{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:CMO4NJXIM5LT3E47IC5VRRNQOS","short_pith_number":"pith:CMO4NJXI","canonical_record":{"source":{"id":"1906.01649","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-04T18:00:07Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"95f94cda3c822228fed7b5da8172d1bfb66bbf4e4369b5655bd9229812af853a","abstract_canon_sha256":"8a4cd6fa936365298c9500bc9d7de04b8ec9993fa7a7ecd72c44e9b14a661997"},"schema_version":"1.0"},"canonical_sha256":"131dc6a6e867573d939f40bb58c5b074a7a06b95e6d8dddcf7cb885d197c82ea","source":{"kind":"arxiv","id":"1906.01649","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01649","created_at":"2026-05-17T23:44:06Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01649v1","created_at":"2026-05-17T23:44:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01649","created_at":"2026-05-17T23:44:06Z"},{"alias_kind":"pith_short_12","alias_value":"CMO4NJXIM5LT","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"CMO4NJXIM5LT3E47","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"CMO4NJXI","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:CMO4NJXIM5LT3E47IC5VRRNQOS","target":"record","payload":{"canonical_record":{"source":{"id":"1906.01649","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-04T18:00:07Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"95f94cda3c822228fed7b5da8172d1bfb66bbf4e4369b5655bd9229812af853a","abstract_canon_sha256":"8a4cd6fa936365298c9500bc9d7de04b8ec9993fa7a7ecd72c44e9b14a661997"},"schema_version":"1.0"},"canonical_sha256":"131dc6a6e867573d939f40bb58c5b074a7a06b95e6d8dddcf7cb885d197c82ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:06.589748Z","signature_b64":"mn291fKJoX9phXu3ev0kLwI4rCWj94W6ceGEF6iM1jjyUEL1D7G44vTkTKWKxIfouqgTXPP2NRWfsLzt3uRsBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"131dc6a6e867573d939f40bb58c5b074a7a06b95e6d8dddcf7cb885d197c82ea","last_reissued_at":"2026-05-17T23:44:06.589192Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:06.589192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.01649","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":"2026-05-17T23:44:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"emrUMWadfHKsVA6Mc5s2NVQKG12Wx4vgKFvlvsMaHiw1xreI89GgFZtnr371aFPM2jtw5hijl8QP11lUnJQxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T03:48:44.688821Z"},"content_sha256":"884681e8127c2ffba1e8336f9b1fd7ef6023c6c207aebdd98f319fd220f62e50","schema_version":"1.0","event_id":"sha256:884681e8127c2ffba1e8336f9b1fd7ef6023c6c207aebdd98f319fd220f62e50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:CMO4NJXIM5LT3E47IC5VRRNQOS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global existence for systems of nonlinear wave equations with bounded, stable asymptotic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Joseph Keir","submitted_at":"2019-06-04T18:00:07Z","abstract_excerpt":"Some systems of nonlinear wave equations admit global solutions for all sufficiently small initial data, while others do not. The (classical) null condition guarantees that such a result holds, but it is too strong to capture certain systems -- most famously the Einstein equations -- which nevertheless admit global solutions for small initial data. The weak null condition has been proposed as a sufficient condition for such a result to hold; it takes the form of a condition on a related set of nonlinear ODEs known as the \"asymptotic system\". Previous results in this direction have required cer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01649","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":"2026-05-17T23:44:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o/o3lL4AondJcVSCCdaUcZBS9X0ZSB0sN4k2AcGUn5OhcTdmy6UmK2NFQ9oU4masFAWfUbyH2zeLivck5IQwDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T03:48:44.689144Z"},"content_sha256":"4e961e789db4cab07e6d5fb7248ff93b65865e9080ea4ccf86ec57de4ef97a6e","schema_version":"1.0","event_id":"sha256:4e961e789db4cab07e6d5fb7248ff93b65865e9080ea4ccf86ec57de4ef97a6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CMO4NJXIM5LT3E47IC5VRRNQOS/bundle.json","state_url":"https://pith.science