{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KXKLHII66JZP4Q7C5MR2X54C4C","short_pith_number":"pith:KXKLHII6","canonical_record":{"source":{"id":"1608.03284","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-10T20:00:59Z","cross_cats_sorted":["cond-mat.stat-mech","gr-qc"],"title_canon_sha256":"afd49cc790f99342893b24e28142812c194570624b5277e12ba9a4dec943b021","abstract_canon_sha256":"0dd14f398cc1e03e1cbd8425a9541c1de660d7e873067abbfe0511f200e7523b"},"schema_version":"1.0"},"canonical_sha256":"55d4b3a11ef272fe43e2eb23abf782e0bb5e1804e0438cfc673615bfc60b29ef","source":{"kind":"arxiv","id":"1608.03284","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03284","created_at":"2026-05-18T00:41:39Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03284v1","created_at":"2026-05-18T00:41:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03284","created_at":"2026-05-18T00:41:39Z"},{"alias_kind":"pith_short_12","alias_value":"KXKLHII66JZP","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KXKLHII66JZP4Q7C","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KXKLHII6","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KXKLHII66JZP4Q7C5MR2X54C4C","target":"record","payload":{"canonical_record":{"source":{"id":"1608.03284","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-10T20:00:59Z","cross_cats_sorted":["cond-mat.stat-mech","gr-qc"],"title_canon_sha256":"afd49cc790f99342893b24e28142812c194570624b5277e12ba9a4dec943b021","abstract_canon_sha256":"0dd14f398cc1e03e1cbd8425a9541c1de660d7e873067abbfe0511f200e7523b"},"schema_version":"1.0"},"canonical_sha256":"55d4b3a11ef272fe43e2eb23abf782e0bb5e1804e0438cfc673615bfc60b29ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:39.379161Z","signature_b64":"qv4sN6/W0goK4JM0FZhpKUIpX9544Ci1oarFTb7ULvCxZQyYOSg/KgGsRh/Ca0u0J0ksB6kub0vDTkf1o1gOCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55d4b3a11ef272fe43e2eb23abf782e0bb5e1804e0438cfc673615bfc60b29ef","last_reissued_at":"2026-05-18T00:41:39.378574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:39.378574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.03284","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":"2026-05-18T00:41:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l/assOUjzjeWPnpuDU0qSBdIk5jTzlQ4NX1dQurnIYR1GoKKa7IZthcA5PDWITaWUqkanvqoYqWNLGUzHJtHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:18:54.580170Z"},"content_sha256":"8a774d1184b8a1bf5e1e2790638f599dc14049fa744a17485b976c7084f9bfb5","schema_version":"1.0","event_id":"sha256:8a774d1184b8a1bf5e1e2790638f599dc14049fa744a17485b976c7084f9bfb5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KXKLHII66JZP4Q7C5MR2X54C4C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","gr-qc"],"primary_cat":"hep-th","authors_text":"Alexander Maloney, Per Kraus","submitted_at":"2016-08-10T20:00:59Z","abstract_excerpt":"Modular covariance of torus one-point functions constrains the three point function coefficients of a two dimensional CFT. This leads to an asymptotic formula for the average value of light-heavy-heavy three point coefficients, generalizing Cardy's formula for the high energy density of states. The derivation uses certain asymptotic properties of one-point conformal blocks on the torus. Our asymptotic formula matches a dual AdS_3 computation of one point functions in a black hole background. This is evidence that the BTZ black hole geometry emerges upon course-graining over a suitable family o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03284","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":"2026-05-18T00:41:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aX9ReQFJSnN86beIGFv55V3G86F98QHkKSIxVibHdFMLd2D0RV/BWY1TLl5+6PoN66/8c12fhjU5FOeOIwRYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:18:54.580534Z"},"content_sha256":"5413959566141197115bb618e153f1f620a5783255ac0928121200bec83cbec6","schema_version":"1.0","event_id":"sha256:5413959566141197115bb618e153f1f620a5783255ac0928121200bec83cbec6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KXKLHII66JZP4Q7C5MR2X54C4C/bundle.json","state_url":"https://pith.science/pith/KXKLHII66JZP4Q7C5MR2X54C4C