{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:K4TJIPAPMOCO32IPPR4DBYSZ2T","short_pith_number":"pith:K4TJIPAP","canonical_record":{"source":{"id":"0712.3775","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2007-12-21T19:09:31Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"1413cd3d04e7b445938f24a7d15b9b5e1c1f80a3811d40947354fa47ec0eca02","abstract_canon_sha256":"29df9a10583b113d8a3466259c659c0665b5d93d9c6fbee18c7a3a8ad807e059"},"schema_version":"1.0"},"canonical_sha256":"5726943c0f6384ede90f7c7830e259d4c3f93176f94d6a56e6aa2e010d1b46f3","source":{"kind":"arxiv","id":"0712.3775","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.3775","created_at":"2026-05-18T04:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"0712.3775v2","created_at":"2026-05-18T04:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.3775","created_at":"2026-05-18T04:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"K4TJIPAPMOCO","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"K4TJIPAPMOCO32IP","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"K4TJIPAP","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:K4TJIPAPMOCO32IPPR4DBYSZ2T","target":"record","payload":{"canonical_record":{"source":{"id":"0712.3775","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2007-12-21T19:09:31Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"1413cd3d04e7b445938f24a7d15b9b5e1c1f80a3811d40947354fa47ec0eca02","abstract_canon_sha256":"29df9a10583b113d8a3466259c659c0665b5d93d9c6fbee18c7a3a8ad807e059"},"schema_version":"1.0"},"canonical_sha256":"5726943c0f6384ede90f7c7830e259d4c3f93176f94d6a56e6aa2e010d1b46f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:04.226385Z","signature_b64":"ncCE7wW9Q6nfoAHk76AdhQFrC8IuzjatG1IHGJyJ4hn0uWfoeQQJoBn/e/DrrGtq6rXqGuIpG8CBsYkseJJyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5726943c0f6384ede90f7c7830e259d4c3f93176f94d6a56e6aa2e010d1b46f3","last_reissued_at":"2026-05-18T04:09:04.225702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:04.225702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.3775","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:09:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+SaT0r25MH9qrDxquLHLNZyH7zGMmlye4aU5fgJCRLIQgyhVnXHxFaCuGVlKZXHiKPhI+SD3XFkWVa1YuGhRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:23:16.232599Z"},"content_sha256":"be2073018d249d7a45a4b87ba8d034548dbf801e3a2a762ddf5cef982793b25a","schema_version":"1.0","event_id":"sha256:be2073018d249d7a45a4b87ba8d034548dbf801e3a2a762ddf5cef982793b25a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:K4TJIPAPMOCO32IPPR4DBYSZ2T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Liouville gravity from Einstein gravity","license":"","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"D. Grumiller, R. Jackiw","submitted_at":"2007-12-21T19:09:31Z","abstract_excerpt":"We show that Liouville gravity arises as the limit of pure Einstein gravity in 2+epsilon dimensions as epsilon goes to zero, provided Newton's constant scales with epsilon. Our procedure - spherical reduction, dualization, limit, dualizing back - passes several consistency tests: geometric properties, interactions with matter and the Bekenstein-Hawking entropy are as expected from Einstein gravity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.3775","kind":"arxiv","version":2},"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":"2026-05-18T04:09:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/bs5I/bwlo5hhX+wSsppePMdxj40mLzifKsJ9FiQffmJhKTXnabYd7+tmFaZ6J9LSra1RniE4eckUPrJNeP7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:23:16.232953Z"},"content_sha256":"0311547736d4cd4f5b680c64d1d1dd292f35c05d1940cae434e8b6942919fd92","schema_version":"1.0","event_id":"sha256:0311547736d4cd4f5b680c64d1d1dd292f35c05d1940cae434e8b6942919fd92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K4TJIPAPMOCO32IPPR4DBYSZ2T/bundle.json","state_url":"https://pith.science/pith/K4TJIPAPMOCO32IPPR4DBYSZ2T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K4TJIPAPMOCO32IPPR4DBYSZ2T/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":"2026-05-22T23:23:16Z","links":{"resolver":"https://pith.science/pith/K4TJIPAPMOCO32IPPR4DBYSZ2T","bundle":"https://pith.science/pith/K4TJIPAPMOCO32IPPR4DBYSZ2T/bundle.json","state":"https://pith.science/pith/K4TJIPAPMOCO32IPPR4DBYSZ2T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K4TJIPAPMOCO32IPPR4DBYSZ2T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:K4TJIPAPMOCO32IPPR4DBYSZ2T","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":"29df9a10583b113d8a3466259c659c0665b5d93d9c6fbee18c7a3a8ad807e059","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"2007-12-21T19:09:31Z","title_canon_sha256":"1413cd3d04e7b445938f24a7d15b9b5e1c1f80a3811d40947354fa47ec0eca02"},"schema_version":"1.0","source":{"id":"0712.3775","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.3775","created_at":"2026-05-18T04:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"0712.3775v2","created_at":"2026-05-18T04:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.3775","created_at":"2026-05-18T04:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"K4TJIPAPMOCO","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"K4TJIPAPMOCO32IP","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"K4TJIPAP","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:0311547736d4cd4f5b680c64d1d1dd292f35c05d1940cae434e8b6942919fd92","target":"graph","created_at":"2026-05-18T04:09:04Z","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 Liouville gravity arises as the limit of pure Einstein gravity in 2+epsilon dimensions as epsilon goes to zero, provided Newton's constant scales with epsilon. Our procedure - spherical reduction, dualization, limit, dualizing back - passes several consistency tests: geometric properties, interactions with matter and the Bekenstein-Hawking entropy are as expected from Einstein gravity.","authors_text":"D. Grumiller, R. Jackiw","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2007-12-21T19:09:31Z","title":"Liouville gravity from Einstein gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.3775","kind":"arxiv","version":2},"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:be2073018d249d7a45a4b87ba8d034548dbf801e3a2a762ddf5cef982793b25a","target":"record","created_at":"2026-05-18T04:09:04Z","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":"29df9a10583b113d8a3466259c659c0665b5d93d9c6fbee18c7a3a8ad807e059","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"2007-12-21T19:09:31Z","title_canon_sha256":"1413cd3d04e7b445938f24a7d15b9b5e1c1f80a3811d40947354fa47ec0eca02"},"schema_version":"1.0","source":{"id":"0712.3775","kind":"arxiv","version":2}},"canonical_sha256":"5726943c0f6384ede90f7c7830e259d4c3f93176f94d6a56e6aa2e010d1b46f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5726943c0f6384ede90f7c7830e259d4c3f93176f94d6a56e6aa2e010d1b46f3","first_computed_at":"2026-05-18T04:09:04.225702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:04.225702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ncCE7wW9Q6nfoAHk76AdhQFrC8IuzjatG1IHGJyJ4hn0uWfoeQQJoBn/e/DrrGtq6rXqGuIpG8CBsYkseJJyCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:04.226385Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.3775","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be2073018d249d7a45a4b87ba8d034548dbf801e3a2a762ddf5cef982793b25a","sha256:0311547736d4cd4f5b680c64d1d1dd292f35c05d1940cae434e8b6942919fd92"],"state_sha256":"cdfd19ca42bb6f7b695fb0646979bf1ee6305b78e64516aae9bff2ea2889b4b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rgZ0gJkqkjlr9NHVBe/PbRtBLRk4lIqJ4wE64zd/Xf9MvJuK8CFNSwV8I7unI0gKE0g9NSAqARKzTKOZja97Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T23:23:16.236193Z","bundle_sha256":"7b782740cf01ee9f013183154cec8660c7986125ea3423248d63299cb69036d2"}}