{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JSBP6KFF7DIDLI3OKZARBW5UM6","short_pith_number":"pith:JSBP6KFF","canonical_record":{"source":{"id":"1510.00014","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-30T20:11:09Z","cross_cats_sorted":[],"title_canon_sha256":"98f547c782b40f49cc8602ecc606b74327c527a759532251e53556e6190ecfd5","abstract_canon_sha256":"b639b1b2f581ed902c9657530e0574119a34a3ad362105000bb5b8f4f115fd9f"},"schema_version":"1.0"},"canonical_sha256":"4c82ff28a5f8d035a36e564110dbb467a2d4c69c803a96dc74ae5a944c175000","source":{"kind":"arxiv","id":"1510.00014","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00014","created_at":"2026-05-18T01:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00014v1","created_at":"2026-05-18T01:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00014","created_at":"2026-05-18T01:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"JSBP6KFF7DID","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JSBP6KFF7DIDLI3O","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JSBP6KFF","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JSBP6KFF7DIDLI3OKZARBW5UM6","target":"record","payload":{"canonical_record":{"source":{"id":"1510.00014","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-30T20:11:09Z","cross_cats_sorted":[],"title_canon_sha256":"98f547c782b40f49cc8602ecc606b74327c527a759532251e53556e6190ecfd5","abstract_canon_sha256":"b639b1b2f581ed902c9657530e0574119a34a3ad362105000bb5b8f4f115fd9f"},"schema_version":"1.0"},"canonical_sha256":"4c82ff28a5f8d035a36e564110dbb467a2d4c69c803a96dc74ae5a944c175000","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:29.248278Z","signature_b64":"ODkV4vErshG/o+mU7CiEMjnch/63rKskuR+Txmh7IXTy9tDzirVGqOuXxAURmf4GdyA7IiHBl+qDtQDLjVpBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c82ff28a5f8d035a36e564110dbb467a2d4c69c803a96dc74ae5a944c175000","last_reissued_at":"2026-05-18T01:14:29.247744Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:29.247744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.00014","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":"2026-05-18T01:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XpWtmqLh5a1FqA0sIEis+P4oogURaEfcvEo9eMFU2GbVYTbAPbAEuZazJIkG0/GfEGFeMdEBlTP7+3FYmofiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:40:57.989554Z"},"content_sha256":"dfd05ae1c4b83306940ffb22310b8f1620a4c338998e022f3ba132548a2e1910","schema_version":"1.0","event_id":"sha256:dfd05ae1c4b83306940ffb22310b8f1620a4c338998e022f3ba132548a2e1910"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JSBP6KFF7DIDLI3OKZARBW5UM6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hawking from Catalan","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A. Liam Fitzpatrick, Jared Kaplan, Junpu Wang, Matthew T. Walters","submitted_at":"2015-09-30T20:11:09Z","abstract_excerpt":"The Virasoro algebra determines all `graviton' matrix elements in AdS$_3$/CFT$_2$. We study the explicit exchange of any number of Virasoro gravitons between heavy and light CFT$_2$ operators at large central charge. These graviton exchanges can be written in terms of new on-shell tree diagrams, organized in a perturbative expansion in $h_H/c$, the heavy operator dimension divided by the central charge. The Virasoro vacuum conformal block, which is the sum of all the tree diagrams, obeys a differential recursion relation generalizing that of the Catalan numbers. We use this recursion relation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00014","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":"2026-05-18T01:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2uLxhFtNyCRaA+0kZdNwJOCO4aimt/nxlKObej4YDCa7EH44+/5M9a+fzvS3mTfnzuB6TBWnKml8KP8ATzNyAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:40:57.989895Z"},"content_sha256":"f5818291f11d8eca60b1c6f2d3325891d25df7a82b08ef0883546a35a93d8b31","schema_version":"1.0","event_id":"sha256:f5818291f11d8eca60b1c6f2d3325891d25df7a82b08ef0883546a35a93d8b31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JSBP6KFF7DIDLI3OKZARBW5UM6/bundle.json","state_url":"https://pith.science