{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6FORBWX2HY3OT362YRAJ3BPXET","short_pith_number":"pith:6FORBWX2","canonical_record":{"source":{"id":"1511.00250","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-01T13:42:06Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"71adbabe56e82e040dc38a110f5b44fd1a6c2cf5b83ab726d8afba5fa0d339ca","abstract_canon_sha256":"41bf5a8419a2e725a36f97aea72fd3d032efe1968cdea87e33dfdf50135cb8ed"},"schema_version":"1.0"},"canonical_sha256":"f15d10dafa3e36e9efdac4409d85f724df6b4375e6fd67e703e081460a808268","source":{"kind":"arxiv","id":"1511.00250","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00250","created_at":"2026-05-18T01:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00250v1","created_at":"2026-05-18T01:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00250","created_at":"2026-05-18T01:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"6FORBWX2HY3O","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6FORBWX2HY3OT362","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6FORBWX2","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6FORBWX2HY3OT362YRAJ3BPXET","target":"record","payload":{"canonical_record":{"source":{"id":"1511.00250","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-01T13:42:06Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"71adbabe56e82e040dc38a110f5b44fd1a6c2cf5b83ab726d8afba5fa0d339ca","abstract_canon_sha256":"41bf5a8419a2e725a36f97aea72fd3d032efe1968cdea87e33dfdf50135cb8ed"},"schema_version":"1.0"},"canonical_sha256":"f15d10dafa3e36e9efdac4409d85f724df6b4375e6fd67e703e081460a808268","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:12.821665Z","signature_b64":"kA6kponCEHe/jQokNv+aqTDeGi1lyJ9T0Xx7M3d34BqjH8z08rWNq4aw2WPJDPGy6p5XbohKropThiiiXqDDDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f15d10dafa3e36e9efdac4409d85f724df6b4375e6fd67e703e081460a808268","last_reissued_at":"2026-05-18T01:28:12.820724Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:12.820724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.00250","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":"2026-05-18T01:28:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oAzRfnVI4l4Ym5VHMxLYW+YTCC6GT0YgbiAuscx2BuVB2sAO7Wo/1CAqZ3w9n+DXSzGAnC3SEOfo7J6C1YavBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:26:23.601282Z"},"content_sha256":"59493e43f04751e053d938a7d4b5d557c49da23c3dfe803892ea3f103766fc6b","schema_version":"1.0","event_id":"sha256:59493e43f04751e053d938a7d4b5d557c49da23c3dfe803892ea3f103766fc6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6FORBWX2HY3OT362YRAJ3BPXET","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On global behavior of solutions of the Maxwell-Klein-Gordon equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Shiwu Yang","submitted_at":"2015-11-01T13:42:06Z","abstract_excerpt":"It is known that the Maxwell-Klein-Gordon equations in $\\mathbb{R}^{3+1}$ admit global solutions with finite energy data. In this paper, we present a new approach to study the asymptotic behavior of these global solutions. We show the quantitative energy flux decay of the solutions with data merely bounded in some weighted energy space. We also establish an integrated local energy decay and a hierarchy of $r$-weighted energy decay. The results in particular hold in the presence of large total charge. This is the first result to give a complete and precise description of the global behavior of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00250","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":"2026-05-18T01:28:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ecxf/YUIxfQ9pfWjeTatjDYh4Gt0hnBTct5GVUpysJBF6cJy3a3OIZJtADgCrdFFyGzJDYBaOIyvqrSCQBzXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:26:23.602111Z"},"content_sha256":"35bdfa618b7ac70f16d038470d511ec1102ec4bf51e874dfd9b814e52ff2ad8c","schema_version":"1.0","event_id":"sha256:35bdfa618b7ac70f16d038470d511ec1102ec4bf51e874dfd9b814e52ff2ad8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6FORBWX2HY3OT362YRAJ3BPXET/bundle.json","state_url":"https://pith.science