{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KSFSO26WJUAP4NTHYK2N4TOQK4","short_pith_number":"pith:KSFSO26W","canonical_record":{"source":{"id":"1411.4910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-18T16:59:58Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"0799b0c81c229cf5b93a5493fbcd1aecaec8b024f5f457ec592df44d5aa4392b","abstract_canon_sha256":"b2288f6917b3c99081e8fbbd4948d80f8218ba6b4bc784d22ff938c5c3ff00ca"},"schema_version":"1.0"},"canonical_sha256":"548b276bd64d00fe3667c2b4de4dd057066d42b504532c2ca394a8dafae1fc1a","source":{"kind":"arxiv","id":"1411.4910","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4910","created_at":"2026-05-18T02:34:50Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4910v1","created_at":"2026-05-18T02:34:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4910","created_at":"2026-05-18T02:34:50Z"},{"alias_kind":"pith_short_12","alias_value":"KSFSO26WJUAP","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KSFSO26WJUAP4NTH","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KSFSO26W","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KSFSO26WJUAP4NTHYK2N4TOQK4","target":"record","payload":{"canonical_record":{"source":{"id":"1411.4910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-18T16:59:58Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"0799b0c81c229cf5b93a5493fbcd1aecaec8b024f5f457ec592df44d5aa4392b","abstract_canon_sha256":"b2288f6917b3c99081e8fbbd4948d80f8218ba6b4bc784d22ff938c5c3ff00ca"},"schema_version":"1.0"},"canonical_sha256":"548b276bd64d00fe3667c2b4de4dd057066d42b504532c2ca394a8dafae1fc1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:50.978220Z","signature_b64":"q3OoDFpClPIppJKnCW6/EpECorWjq/Lezp5vrGrAE2JT/mGFvR/FEsHBwa6sFpmhpGVgarul+vQJf5sv/p5+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"548b276bd64d00fe3667c2b4de4dd057066d42b504532c2ca394a8dafae1fc1a","last_reissued_at":"2026-05-18T02:34:50.977753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:50.977753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.4910","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":"2026-05-18T02:34:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Pes5csauZAFSEImiIt5dNEgcxuA9ePYMU2+xxoE4MPVym6x4/3JQC9r0Go925XYJ6DwvhrUZ3j7PlgxacNUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:26:34.390573Z"},"content_sha256":"3281b279dd06265f5e35cb1446813524d18dad8342551835100acfa590372622","schema_version":"1.0","event_id":"sha256:3281b279dd06265f5e35cb1446813524d18dad8342551835100acfa590372622"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KSFSO26WJUAP4NTHYK2N4TOQK4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The hyperboloidal foliation method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.AP","authors_text":"Philippe G. LeFloch, Yue Ma","submitted_at":"2014-11-18T16:59:58Z","abstract_excerpt":"The Hyperboloidal Foliation Method presented in this monograph is based on a (3+1)-foliation of Minkowski spacetime by hyperboloidal hypersurfaces. It allows us to establish global-in-time existence results for systems of nonlinear wave equations posed on a curved spacetime and to derive uniform energy bounds and optimal rates of decay in time. We are also able to encompass the wave equation and the Klein-Gordon equation in a unified framework and to establish a well-posedness theory for nonlinear wave-Klein-Gordon systems and a large class of nonlinear interactions. The hyperboloidal foliatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4910","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":"2026-05-18T02:34:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sTdqW0QtrA+2rRcGhgYYS3eDhcrB9KWJLeGlCl4ETeeUDmNNUQOPgUs0f2yo2Nrt2lverp4O05TpD+NiCxS/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:26:34.391236Z"},"content_sha256":"deb920e70bba668f1900759d16387a729df62526162eba77cf8b824bb95330ac","schema_version":"1.0","event_id":"sha256:deb920e70bba668f1900759d16387a729df62526162eba77cf8b824bb95330ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KSFSO26WJUAP4NTHYK2N4TOQK4/bundle.json","state_url":"https://pith.science