{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RML2GOLJYR2Q7AO4GBWQQTUGMO","short_pith_number":"pith:RML2GOLJ","canonical_record":{"source":{"id":"1511.08002","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-25T09:39:02Z","cross_cats_sorted":[],"title_canon_sha256":"b00f0d87d3f057ee2ebb793247575dd0cf2ff90b27513263db5db0d87c09e6f8","abstract_canon_sha256":"926732c6cde99b5b6ffabde13412021991714f58a4f9818fea749dd442ff8073"},"schema_version":"1.0"},"canonical_sha256":"8b17a33969c4750f81dc306d084e866397096c0569415b803766de7868d84310","source":{"kind":"arxiv","id":"1511.08002","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08002","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08002v3","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08002","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"pith_short_12","alias_value":"RML2GOLJYR2Q","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RML2GOLJYR2Q7AO4","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RML2GOLJ","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RML2GOLJYR2Q7AO4GBWQQTUGMO","target":"record","payload":{"canonical_record":{"source":{"id":"1511.08002","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-25T09:39:02Z","cross_cats_sorted":[],"title_canon_sha256":"b00f0d87d3f057ee2ebb793247575dd0cf2ff90b27513263db5db0d87c09e6f8","abstract_canon_sha256":"926732c6cde99b5b6ffabde13412021991714f58a4f9818fea749dd442ff8073"},"schema_version":"1.0"},"canonical_sha256":"8b17a33969c4750f81dc306d084e866397096c0569415b803766de7868d84310","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:16.409087Z","signature_b64":"tM/qs+20m+Te/uakPqBFdLih3UPGYiEZl67VkpihWGPicNhUMS8krhNdixVY+K+cBRtU4l0/XqM+J/Tw1YVFDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b17a33969c4750f81dc306d084e866397096c0569415b803766de7868d84310","last_reissued_at":"2026-05-18T01:20:16.408433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:16.408433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.08002","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"faOkxB2XUzYYgK+AFXUzDrhCFDv2sLPbDg//lxXLA9nUbeOeJdv0yifsT8y9ASPwVLpaJ1Jepq8mBqb1d7Y6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:30:01.296595Z"},"content_sha256":"a0256c0ad638492b7d6c764366f9b818cdc20dd912a99d72427a0f16709f6778","schema_version":"1.0","event_id":"sha256:a0256c0ad638492b7d6c764366f9b818cdc20dd912a99d72427a0f16709f6778"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RML2GOLJYR2Q7AO4GBWQQTUGMO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kerr/Fluid Duality and Singularity of Solutions to the Fluid Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Ippei Fujisawa, Ryuichi Nakayama","submitted_at":"2015-11-25T09:39:02Z","abstract_excerpt":"An equation for a viscous incompressible fluid on a spheroidal surface which is dual to the perturbation around the near-near horizon extreme Kerr (n-NHEK) black hole is derived. It is also shown that an expansion scalar $\\theta$ of a congruence of null geodesics on the null horizon of the perturbed n-NHEK spacetime, which is dual to a viscous incompressible fluid, is not positive semi-definite, even if initial conditions on the velocity are smooth. Unless initial conditions are elaborated, caustics of null congruence will occur on the horizon in the future. A similar result is obtained for a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08002","kind":"arxiv","version":3},"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":"2026-05-18T01:20:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VNpNUODDXd/hHj6Cvlu0yiVEBglUM+budSOwBPWe2GCVJM4Vrk0SGnrBXriXQzrfo1mWAP+RvCThyo+Oi2SzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:30:01.296943Z"},"content_sha256":"420e295a1d08d7bf39938d9c3d9efc8298583a0216c5bb0c1609f44400047441","schema_version":"1.0","event_id":"sha256:420e295a1d08d7bf39938d9c3d9efc8298583a0216c5bb0c1609f44400047441"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RML2GOLJYR2Q7AO4GBWQQTUGMO/bundle.json","state_url":"https://pith.science/pith/RML2GOLJYR2Q7AO4GBWQQTUGMO