{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5SBZKKEK4D6MVS5GX2ZPJS5Q2I","short_pith_number":"pith:5SBZKKEK","canonical_record":{"source":{"id":"1610.03581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-12T02:20:36Z","cross_cats_sorted":[],"title_canon_sha256":"449b2fdb1ce113de8f9b66599e078eb502ca0b04acae54f2958113b2aa6c8982","abstract_canon_sha256":"0f90dacf15d49596cfde49b5001d12b3493bb0f34421d0c2f0c1b5da123d8149"},"schema_version":"1.0"},"canonical_sha256":"ec8395288ae0fccacba6beb2f4cbb0d229d6be650784ba83784497eb17e819e7","source":{"kind":"arxiv","id":"1610.03581","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03581","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03581v2","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03581","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"5SBZKKEK4D6M","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5SBZKKEK4D6MVS5G","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5SBZKKEK","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5SBZKKEK4D6MVS5GX2ZPJS5Q2I","target":"record","payload":{"canonical_record":{"source":{"id":"1610.03581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-12T02:20:36Z","cross_cats_sorted":[],"title_canon_sha256":"449b2fdb1ce113de8f9b66599e078eb502ca0b04acae54f2958113b2aa6c8982","abstract_canon_sha256":"0f90dacf15d49596cfde49b5001d12b3493bb0f34421d0c2f0c1b5da123d8149"},"schema_version":"1.0"},"canonical_sha256":"ec8395288ae0fccacba6beb2f4cbb0d229d6be650784ba83784497eb17e819e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:04.856078Z","signature_b64":"aQqTOBk5VPlq8sUksTFspJmsLvRYy/KFWGPqNRQ6IXO1Xgy1w6g+SblGXhqVy3RZhdjpcpvpJUuUZieg1smZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec8395288ae0fccacba6beb2f4cbb0d229d6be650784ba83784497eb17e819e7","last_reissued_at":"2026-05-18T00:45:04.855566Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:04.855566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.03581","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":"2026-05-18T00:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B4OV6O0sqQ91XLxx8gRhVJid6MzKwc7Cm3W9KsnWsyZSi6yYHUZV6/q3JcekgKzlELnlYflgs5MoGY7XSIIkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:54:41.032456Z"},"content_sha256":"ccf80b33fc999efb71adc0cca3b179ecfbc2f9653899c3a57702f10ca51a655f","schema_version":"1.0","event_id":"sha256:ccf80b33fc999efb71adc0cca3b179ecfbc2f9653899c3a57702f10ca51a655f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5SBZKKEK4D6MVS5GX2ZPJS5Q2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global well-posedness for the massive Maxwell-Klein-Gordon equation with small critical Sobolev data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cristian Gavrus","submitted_at":"2016-10-12T02:20:36Z","abstract_excerpt":"In this paper we prove global well-posedness and modified scattering for the massive Maxwell-Klein-Gordon equation in the Coulomb gauge on $\\mathbb{R}^{1+d}$ $(d \\geq 4)$ for data with small critical Sobolev norm. This extends to the general case $ m^2 > 0 $ the results of Krieger-Sterbenz-Tataru ($d=4,5 $) and Rodnianski-Tao ($ d \\geq 6 $), who considered the case $ m=0$.\n  We proceed by generalizing the global parametrix construction for the covariant wave operator and the functional framework from the massless case to the Klein-Gordon setting. The equation exhibits a trilinear cancelation s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03581","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":""},"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":"2026-05-18T00:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ve3IeqdS/1UIeAhLIN2Eb9X+78vZJZAm1WUzCy/ISfYOuBFvPLD9B/JwEulcnz8obUy1pVHmfjk12bXG8uSjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:54:41.032797Z"},"content_sha256":"43277044ccc4148f1e64addbababd42c82a12fdf76030ec8240af6b72da46d85","schema_version":"1.0","event_id":"sha256:43277044ccc4148f1e64addbababd42c82a12fdf76030ec8240af6b72da46d85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5SBZKKEK4D6MVS5GX2ZPJS5Q2I/bundle.json","state