/pith/JSBP6KFF7DIDLI3OKZARBW5UM6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JSBP6KFF7DIDLI3OKZARBW5UM6/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":"2026-06-01T19:40:57Z","links":{"resolver":"https://pith.science/pith/JSBP6KFF7DIDLI3OKZARBW5UM6","bundle":"https://pith.science/pith/JSBP6KFF7DIDLI3OKZARBW5UM6/bundle.json","state":"https://pith.science/pith/JSBP6KFF7DIDLI3OKZARBW5UM6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JSBP6KFF7DIDLI3OKZARBW5UM6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JSBP6KFF7DIDLI3OKZARBW5UM6","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":"b639b1b2f581ed902c9657530e0574119a34a3ad362105000bb5b8f4f115fd9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-30T20:11:09Z","title_canon_sha256":"98f547c782b40f49cc8602ecc606b74327c527a759532251e53556e6190ecfd5"},"schema_version":"1.0","source":{"id":"1510.00014","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00014","created_at":"2026-05-18T01:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00014v1","created_at":"2026-05-18T01:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00014","created_at":"2026-05-18T01:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"JSBP6KFF7DID","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JSBP6KFF7DIDLI3O","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JSBP6KFF","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:f5818291f11d8eca60b1c6f2d3325891d25df7a82b08ef0883546a35a93d8b31","target":"graph","created_at":"2026-05-18T01:14:29Z","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":"The Virasoro algebra determines all `graviton' matrix elements in AdS$_3$/CFT$_2$. We study the explicit exchange of any number of Virasoro gravitons between heavy and light CFT$_2$ operators at large central charge. These graviton exchanges can be written in terms of new on-shell tree diagrams, organized in a perturbative expansion in $h_H/c$, the heavy operator dimension divided by the central charge. The Virasoro vacuum conformal block, which is the sum of all the tree diagrams, obeys a differential recursion relation generalizing that of the Catalan numbers. We use this recursion relation ","authors_text":"A. Liam Fitzpatrick, Jared Kaplan, Junpu Wang, Matthew T. Walters","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-30T20:11:09Z","title":"Hawking from Catalan"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00014","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:dfd05ae1c4b83306940ffb22310b8f1620a4c338998e022f3ba132548a2e1910","target":"record","created_at":"2026-05-18T01:14:29Z","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":"b639b1b2f581ed902c9657530e0574119a34a3ad362105000bb5b8f4f115fd9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-30T20:11:09Z","title_canon_sha256":"98f547c782b40f49cc8602ecc606b74327c527a759532251e53556e6190ecfd5"},"schema_version":"1.0","source":{"id":"1510.00014","kind":"arxiv","version":1}},"canonical_sha256":"4c82ff28a5f8d035a36e564110dbb467a2d4c69c803a96dc74ae5a944c175000","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c82ff28a5f8d035a36e564110dbb467a2d4c69c803a96dc74ae5a944c175000","first_computed_at":"2026-05-18T01:14:29.247744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:29.247744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ODkV4vErshG/o+mU7CiEMjnch/63rKskuR+Txmh7IXTy9tDzirVGqOuXxAURmf4GdyA7IiHBl+qDtQDLjVpBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:29.248278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00014","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfd05ae1c4b83306940ffb22310b8f1620a4c338998e022f3ba132548a2e1910","sha256:f5818291f11d8eca60b1c6f2d3325891d25df7a82b08ef0883546a35a93d8b31"],"state_sha256":"6b96f42c6bf2381d412f68c3a7acbb0c37fb98c89e602fe63658cd08420b9607"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"21WpEr1b9BSaxLTUYJQhyMlpX2QyYZKtTD0VEDRWICyJVhQb9lbcfK56MR5Jyj2iJytMXkzWA4KOmPVFUDKVAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:40:57.991997Z","bundle_sha256":"d8139868036926a69c0dadb6a16cb2081e7dea6b6524322da224a9beddb355ef"}}