{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:J2SS3VCV2VYV5OSB557GHJWTSK","short_pith_number":"pith:J2SS3VCV","canonical_record":{"source":{"id":"1512.08004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-25T14:35:56Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"01c89daf9baa57889d0a79a8a539e37a2f2c74d1b6148347e9986b786020454f","abstract_canon_sha256":"4a73d38620a4e0003f3108965a54c8367802a8fed20243a6cf7902dcff7bb584"},"schema_version":"1.0"},"canonical_sha256":"4ea52dd455d5715eba41ef7e63a6d392a56a73778d1757cec9df9e6702358036","source":{"kind":"arxiv","id":"1512.08004","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08004","created_at":"2026-07-05T01:06:05Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08004v2","created_at":"2026-07-05T01:06:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08004","created_at":"2026-07-05T01:06:05Z"},{"alias_kind":"pith_short_12","alias_value":"J2SS3VCV2VYV","created_at":"2026-07-05T01:06:05Z"},{"alias_kind":"pith_short_16","alias_value":"J2SS3VCV2VYV5OSB","created_at":"2026-07-05T01:06:05Z"},{"alias_kind":"pith_short_8","alias_value":"J2SS3VCV","created_at":"2026-07-05T01:06:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:J2SS3VCV2VYV5OSB557GHJWTSK","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-25T14:35:56Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"01c89daf9baa57889d0a79a8a539e37a2f2c74d1b6148347e9986b786020454f","abstract_canon_sha256":"4a73d38620a4e0003f3108965a54c8367802a8fed20243a6cf7902dcff7bb584"},"schema_version":"1.0"},"canonical_sha256":"4ea52dd455d5715eba41ef7e63a6d392a56a73778d1757cec9df9e6702358036","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:06:05.653305Z","signature_b64":"umqXKYavod1tG5584J+wYlMEnJnxlG/UolHoxYUbUBLbAf4rED1e19FX6hUiOcW4GAMLuV3Hjus1kIisYrS2BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ea52dd455d5715eba41ef7e63a6d392a56a73778d1757cec9df9e6702358036","last_reissued_at":"2026-07-05T01:06:05.652920Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:06:05.652920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08004","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":"2026-07-05T01:06:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AfWmBoo2WiAUbLtuvymNbEkuGMS6wMaoKvMc9c3grdEBV2DgNVUzEBIo6Q9sOz22P+DSkJZuULJoMz9G7IG2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T04:30:21.930694Z"},"content_sha256":"f3e621f6e368bd7da525ee4a371353c60870e26fb5cdeddc5b8f55a89daffc12","schema_version":"1.0","event_id":"sha256:f3e621f6e368bd7da525ee4a371353c60870e26fb5cdeddc5b8f55a89daffc12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:J2SS3VCV2VYV5OSB557GHJWTSK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of linear waves near the Cauchy horizon of cosmological black holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.AP","authors_text":"Andras Vasy, Peter Hintz","submitted_at":"2015-12-25T14:35:56Z","abstract_excerpt":"We show that linear scalar waves are bounded and continuous up to the Cauchy horizon of Reissner-Nordstr\\\"om-de Sitter and Kerr-de Sitter spacetimes, and in fact decay exponentially fast to a constant along the Cauchy horizon. We obtain our results by modifying the spacetime beyond the Cauchy horizon in a suitable manner, which puts the wave equation into a framework in which a number of standard as well as more recent microlocal regularity and scattering theory results apply. In particular, the conormal regularity of waves at the Cauchy horizon - which yields the boundedness statement - is a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08004","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1512.08004/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:06:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aad0dqriIOrCOsGhyKS8c8qHR07HZgbFcKdGlfSIRzPiwooG9VJJcweYuKlFBmJvmdehObgd9v0AUl3epTgPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T04:30:21.931414Z"},"content_sha256":"7632199adafe0636c44271ae3cfe5cdec2336c5efddf37594a586f075e2297bd","schema_version":"1.0","event_id":"sha256:7632199adafe0636c44271ae3cfe5cdec2336c5efddf37594a586f075e2297bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J2SS3VCV2VYV5OSB557GHJWTSK/bundle.json","state_url":"https://pith.science/pith/J2SS3VCV2VYV5OSB