{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DT2CXKXPNKLIXGZ6LI44JZQXVD","short_pith_number":"pith:DT2CXKXP","canonical_record":{"source":{"id":"1305.0154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-01T12:17:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4dd7fc3eeb30410e183493a56e98d61e275ea3752853ffc29ab7e87e17902d32","abstract_canon_sha256":"410249172a9af68dd471adfdd61773d31f3abaee3efd145fea24c34c90a931a4"},"schema_version":"1.0"},"canonical_sha256":"1cf42baaef6a968b9b3e5a39c4e617a8fdb2ef36b4bca617f57cba15deaeeb69","source":{"kind":"arxiv","id":"1305.0154","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0154","created_at":"2026-05-18T01:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0154v1","created_at":"2026-05-18T01:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0154","created_at":"2026-05-18T01:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"DT2CXKXPNKLI","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DT2CXKXPNKLIXGZ6","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DT2CXKXP","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DT2CXKXPNKLIXGZ6LI44JZQXVD","target":"record","payload":{"canonical_record":{"source":{"id":"1305.0154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-01T12:17:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4dd7fc3eeb30410e183493a56e98d61e275ea3752853ffc29ab7e87e17902d32","abstract_canon_sha256":"410249172a9af68dd471adfdd61773d31f3abaee3efd145fea24c34c90a931a4"},"schema_version":"1.0"},"canonical_sha256":"1cf42baaef6a968b9b3e5a39c4e617a8fdb2ef36b4bca617f57cba15deaeeb69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:50:13.690180Z","signature_b64":"NHE9QGrIRnT+YSVXo9NnZCRYqaSSeoLUllj640ypQe7B081luqkQ7Y8WzU5HglGlrhWr40JuhvQIdxVIgaxzCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cf42baaef6a968b9b3e5a39c4e617a8fdb2ef36b4bca617f57cba15deaeeb69","last_reissued_at":"2026-05-18T01:50:13.689529Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:50:13.689529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.0154","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":"2026-05-18T01:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UE6AS5liZ64MDnbO4gzakl9/4/J16y2McDTs8e+pPHoUT37UuH1yY+kvepxjDWL2atzunnaa6bhq2vyBR28gDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:07:17.886184Z"},"content_sha256":"7970e82920abb29edbfb95a5142152878a6ea2d95ab226afb7f12c3ddc4c7602","schema_version":"1.0","event_id":"sha256:7970e82920abb29edbfb95a5142152878a6ea2d95ab226afb7f12c3ddc4c7602"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DT2CXKXPNKLIXGZ6LI44JZQXVD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral dimension of Liouville quantum gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"R\\'emi Rhodes, Vincent Vargas","submitted_at":"2013-05-01T12:17:59Z","abstract_excerpt":"This paper is concerned with computing the spectral dimension of 2d-Liouville quantum gravity. As a warm-up, we first treat the simple case of boundary Liouville quantum gravity. We prove that the spectral dimension is 1 via an exact expression for the boundary Liouville Brownian motion and heat kernel. Then we treat the 2d-case via a decomposition of time integral transforms of the Liouville heat kernel into Gaussian multiplicative chaos of Brownian bridges. We show that the spectral dimension is 2 in this case, as announced by physicists (see Ambj\\orn and al. in \\cite{amb}) fifteen years ago"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0154","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":"2026-05-18T01:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+MSwfbmykbk4hJSjYu12tHcvFGfBLYU1UYNYUrDtf47AnLpM8JEHo1SFOwrjbhdB3A69Je4l+nF1FnLLdpDeBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:07:17.886550Z"},"content_sha256":"eb2a02d00367cfd459a1d4c81563c3c4091334007bb4897690e4f919a6b569e3","schema_version":"1.0","event_id":"sha256:eb2a02d00367cfd459a1d4c81563c3c4091334007bb4897690e4f919a6b569e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DT2CXKXPNKLIXGZ6LI44JZQXVD/bundle.json