:46:22Z","title_canon_sha256":"20a2ccb8fe1f823e7105dc1500c96051d7fe42b4e36f4ac7d0bc50d30f0d028c"},"schema_version":"1.0","source":{"id":"1301.2876","kind":"arxiv","version":4}},"canonical_sha256":"830a091a5572a2038327b3797d6e19ed781e2fd1c56d08aefd283017278848d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"830a091a5572a2038327b3797d6e19ed781e2fd1c56d08aefd283017278848d9","first_computed_at":"2026-05-18T01:06:24.879381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:24.879381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ekZ6FPEuD829NlLSPnyba7g8fofUOFTyg0owbMBbTGJuM4b6tbCmCcqnvvtBg8mzDhQj1PKDBbjO1IVF7NuwAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:24.879773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2876","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e323b959f4e0c9553756e4b9ffb81b86750838ba5e9f1ae119878a698176c090","sha256:d83609b437bb251867b1e6b5a9173797f3753dc8285625485747f90b9a3c59eb"],"state_sha256":"28e943353d72184fe92cc33178a12395a2a150a4b6488a1149edc01c29b4aad8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hqnWnEwF6FMFB8SYjyiDvrGI7L9aymZSt9yXIbe9LkfEolqoh8JB5zt+w2AwxhLpeW0dLiNyDuazl9vh9CIaDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T03:51:19.348400Z","bundle_sha256":"8bdb7de0755ab2956e895cbbcf0807395ea278c9115b7d33e34bee7dfd69b2f8"}}