557GHJWTSK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J2SS3VCV2VYV5OSB557GHJWTSK/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":"2026-08-11T04:30:21Z","links":{"resolver":"https://pith.science/pith/J2SS3VCV2VYV5OSB557GHJWTSK","bundle":"https://pith.science/pith/J2SS3VCV2VYV5OSB557GHJWTSK/bundle.json","state":"https://pith.science/pith/J2SS3VCV2VYV5OSB557GHJWTSK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J2SS3VCV2VYV5OSB557GHJWTSK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:J2SS3VCV2VYV5OSB557GHJWTSK","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":"4a73d38620a4e0003f3108965a54c8367802a8fed20243a6cf7902dcff7bb584","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-25T14:35:56Z","title_canon_sha256":"01c89daf9baa57889d0a79a8a539e37a2f2c74d1b6148347e9986b786020454f"},"schema_version":"1.0","source":{"id":"1512.08004","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08004","created_at":"2026-07-05T01:06:05Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08004v2","created_at":"2026-07-05T01:06:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08004","created_at":"2026-07-05T01:06:05Z"},{"alias_kind":"pith_short_12","alias_value":"J2SS3VCV2VYV","created_at":"2026-07-05T01:06:05Z"},{"alias_kind":"pith_short_16","alias_value":"J2SS3VCV2VYV5OSB","created_at":"2026-07-05T01:06:05Z"},{"alias_kind":"pith_short_8","alias_value":"J2SS3VCV","created_at":"2026-07-05T01:06:05Z"}],"graph_snapshots":[{"event_id":"sha256:7632199adafe0636c44271ae3cfe5cdec2336c5efddf37594a586f075e2297bd","target":"graph","created_at":"2026-07-05T01:06:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1512.08004/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that linear scalar waves are bounded and continuous up to the Cauchy horizon of Reissner-Nordstr\\\"om-de Sitter and Kerr-de Sitter spacetimes, and in fact decay exponentially fast to a constant along the Cauchy horizon. We obtain our results by modifying the spacetime beyond the Cauchy horizon in a suitable manner, which puts the wave equation into a framework in which a number of standard as well as more recent microlocal regularity and scattering theory results apply. In particular, the conormal regularity of waves at the Cauchy horizon - which yields the boundedness statement - is a ","authors_text":"Andras Vasy, Peter Hintz","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-25T14:35:56Z","title":"Analysis of linear waves near the Cauchy horizon of cosmological black holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08004","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:f3e621f6e368bd7da525ee4a371353c60870e26fb5cdeddc5b8f55a89daffc12","target":"record","created_at":"2026-07-05T01:06:05Z","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":"4a73d38620a4e0003f3108965a54c8367802a8fed20243a6cf7902dcff7bb584","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-25T14:35:56Z","title_canon_sha256":"01c89daf9baa57889d0a79a8a539e37a2f2c74d1b6148347e9986b786020454f"},"schema_version":"1.0","source":{"id":"1512.08004","kind":"arxiv","version":2}},"canonical_sha256":"4ea52dd455d5715eba41ef7e63a6d392a56a73778d1757cec9df9e6702358036","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ea52dd455d5715eba41ef7e63a6d392a56a73778d1757cec9df9e6702358036","first_computed_at":"2026-07-05T01:06:05.652920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:06:05.652920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"umqXKYavod1tG5584J+wYlMEnJnxlG/UolHoxYUbUBLbAf4rED1e19FX6hUiOcW4GAMLuV3Hjus1kIisYrS2BA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:06:05.653305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08004","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3e621f6e368bd7da525ee4a371353c60870e26fb5cdeddc5b8f55a89daffc12","sha256:7632199adafe0636c44271ae3cfe5cdec2336c5efddf37594a586f075e2297bd"],"state_sha256":"c0f5d453d9e794239595a42a480097726005317801d880cbd1abdf38c09ffe6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TOX/0+2WmZQonLxjKP3e0mynMpPMe+nuTy1NCiJuSI3nds9MUe7YsPG3pXgvdAqzfT8ZmKdr04g4MyqXBVMZAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T04:30:21.936156Z","bundle_sha256":"544dfa77e83660009a88920af6652308f18766cba9b5659f1626119fad088089"}}