{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SETPUODNHPKKDFCUVTN4ESBILL","short_pith_number":"pith:SETPUODN","canonical_record":{"source":{"id":"1503.01562","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-05T07:17:03Z","cross_cats_sorted":[],"title_canon_sha256":"25208d7593c9e2bcaeaef656352b48b68c7dd988695ee2ec9df9f3f48167c9b2","abstract_canon_sha256":"72c33d2421fe6785c8889a23d1c56262813e29846dece6650b89a9f5bd22b059"},"schema_version":"1.0"},"canonical_sha256":"9126fa386d3bd4a19454acdbc248285ad7fe0d34a6903e3fa04392e190982f39","source":{"kind":"arxiv","id":"1503.01562","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01562","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01562v1","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01562","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"SETPUODNHPKK","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"SETPUODNHPKKDFCU","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"SETPUODN","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SETPUODNHPKKDFCUVTN4ESBILL","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01562","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-05T07:17:03Z","cross_cats_sorted":[],"title_canon_sha256":"25208d7593c9e2bcaeaef656352b48b68c7dd988695ee2ec9df9f3f48167c9b2","abstract_canon_sha256":"72c33d2421fe6785c8889a23d1c56262813e29846dece6650b89a9f5bd22b059"},"schema_version":"1.0"},"canonical_sha256":"9126fa386d3bd4a19454acdbc248285ad7fe0d34a6903e3fa04392e190982f39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:14.774284Z","signature_b64":"fBir7nKi+sKkk1drqtLaC49BNAzVxj1CTCjALQTdtblfE0nP2L7ItMY9X0neXh1hcTq0pJTY1uLsUK8xXMKPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9126fa386d3bd4a19454acdbc248285ad7fe0d34a6903e3fa04392e190982f39","last_reissued_at":"2026-05-18T01:04:14.773862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:14.773862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01562","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":"2026-05-18T01:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ENRlw8Yomq5U8YV+91jkyK0k19YvSoW/QAnzgNJoL77vgRqDlelp5xZqCWevylwDgLVpkQYbdJQjnOXRv0moBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:25:37.952379Z"},"content_sha256":"421b90a21c15f1c0488843d3981994bfa654a9bbe24bf71c97ee44f09c389b31","schema_version":"1.0","event_id":"sha256:421b90a21c15f1c0488843d3981994bfa654a9bbe24bf71c97ee44f09c389b31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SETPUODNHPKKDFCUVTN4ESBILL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Tataru, Sung-Jin Oh","submitted_at":"2015-03-05T07:17:03Z","abstract_excerpt":"This article constitutes the final and main part of a three-paper sequence, whose goal is to prove global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon equation (MKG) on $\\mathbb{R}^{1+4}$ for arbitrary finite energy initial data. Using the successively stronger continuation/scattering criteria established in the previous two papers, we carry out a blow-up analysis and deduce that the failure of global well-posedness and scattering implies the existence of a nontrivial stationary or self-similar solution to MKG. Then, by establishing that such solutions do not exist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01562","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":"2026-05-18T01:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SOH5lKtIYf+zpBQJXdTznhrO/JIE5l4qtG9sO6T5w0Odvk7+NJiZYjNdEkRrKhKRjR7kxa1r3TSzEmcJBJ9pBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:25:37.952728Z"},"content_sha256":"b85623ed7857e960dcdf70bad76876e0b546c11ccc91d2a43ae9352b5c486800","schema_version":"1.0","event_id":"sha256:b85623ed7857e960dcdf70bad76876e0b546c11ccc91d2a43ae9352b5c486800"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SETPUODNHPKKDFCUVTN4ESBILL/bundle.json","state_url":"https://pith.science/pith/SETPUODNHPKKDFCUVTN4ESBILL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SETPUODNHPKKDFCUVTN4ESBILL/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":"2026-06-03T05:25:37Z","links":{"resolver":"https://pith.science/pith/SETPUODNHPKKDFCUVTN4ESBILL","bundle":"https://pith.science/pith/SETPUODNHPKKDFCUVTN4ESBILL/bundle.json","state":"https://pith.science/pith/SETPUODNHPKKDFCUVTN4ESBILL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SETPUODNHPKKDFCUVTN4ESBILL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SETPUODNHPKKDFCUVTN4ESBILL","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":"72c33d2421fe6785c8889a23d1c56262813e29846dece6650b89a9f5bd22b059","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-05T07:17:03Z","title_canon_sha256":"25208d7593c9e2bcaeaef656352b48b68c7dd988695ee2ec9df9f3f48167c9b2"},"schema_version":"1.0","source":{"id":"1503.01562","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01562","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01562v1","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01562","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"SETPUODNHPKK","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"SETPUODNHPKKDFCU","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"SETPUODN","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:b85623ed7857e960dcdf70bad76876e0b546c11ccc91d2a43ae9352b5c486800","target":"graph","created_at":"2026-05-18T01:04:14Z","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":"This article constitutes the final and main part of a three-paper sequence, whose goal is to prove global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon equation (MKG) on $\\mathbb{R}^{1+4}$ for arbitrary finite energy initial data. Using the successively stronger continuation/scattering criteria established in the previous two papers, we carry out a blow-up analysis and deduce that the failure of global well-posedness and scattering implies the existence of a nontrivial stationary or self-similar solution to MKG. Then, by establishing that such solutions do not exist","authors_text":"Daniel Tataru, Sung-Jin Oh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-05T07:17:03Z","title":"Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01562","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":"sha256:421b90a21c15f1c0488843d3981994bfa654a9bbe24bf71c97ee44f09c389b31","target":"record","created_at":"2026-05-18T01:04:14Z","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":"72c33d2421fe6785c8889a23d1c56262813e29846dece6650b89a9f5bd22b059","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-05T07:17:03Z","title_canon_sha256":"25208d7593c9e2bcaeaef656352b48b68c7dd988695ee2ec9df9f3f48167c9b2"},"schema_version":"1.0","source":{"id":"1503.01562","kind":"arxiv","version":1}},"canonical_sha256":"9126fa386d3bd4a19454acdbc248285ad7fe0d34a6903e3fa04392e190982f39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9126fa386d3bd4a19454acdbc248285ad7fe0d34a6903e3fa04392e190982f39","first_computed_at":"2026-05-18T01:04:14.773862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:14.773862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fBir7nKi+sKkk1drqtLaC49BNAzVxj1CTCjALQTdtblfE0nP2L7ItMY9X0neXh1hcTq0pJTY1uLsUK8xXMKPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:14.774284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01562","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:421b90a21c15f1c0488843d3981994bfa654a9bbe24bf71c97ee44f09c389b31","sha256:b85623ed7857e960dcdf70bad76876e0b546c11ccc91d2a43ae9352b5c486800"],"state_sha256":"bb48ecd3461a1933e43f5cadf167a670ba671a4bc29c94c4c163065926e76d1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vicArwKTH60/RvTbyPiojOXauBXN5fh2nwvtMGNYmAPqYBvKip10DNon/c9jiD8gBQ+9depITqJOKBHUFylCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:25:37.954715Z","bundle_sha256":"f414136f9b7041a14b65e6c942132d83a8cc93e1a7a45258863b03890d036a6a"}}