/pith/CMO4NJXIM5LT3E47IC5VRRNQOS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CMO4NJXIM5LT3E47IC5VRRNQOS/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":"2026-06-30T03:48:44Z","links":{"resolver":"https://pith.science/pith/CMO4NJXIM5LT3E47IC5VRRNQOS","bundle":"https://pith.science/pith/CMO4NJXIM5LT3E47IC5VRRNQOS/bundle.json","state":"https://pith.science/pith/CMO4NJXIM5LT3E47IC5VRRNQOS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CMO4NJXIM5LT3E47IC5VRRNQOS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CMO4NJXIM5LT3E47IC5VRRNQOS","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":"8a4cd6fa936365298c9500bc9d7de04b8ec9993fa7a7ecd72c44e9b14a661997","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-04T18:00:07Z","title_canon_sha256":"95f94cda3c822228fed7b5da8172d1bfb66bbf4e4369b5655bd9229812af853a"},"schema_version":"1.0","source":{"id":"1906.01649","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01649","created_at":"2026-05-17T23:44:06Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01649v1","created_at":"2026-05-17T23:44:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01649","created_at":"2026-05-17T23:44:06Z"},{"alias_kind":"pith_short_12","alias_value":"CMO4NJXIM5LT","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"CMO4NJXIM5LT3E47","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"CMO4NJXI","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:4e961e789db4cab07e6d5fb7248ff93b65865e9080ea4ccf86ec57de4ef97a6e","target":"graph","created_at":"2026-05-17T23:44:06Z","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":"Some systems of nonlinear wave equations admit global solutions for all sufficiently small initial data, while others do not. The (classical) null condition guarantees that such a result holds, but it is too strong to capture certain systems -- most famously the Einstein equations -- which nevertheless admit global solutions for small initial data. The weak null condition has been proposed as a sufficient condition for such a result to hold; it takes the form of a condition on a related set of nonlinear ODEs known as the \"asymptotic system\". Previous results in this direction have required cer","authors_text":"Joseph Keir","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-04T18:00:07Z","title":"Global existence for systems of nonlinear wave equations with bounded, stable asymptotic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01649","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":"sha256:884681e8127c2ffba1e8336f9b1fd7ef6023c6c207aebdd98f319fd220f62e50","target":"record","created_at":"2026-05-17T23:44:06Z","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":"8a4cd6fa936365298c9500bc9d7de04b8ec9993fa7a7ecd72c44e9b14a661997","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-04T18:00:07Z","title_canon_sha256":"95f94cda3c822228fed7b5da8172d1bfb66bbf4e4369b5655bd9229812af853a"},"schema_version":"1.0","source":{"id":"1906.01649","kind":"arxiv","version":1}},"canonical_sha256":"131dc6a6e867573d939f40bb58c5b074a7a06b95e6d8dddcf7cb885d197c82ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"131dc6a6e867573d939f40bb58c5b074a7a06b95e6d8dddcf7cb885d197c82ea","first_computed_at":"2026-05-17T23:44:06.589192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:06.589192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mn291fKJoX9phXu3ev0kLwI4rCWj94W6ceGEF6iM1jjyUEL1D7G44vTkTKWKxIfouqgTXPP2NRWfsLzt3uRsBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:06.589748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.01649","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:884681e8127c2ffba1e8336f9b1fd7ef6023c6c207aebdd98f319fd220f62e50","sha256:4e961e789db4cab07e6d5fb7248ff93b65865e9080ea4ccf86ec57de4ef97a6e"],"state_sha256":"e8a455c5711248988c1cdeeb4643809aae06afc7ab001c8800370ad49fce21a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+lKmYX0fXsa70HPBgfWyRZ+rjisRvMByzq0MQUE46LrWk42jWd1Vl+1KHCsXx8Yx9fzDroUhZYnhfeVkzHoYCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T03:48:44.690889Z","bundle_sha256":"a1e143a6c5623413d5fc363316a588c637816e22a845761bb84e05aad92fba9e"}}