","state_url":"https://pith.science/pith/DT2CXKXPNKLIXGZ6LI44JZQXVD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DT2CXKXPNKLIXGZ6LI44JZQXVD/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":"2026-05-30T05:07:17Z","links":{"resolver":"https://pith.science/pith/DT2CXKXPNKLIXGZ6LI44JZQXVD","bundle":"https://pith.science/pith/DT2CXKXPNKLIXGZ6LI44JZQXVD/bundle.json","state":"https://pith.science/pith/DT2CXKXPNKLIXGZ6LI44JZQXVD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DT2CXKXPNKLIXGZ6LI44JZQXVD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DT2CXKXPNKLIXGZ6LI44JZQXVD","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":"410249172a9af68dd471adfdd61773d31f3abaee3efd145fea24c34c90a931a4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-01T12:17:59Z","title_canon_sha256":"4dd7fc3eeb30410e183493a56e98d61e275ea3752853ffc29ab7e87e17902d32"},"schema_version":"1.0","source":{"id":"1305.0154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0154","created_at":"2026-05-18T01:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0154v1","created_at":"2026-05-18T01:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0154","created_at":"2026-05-18T01:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"DT2CXKXPNKLI","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DT2CXKXPNKLIXGZ6","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DT2CXKXP","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:eb2a02d00367cfd459a1d4c81563c3c4091334007bb4897690e4f919a6b569e3","target":"graph","created_at":"2026-05-18T01:50:13Z","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":"This paper is concerned with computing the spectral dimension of 2d-Liouville quantum gravity. As a warm-up, we first treat the simple case of boundary Liouville quantum gravity. We prove that the spectral dimension is 1 via an exact expression for the boundary Liouville Brownian motion and heat kernel. Then we treat the 2d-case via a decomposition of time integral transforms of the Liouville heat kernel into Gaussian multiplicative chaos of Brownian bridges. We show that the spectral dimension is 2 in this case, as announced by physicists (see Ambj\\orn and al. in \\cite{amb}) fifteen years ago","authors_text":"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":"2013-05-01T12:17:59Z","title":"Spectral dimension of Liouville quantum gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0154","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":"sha256:7970e82920abb29edbfb95a5142152878a6ea2d95ab226afb7f12c3ddc4c7602","target":"record","created_at":"2026-05-18T01:50:13Z","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":"410249172a9af68dd471adfdd61773d31f3abaee3efd145fea24c34c90a931a4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-01T12:17:59Z","title_canon_sha256":"4dd7fc3eeb30410e183493a56e98d61e275ea3752853ffc29ab7e87e17902d32"},"schema_version":"1.0","source":{"id":"1305.0154","kind":"arxiv","version":1}},"canonical_sha256":"1cf42baaef6a968b9b3e5a39c4e617a8fdb2ef36b4bca617f57cba15deaeeb69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cf42baaef6a968b9b3e5a39c4e617a8fdb2ef36b4bca617f57cba15deaeeb69","first_computed_at":"2026-05-18T01:50:13.689529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:50:13.689529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NHE9QGrIRnT+YSVXo9NnZCRYqaSSeoLUllj640ypQe7B081luqkQ7Y8WzU5HglGlrhWr40JuhvQIdxVIgaxzCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:50:13.690180Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7970e82920abb29edbfb95a5142152878a6ea2d95ab226afb7f12c3ddc4c7602","sha256:eb2a02d00367cfd459a1d4c81563c3c4091334007bb4897690e4f919a6b569e3"],"state_sha256":"04114922419bbabd27a13e7460e34d458b75b179bd301a93ac4938ae5fbc726f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"htOonskCHeodhetH6q/3PG2zTodwM6LLHvuTwVFq9iTgJemGS4XhPA3eK5fjWavmKZ9KjumVWOtl33FGY4UQAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:07:17.888582Z","bundle_sha256":"1b3fd5c1906a5cc65bcd9e84a64abad22023a03fe85ae7a163eb11621af43963"}}