/pith/6FORBWX2HY3OT362YRAJ3BPXET/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6FORBWX2HY3OT362YRAJ3BPXET/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":"2026-06-06T16:26:23Z","links":{"resolver":"https://pith.science/pith/6FORBWX2HY3OT362YRAJ3BPXET","bundle":"https://pith.science/pith/6FORBWX2HY3OT362YRAJ3BPXET/bundle.json","state":"https://pith.science/pith/6FORBWX2HY3OT362YRAJ3BPXET/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6FORBWX2HY3OT362YRAJ3BPXET/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6FORBWX2HY3OT362YRAJ3BPXET","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":"41bf5a8419a2e725a36f97aea72fd3d032efe1968cdea87e33dfdf50135cb8ed","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-01T13:42:06Z","title_canon_sha256":"71adbabe56e82e040dc38a110f5b44fd1a6c2cf5b83ab726d8afba5fa0d339ca"},"schema_version":"1.0","source":{"id":"1511.00250","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00250","created_at":"2026-05-18T01:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00250v1","created_at":"2026-05-18T01:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00250","created_at":"2026-05-18T01:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"6FORBWX2HY3O","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6FORBWX2HY3OT362","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6FORBWX2","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:35bdfa618b7ac70f16d038470d511ec1102ec4bf51e874dfd9b814e52ff2ad8c","target":"graph","created_at":"2026-05-18T01:28:12Z","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":"It is known that the Maxwell-Klein-Gordon equations in $\\mathbb{R}^{3+1}$ admit global solutions with finite energy data. In this paper, we present a new approach to study the asymptotic behavior of these global solutions. We show the quantitative energy flux decay of the solutions with data merely bounded in some weighted energy space. We also establish an integrated local energy decay and a hierarchy of $r$-weighted energy decay. The results in particular hold in the presence of large total charge. This is the first result to give a complete and precise description of the global behavior of ","authors_text":"Shiwu Yang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-01T13:42:06Z","title":"On global behavior of solutions of the Maxwell-Klein-Gordon equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00250","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":"sha256:59493e43f04751e053d938a7d4b5d557c49da23c3dfe803892ea3f103766fc6b","target":"record","created_at":"2026-05-18T01:28:12Z","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":"41bf5a8419a2e725a36f97aea72fd3d032efe1968cdea87e33dfdf50135cb8ed","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-01T13:42:06Z","title_canon_sha256":"71adbabe56e82e040dc38a110f5b44fd1a6c2cf5b83ab726d8afba5fa0d339ca"},"schema_version":"1.0","source":{"id":"1511.00250","kind":"arxiv","version":1}},"canonical_sha256":"f15d10dafa3e36e9efdac4409d85f724df6b4375e6fd67e703e081460a808268","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f15d10dafa3e36e9efdac4409d85f724df6b4375e6fd67e703e081460a808268","first_computed_at":"2026-05-18T01:28:12.820724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:12.820724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kA6kponCEHe/jQokNv+aqTDeGi1lyJ9T0Xx7M3d34BqjH8z08rWNq4aw2WPJDPGy6p5XbohKropThiiiXqDDDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:12.821665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.00250","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59493e43f04751e053d938a7d4b5d557c49da23c3dfe803892ea3f103766fc6b","sha256:35bdfa618b7ac70f16d038470d511ec1102ec4bf51e874dfd9b814e52ff2ad8c"],"state_sha256":"2d15368962aac1507c40ccd6cf0bc61f33f26c1ac53441af232dd7b325183ecc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9N5leq8PdIHOjzzHIxNGtoDmD38iPbfTmTem0PN/1RfdJylg1AP/1q9Bs9NIneJghurtljwDXLcgfc4pIanxAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:26:23.605546Z","bundle_sha256":"ac23b1f68eac2bdba772c72e9cdf8c2ffecd8f6f90939589c900b4e2535bf30b"}}