{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VMXWCTC3QGDEDMERTWDTJ4VSEC","short_pith_number":"pith:VMXWCTC3","canonical_record":{"source":{"id":"1506.03804","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-11T19:54:28Z","cross_cats_sorted":["math-ph","math.CV","math.MP"],"title_canon_sha256":"422628af9ab82e264b85331c4d735a1ed0b401a4a55401a58ef4271d79c3a96f","abstract_canon_sha256":"c7a3afdae42fed153ebb56b30679cb689603b54cd3dc9c9c01bc1726b0b941a1"},"schema_version":"1.0"},"canonical_sha256":"ab2f614c5b818641b0919d8734f2b2209a51860d6f4edc7775784339f8ffafc7","source":{"kind":"arxiv","id":"1506.03804","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03804","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03804v4","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03804","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"pith_short_12","alias_value":"VMXWCTC3QGDE","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VMXWCTC3QGDEDMER","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VMXWCTC3","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VMXWCTC3QGDEDMERTWDTJ4VSEC","target":"record","payload":{"canonical_record":{"source":{"id":"1506.03804","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-11T19:54:28Z","cross_cats_sorted":["math-ph","math.CV","math.MP"],"title_canon_sha256":"422628af9ab82e264b85331c4d735a1ed0b401a4a55401a58ef4271d79c3a96f","abstract_canon_sha256":"c7a3afdae42fed153ebb56b30679cb689603b54cd3dc9c9c01bc1726b0b941a1"},"schema_version":"1.0"},"canonical_sha256":"ab2f614c5b818641b0919d8734f2b2209a51860d6f4edc7775784339f8ffafc7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:41.989897Z","signature_b64":"1i040h9yv7ONrmrdC4LCQH/lxYPutxYH9IdYoXa97PrX+tamxUA31bntnxneC27fOSx9sU3D7GSgnkbJgLeYCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab2f614c5b818641b0919d8734f2b2209a51860d6f4edc7775784339f8ffafc7","last_reissued_at":"2026-05-18T00:03:41.989421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:41.989421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.03804","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":"2026-05-18T00:03:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OZV5nSbZOf71Hrwv8JtUxK+fFiy2cQBj0bOGFhSdXP1G+jyNuH5S5tghTkxjcQ4OOU1FIrAedUibcLVxv6aiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:21:47.150371Z"},"content_sha256":"fe596d5736de18128b91671db4e36b95b3328c7069fe05b9025ef239b953123a","schema_version":"1.0","event_id":"sha256:fe596d5736de18128b91671db4e36b95b3328c7069fe05b9025ef239b953123a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VMXWCTC3QGDEDMERTWDTJ4VSEC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Liouville quantum gravity spheres as matings of finite-diameter trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP"],"primary_cat":"math.PR","authors_text":"Jason Miller, Scott Sheffield","submitted_at":"2015-06-11T19:54:28Z","abstract_excerpt":"We show that the unit area Liouville quantum gravity sphere can be constructed in two equivalent ways. The first, which was introduced by the authors and Duplantier, uses a Bessel excursion measure to produce a Gaussian free field variant on the cylinder. The second uses a correlated Brownian loop and a \"mating of trees\" to produce a Liouville quantum gravity sphere decorated by a space-filling path.\n  In the special case that $\\gamma=\\sqrt{8/3}$, we present a third equivalent construction, which uses the excursion measure of a $3/2$-stable L\\'evy process (with only upward jumps) to produce