_url":"https://pith.science/pith/5SBZKKEK4D6MVS5GX2ZPJS5Q2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5SBZKKEK4D6MVS5GX2ZPJS5Q2I/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":"2026-06-23T06:54:41Z","links":{"resolver":"https://pith.science/pith/5SBZKKEK4D6MVS5GX2ZPJS5Q2I","bundle":"https://pith.science/pith/5SBZKKEK4D6MVS5GX2ZPJS5Q2I/bundle.json","state":"https://pith.science/pith/5SBZKKEK4D6MVS5GX2ZPJS5Q2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5SBZKKEK4D6MVS5GX2ZPJS5Q2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5SBZKKEK4D6MVS5GX2ZPJS5Q2I","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":"0f90dacf15d49596cfde49b5001d12b3493bb0f34421d0c2f0c1b5da123d8149","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-12T02:20:36Z","title_canon_sha256":"449b2fdb1ce113de8f9b66599e078eb502ca0b04acae54f2958113b2aa6c8982"},"schema_version":"1.0","source":{"id":"1610.03581","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03581","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03581v2","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03581","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"5SBZKKEK4D6M","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5SBZKKEK4D6MVS5G","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5SBZKKEK","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:43277044ccc4148f1e64addbababd42c82a12fdf76030ec8240af6b72da46d85","target":"graph","created_at":"2026-05-18T00:45:04Z","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":"In this paper we prove global well-posedness and modified scattering for the massive Maxwell-Klein-Gordon equation in the Coulomb gauge on $\\mathbb{R}^{1+d}$ $(d \\geq 4)$ for data with small critical Sobolev norm. This extends to the general case $ m^2 > 0 $ the results of Krieger-Sterbenz-Tataru ($d=4,5 $) and Rodnianski-Tao ($ d \\geq 6 $), who considered the case $ m=0$.\n  We proceed by generalizing the global parametrix construction for the covariant wave operator and the functional framework from the massless case to the Klein-Gordon setting. The equation exhibits a trilinear cancelation s","authors_text":"Cristian Gavrus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-12T02:20:36Z","title":"Global well-posedness for the massive Maxwell-Klein-Gordon equation with small critical Sobolev data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03581","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:ccf80b33fc999efb71adc0cca3b179ecfbc2f9653899c3a57702f10ca51a655f","target":"record","created_at":"2026-05-18T00:45:04Z","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":"0f90dacf15d49596cfde49b5001d12b3493bb0f34421d0c2f0c1b5da123d8149","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-12T02:20:36Z","title_canon_sha256":"449b2fdb1ce113de8f9b66599e078eb502ca0b04acae54f2958113b2aa6c8982"},"schema_version":"1.0","source":{"id":"1610.03581","kind":"arxiv","version":2}},"canonical_sha256":"ec8395288ae0fccacba6beb2f4cbb0d229d6be650784ba83784497eb17e819e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec8395288ae0fccacba6beb2f4cbb0d229d6be650784ba83784497eb17e819e7","first_computed_at":"2026-05-18T00:45:04.855566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:04.855566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aQqTOBk5VPlq8sUksTFspJmsLvRYy/KFWGPqNRQ6IXO1Xgy1w6g+SblGXhqVy3RZhdjpcpvpJUuUZieg1smZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:04.856078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03581","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccf80b33fc999efb71adc0cca3b179ecfbc2f9653899c3a57702f10ca51a655f","sha256:43277044ccc4148f1e64addbababd42c82a12fdf76030ec8240af6b72da46d85"],"state_sha256":"1bbeeb563a8765934b4a88c32cf8c3584a02bd28e000c61b8ec473b1216c38e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9wP+DaVo5Br+GGqYjwMZr291RFqh9Y1MTzRdzhACPSI+pbxFYVexXpzEiVQh1wTZ9ZOPs5jrHnVhxxY96Em3Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:54:41.034659Z","bundle_sha256":"63dab1f5834834d29249d0f5d3e6cf9041fcbee32947787c57083098c2456e28"}}