/pith/KSFSO26WJUAP4NTHYK2N4TOQK4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KSFSO26WJUAP4NTHYK2N4TOQK4/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":"2026-06-11T08:26:34Z","links":{"resolver":"https://pith.science/pith/KSFSO26WJUAP4NTHYK2N4TOQK4","bundle":"https://pith.science/pith/KSFSO26WJUAP4NTHYK2N4TOQK4/bundle.json","state":"https://pith.science/pith/KSFSO26WJUAP4NTHYK2N4TOQK4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KSFSO26WJUAP4NTHYK2N4TOQK4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KSFSO26WJUAP4NTHYK2N4TOQK4","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":"b2288f6917b3c99081e8fbbd4948d80f8218ba6b4bc784d22ff938c5c3ff00ca","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-18T16:59:58Z","title_canon_sha256":"0799b0c81c229cf5b93a5493fbcd1aecaec8b024f5f457ec592df44d5aa4392b"},"schema_version":"1.0","source":{"id":"1411.4910","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4910","created_at":"2026-05-18T02:34:50Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4910v1","created_at":"2026-05-18T02:34:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4910","created_at":"2026-05-18T02:34:50Z"},{"alias_kind":"pith_short_12","alias_value":"KSFSO26WJUAP","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KSFSO26WJUAP4NTH","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KSFSO26W","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:deb920e70bba668f1900759d16387a729df62526162eba77cf8b824bb95330ac","target":"graph","created_at":"2026-05-18T02:34:50Z","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 Hyperboloidal Foliation Method presented in this monograph is based on a (3+1)-foliation of Minkowski spacetime by hyperboloidal hypersurfaces. It allows us to establish global-in-time existence results for systems of nonlinear wave equations posed on a curved spacetime and to derive uniform energy bounds and optimal rates of decay in time. We are also able to encompass the wave equation and the Klein-Gordon equation in a unified framework and to establish a well-posedness theory for nonlinear wave-Klein-Gordon systems and a large class of nonlinear interactions. The hyperboloidal foliatio","authors_text":"Philippe G. LeFloch, Yue Ma","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-18T16:59:58Z","title":"The hyperboloidal foliation method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4910","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":"sha256:3281b279dd06265f5e35cb1446813524d18dad8342551835100acfa590372622","target":"record","created_at":"2026-05-18T02:34:50Z","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":"b2288f6917b3c99081e8fbbd4948d80f8218ba6b4bc784d22ff938c5c3ff00ca","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-18T16:59:58Z","title_canon_sha256":"0799b0c81c229cf5b93a5493fbcd1aecaec8b024f5f457ec592df44d5aa4392b"},"schema_version":"1.0","source":{"id":"1411.4910","kind":"arxiv","version":1}},"canonical_sha256":"548b276bd64d00fe3667c2b4de4dd057066d42b504532c2ca394a8dafae1fc1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"548b276bd64d00fe3667c2b4de4dd057066d42b504532c2ca394a8dafae1fc1a","first_computed_at":"2026-05-18T02:34:50.977753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:34:50.977753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q3OoDFpClPIppJKnCW6/EpECorWjq/Lezp5vrGrAE2JT/mGFvR/FEsHBwa6sFpmhpGVgarul+vQJf5sv/p5+Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:34:50.978220Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4910","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3281b279dd06265f5e35cb1446813524d18dad8342551835100acfa590372622","sha256:deb920e70bba668f1900759d16387a729df62526162eba77cf8b824bb95330ac"],"state_sha256":"542fd1933cf7b8207e05411fb9f60271e000198d96b063f95143d912748358f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OEI0PUtzv4CuviPj3BL5LTzR3v3cbqPq/95w1iqQD6NFs4LnDuOkG4fgqxaj4NyfUvBt/GsW3gnNpta4KuDNDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T08:26:34.394787Z","bundle_sha256":"e7869e0bbc2e39a6f068991640c1ffd532a01ce206c558bc0118a672558f168a"}}