a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03804","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":"2026-05-18T00:03:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ShzZIR39zMj9aH9pzoM/DorNgVjVeQR6SzcBrA6F4N944AwwGmTHDjmHITM95QDlmDMVeQv/l8AUsT8AWqsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:21:47.151037Z"},"content_sha256":"dda1dcdb7cc8c1f3a7234dee59d81cc5ae9a9974134876ecfedf96e6f35c0d8f","schema_version":"1.0","event_id":"sha256:dda1dcdb7cc8c1f3a7234dee59d81cc5ae9a9974134876ecfedf96e6f35c0d8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VMXWCTC3QGDEDMERTWDTJ4VSEC/bundle.json","state_url":"https://pith.science/pith/VMXWCTC3QGDEDMERTWDTJ4VSEC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VMXWCTC3QGDEDMERTWDTJ4VSEC/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":"2026-05-27T18:21:47Z","links":{"resolver":"https://pith.science/pith/VMXWCTC3QGDEDMERTWDTJ4VSEC","bundle":"https://pith.science/pith/VMXWCTC3QGDEDMERTWDTJ4VSEC/bundle.json","state":"https://pith.science/pith/VMXWCTC3QGDEDMERTWDTJ4VSEC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VMXWCTC3QGDEDMERTWDTJ4VSEC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VMXWCTC3QGDEDMERTWDTJ4VSEC","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":"c7a3afdae42fed153ebb56b30679cb689603b54cd3dc9c9c01bc1726b0b941a1","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-11T19:54:28Z","title_canon_sha256":"422628af9ab82e264b85331c4d735a1ed0b401a4a55401a58ef4271d79c3a96f"},"schema_version":"1.0","source":{"id":"1506.03804","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03804","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03804v4","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03804","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"pith_short_12","alias_value":"VMXWCTC3QGDE","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VMXWCTC3QGDEDMER","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VMXWCTC3","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:dda1dcdb7cc8c1f3a7234dee59d81cc5ae9a9974134876ecfedf96e6f35c0d8f","target":"graph","created_at":"2026-05-18T00:03:41Z","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 show that the unit area Liouville quantum gravity sphere can be constructed in two equivalent ways. The first, which was introduced by the authors and Duplantier, uses a Bessel excursion measure to produce a Gaussian free field variant on the cylinder. The second uses a correlated Brownian loop and a \"mating of trees\" to produce a Liouville quantum gravity sphere decorated by a space-filling path.\n  In the special case that $\\gamma=\\sqrt{8/3}$, we present a third equivalent construction, which uses the excursion measure of a $3/2$-stable L\\'evy process (with only upward jumps) to produce a ","authors_text":"Jason Miller, Scott Sheffield","cross_cats":["math-ph","math.CV","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-11T19:54:28Z","title":"Liouville quantum gravity spheres as matings of finite-diameter trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03804","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:fe596d5736de18128b91671db4e36b95b3328c7069fe05b9025ef239b953123a","target":"record","created_at":"2026-05-18T00:03:41Z","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":"c7a3afdae42fed153ebb56b30679cb689603b54cd3dc9c9c01bc1726b0b941a1","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-11T19:54:28Z","title_canon_sha256":"422628af9ab82e264b85331c4d735a1ed0b401a4a55401a58ef4271d79c3a96f"},"schema_version":"1.0","source":{"id":"1506.03804","kind":"arxiv","version":4}},"canonical_sha256":"ab2f614c5b818641b0919d8734f2b2209a51860d6f4edc7775784339f8ffafc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab2f614c5b818641b0919d8734f2b2209a51860d6f4edc7775784339f8ffafc7","first_computed_at":"2026-05-18T00:03:41.989421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:41.989421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1i040h9yv7ONrmrdC4LCQH/lxYPutxYH9IdYoXa97PrX+tamxUA31bntnxneC27fOSx9sU3D7GSgnkbJgLeYCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:41.989897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03804","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe596d5736de18128b91671db4e36b95b3328c7069fe05b9025ef239b953123a","sha256:dda1dcdb7cc8c1f3a7234dee59d81cc5ae9a9974134876ecfedf96e6f35c0d8f"],"state_sha256":"05a7a5d252c03720dfa56655575e62ec5d4f29debe5a304f2c37b48e1efc98a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iLuuWa4rlzZnHjdw7NSxhY1j34yE4OFhlaTR/aKSo70mw71oe/sDBtTyrTT7mjlo/d0uvVZNjuwe15cQ2lAhBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:21:47.154590Z","bundle_sha256":"a5fafe330c0d009401e90dec9a552988244ee5b699ad0dd69fe5a39ee05c883c"}}