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KXKLHII66JZP4Q7C5MR2X54C4C/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":"2026-06-04T19:18:54Z","links":{"resolver":"https://pith.science/pith/KXKLHII66JZP4Q7C5MR2X54C4C","bundle":"https://pith.science/pith/KXKLHII66JZP4Q7C5MR2X54C4C/bundle.json","state":"https://pith.science/pith/KXKLHII66JZP4Q7C5MR2X54C4C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KXKLHII66JZP4Q7C5MR2X54C4C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KXKLHII66JZP4Q7C5MR2X54C4C","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":"0dd14f398cc1e03e1cbd8425a9541c1de660d7e873067abbfe0511f200e7523b","cross_cats_sorted":["cond-mat.stat-mech","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-10T20:00:59Z","title_canon_sha256":"afd49cc790f99342893b24e28142812c194570624b5277e12ba9a4dec943b021"},"schema_version":"1.0","source":{"id":"1608.03284","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03284","created_at":"2026-05-18T00:41:39Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03284v1","created_at":"2026-05-18T00:41:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03284","created_at":"2026-05-18T00:41:39Z"},{"alias_kind":"pith_short_12","alias_value":"KXKLHII66JZP","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KXKLHII66JZP4Q7C","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KXKLHII6","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:5413959566141197115bb618e153f1f620a5783255ac0928121200bec83cbec6","target":"graph","created_at":"2026-05-18T00:41:39Z","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":"Modular covariance of torus one-point functions constrains the three point function coefficients of a two dimensional CFT. This leads to an asymptotic formula for the average value of light-heavy-heavy three point coefficients, generalizing Cardy's formula for the high energy density of states. The derivation uses certain asymptotic properties of one-point conformal blocks on the torus. Our asymptotic formula matches a dual AdS_3 computation of one point functions in a black hole background. This is evidence that the BTZ black hole geometry emerges upon course-graining over a suitable family o","authors_text":"Alexander Maloney, Per Kraus","cross_cats":["cond-mat.stat-mech","gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-10T20:00:59Z","title":"A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03284","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":"sha256:8a774d1184b8a1bf5e1e2790638f599dc14049fa744a17485b976c7084f9bfb5","target":"record","created_at":"2026-05-18T00:41:39Z","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":"0dd14f398cc1e03e1cbd8425a9541c1de660d7e873067abbfe0511f200e7523b","cross_cats_sorted":["cond-mat.stat-mech","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-10T20:00:59Z","title_canon_sha256":"afd49cc790f99342893b24e28142812c194570624b5277e12ba9a4dec943b021"},"schema_version":"1.0","source":{"id":"1608.03284","kind":"arxiv","version":1}},"canonical_sha256":"55d4b3a11ef272fe43e2eb23abf782e0bb5e1804e0438cfc673615bfc60b29ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55d4b3a11ef272fe43e2eb23abf782e0bb5e1804e0438cfc673615bfc60b29ef","first_computed_at":"2026-05-18T00:41:39.378574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:39.378574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qv4sN6/W0goK4JM0FZhpKUIpX9544Ci1oarFTb7ULvCxZQyYOSg/KgGsRh/Ca0u0J0ksB6kub0vDTkf1o1gOCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:39.379161Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03284","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a774d1184b8a1bf5e1e2790638f599dc14049fa744a17485b976c7084f9bfb5","sha256:5413959566141197115bb618e153f1f620a5783255ac0928121200bec83cbec6"],"state_sha256":"cfd85db4ef905bb46f08ae84215a6e607f237827502a5c0366b866bb0250bdc5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fOheQ3grwCC8r4hn8B/d3y6w7m0AZVv2WIGILub75B8Z+QRO9XmY+xyztC+/ZFH7qH+Nq0OAlewAz/LwxIqODA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:18:54.582463Z","bundle_sha256":"532dcc5e7263a68a7053ebb112b2c7a29bcf1851da5ba115f0c89a4a3bf81383"}}