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RML2GOLJYR2Q7AO4GBWQQTUGMO/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":"2026-06-24T16:30:01Z","links":{"resolver":"https://pith.science/pith/RML2GOLJYR2Q7AO4GBWQQTUGMO","bundle":"https://pith.science/pith/RML2GOLJYR2Q7AO4GBWQQTUGMO/bundle.json","state":"https://pith.science/pith/RML2GOLJYR2Q7AO4GBWQQTUGMO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RML2GOLJYR2Q7AO4GBWQQTUGMO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RML2GOLJYR2Q7AO4GBWQQTUGMO","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":"926732c6cde99b5b6ffabde13412021991714f58a4f9818fea749dd442ff8073","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-25T09:39:02Z","title_canon_sha256":"b00f0d87d3f057ee2ebb793247575dd0cf2ff90b27513263db5db0d87c09e6f8"},"schema_version":"1.0","source":{"id":"1511.08002","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08002","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08002v3","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08002","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"pith_short_12","alias_value":"RML2GOLJYR2Q","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RML2GOLJYR2Q7AO4","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RML2GOLJ","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:420e295a1d08d7bf39938d9c3d9efc8298583a0216c5bb0c1609f44400047441","target":"graph","created_at":"2026-05-18T01:20:16Z","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":"An equation for a viscous incompressible fluid on a spheroidal surface which is dual to the perturbation around the near-near horizon extreme Kerr (n-NHEK) black hole is derived. It is also shown that an expansion scalar $\\theta$ of a congruence of null geodesics on the null horizon of the perturbed n-NHEK spacetime, which is dual to a viscous incompressible fluid, is not positive semi-definite, even if initial conditions on the velocity are smooth. Unless initial conditions are elaborated, caustics of null congruence will occur on the horizon in the future. A similar result is obtained for a ","authors_text":"Ippei Fujisawa, Ryuichi Nakayama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-25T09:39:02Z","title":"Kerr/Fluid Duality and Singularity of Solutions to the Fluid Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08002","kind":"arxiv","version":3},"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:a0256c0ad638492b7d6c764366f9b818cdc20dd912a99d72427a0f16709f6778","target":"record","created_at":"2026-05-18T01:20:16Z","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":"926732c6cde99b5b6ffabde13412021991714f58a4f9818fea749dd442ff8073","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-25T09:39:02Z","title_canon_sha256":"b00f0d87d3f057ee2ebb793247575dd0cf2ff90b27513263db5db0d87c09e6f8"},"schema_version":"1.0","source":{"id":"1511.08002","kind":"arxiv","version":3}},"canonical_sha256":"8b17a33969c4750f81dc306d084e866397096c0569415b803766de7868d84310","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b17a33969c4750f81dc306d084e866397096c0569415b803766de7868d84310","first_computed_at":"2026-05-18T01:20:16.408433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:16.408433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tM/qs+20m+Te/uakPqBFdLih3UPGYiEZl67VkpihWGPicNhUMS8krhNdixVY+K+cBRtU4l0/XqM+J/Tw1YVFDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:16.409087Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08002","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0256c0ad638492b7d6c764366f9b818cdc20dd912a99d72427a0f16709f6778","sha256:420e295a1d08d7bf39938d9c3d9efc8298583a0216c5bb0c1609f44400047441"],"state_sha256":"4f7f7196c98b3ed559cf8621ecc3ee0209dfaed940dc5fc3749d26e21aaf4845"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fOGNO4enQOBP3/cRFkR2mfi9kHdRZIPW5DqnxFE/8ar1XaHonglt26+4CeC+54R0EjtDnd6uUP5DKFuW8XPrCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T16:30:01.298882Z","bundle_sha256":"20b64c9558c3cda4cc5a63ce6bd1c4ee40269acd3e8f14eec2717348eb381a3b"}}