{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GPDKE6S6T6576KLHN6I6WYW2VS","short_pith_number":"pith:GPDKE6S6","canonical_record":{"source":{"id":"1312.5476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-19T10:58:37Z","cross_cats_sorted":["gr-qc","math.DG"],"title_canon_sha256":"a6f18a4995055880e72a0f561176c4128381811f40ce2fe0c2211b54027d14f4","abstract_canon_sha256":"6c404ff7b28ea17686a96d44d32f32b6637b0e594841bba2d15df650026977fb"},"schema_version":"1.0"},"canonical_sha256":"33c6a27a5e9fbbff29676f91eb62daac8c78dec6cea78b0558a7797bced74e3c","source":{"kind":"arxiv","id":"1312.5476","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5476","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5476v1","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5476","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"GPDKE6S6T657","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GPDKE6S6T6576KLH","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GPDKE6S6","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GPDKE6S6T6576KLHN6I6WYW2VS","target":"record","payload":{"canonical_record":{"source":{"id":"1312.5476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-19T10:58:37Z","cross_cats_sorted":["gr-qc","math.DG"],"title_canon_sha256":"a6f18a4995055880e72a0f561176c4128381811f40ce2fe0c2211b54027d14f4","abstract_canon_sha256":"6c404ff7b28ea17686a96d44d32f32b6637b0e594841bba2d15df650026977fb"},"schema_version":"1.0"},"canonical_sha256":"33c6a27a5e9fbbff29676f91eb62daac8c78dec6cea78b0558a7797bced74e3c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:14.693866Z","signature_b64":"PTplcf+dFHk0emIC01yPs53mgQJLvJl2qszIvrgOxOWJf2wFTU6nX0VYwpr0v+cSLnDI/qUkPIg/Udjr1ZBmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33c6a27a5e9fbbff29676f91eb62daac8c78dec6cea78b0558a7797bced74e3c","last_reissued_at":"2026-05-18T03:04:14.693408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:14.693408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.5476","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":"2026-05-18T03:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aV/sbP35j2LWvsVbkfgQlNm9WkEGBOruA3ydKlovoZBPinExdqilV5J4nqlg7dQhfQ2ja+JXHzKlYtF4GRKZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:57:20.584607Z"},"content_sha256":"e8986e9622fd6bfc7e92bd50fdaa86aa6f6d54f73ce53b731eb0f03795bc08a6","schema_version":"1.0","event_id":"sha256:e8986e9622fd6bfc7e92bd50fdaa86aa6f6d54f73ce53b731eb0f03795bc08a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GPDKE6S6T6576KLHN6I6WYW2VS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The global existence of Yang-Mills fields on curved space-times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.DG"],"primary_cat":"math.AP","authors_text":"Sari Ghanem","submitted_at":"2013-12-19T10:58:37Z","abstract_excerpt":"This is an introductory chapter in a series in which we take a systematic study of the Yang-Mills equations on curved space-times. In this first, we provide standard material that consists in writing the proof of the global existence of Yang-Mills fields on arbitrary curved space-times using the Klainerman-Rodnianski parametrix combined with suitable Gr\\\"onwall type inequalities. While the Chru\\'sciel-Shatah argument requires a simultaneous control of the $L^{\\infty}_{loc}$ and the $H^{2}_{loc}$ norms of the Yang-Mills curvature, we can get away by controlling only the $H^{1}_{loc}$ norm inste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5476","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":"2026-05-18T03:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d2ackrDK1UaGaeqKOsF4Kd0Z2uRUclAQq4vC24wSE7lqCxDLiSG9ES8rkZPYR4Xcn4TGhWNCfVXFbggFp9gABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:57:20.584945Z"},"content_sha256":"b550b2c409db7b79f8cdd562ff5a361286607ebd556f2c3647fda87db1da5c00","schema_version":"1.0","event_id":"sha256:b550b2c409db7b79f8cdd562ff5a361286607ebd556f2c3647fda87db1da5c00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GPDKE6S6T6576KLHN6I6WYW2VS/bundle.json","state_url":"https://pith.science/pith/GPDKE6S6T6576KLHN6I6WYW2VS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GPDKE6S6T6576KLHN6I6WYW2VS/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":"2026-06-22T18:57:20Z","links":{"resolver":"https://pith.science/pith/GPDKE6S6T6576KLHN6I6WYW2VS","bundle":"https://pith.science/pith/GPDKE6S6T6576KLHN6I6WYW2VS/bundle.json","state":"https://pith.science/pith/GPDKE6S6T6576KLHN6I6WYW2VS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GPDKE6S6T6576KLHN6I6WYW2VS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GPDKE6S6T6576KLHN6I6WYW2VS","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":"6c404ff7b28ea17686a96d44d32f32b6637b0e594841bba2d15df650026977fb","cross_cats_sorted":["gr-qc","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-19T10:58:37Z","title_canon_sha256":"a6f18a4995055880e72a0f561176c4128381811f40ce2fe0c2211b54027d14f4"},"schema_version":"1.0","source":{"id":"1312.5476","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5476","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5476v1","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5476","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"GPDKE6S6T657","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GPDKE6S6T6576KLH","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GPDKE6S6","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:b550b2c409db7b79f8cdd562ff5a361286607ebd556f2c3647fda87db1da5c00","target":"graph","created_at":"2026-05-18T03:04:14Z","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 is an introductory chapter in a series in which we take a systematic study of the Yang-Mills equations on curved space-times. In this first, we provide standard material that consists in writing the proof of the global existence of Yang-Mills fields on arbitrary curved space-times using the Klainerman-Rodnianski parametrix combined with suitable Gr\\\"onwall type inequalities. While the Chru\\'sciel-Shatah argument requires a simultaneous control of the $L^{\\infty}_{loc}$ and the $H^{2}_{loc}$ norms of the Yang-Mills curvature, we can get away by controlling only the $H^{1}_{loc}$ norm inste","authors_text":"Sari Ghanem","cross_cats":["gr-qc","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-19T10:58:37Z","title":"The global existence of Yang-Mills fields on curved space-times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5476","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:e8986e9622fd6bfc7e92bd50fdaa86aa6f6d54f73ce53b731eb0f03795bc08a6","target":"record","created_at":"2026-05-18T03:04:14Z","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":"6c404ff7b28ea17686a96d44d32f32b6637b0e594841bba2d15df650026977fb","cross_cats_sorted":["gr-qc","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-19T10:58:37Z","title_canon_sha256":"a6f18a4995055880e72a0f561176c4128381811f40ce2fe0c2211b54027d14f4"},"schema_version":"1.0","source":{"id":"1312.5476","kind":"arxiv","version":1}},"canonical_sha256":"33c6a27a5e9fbbff29676f91eb62daac8c78dec6cea78b0558a7797bced74e3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33c6a27a5e9fbbff29676f91eb62daac8c78dec6cea78b0558a7797bced74e3c","first_computed_at":"2026-05-18T03:04:14.693408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:14.693408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PTplcf+dFHk0emIC01yPs53mgQJLvJl2qszIvrgOxOWJf2wFTU6nX0VYwpr0v+cSLnDI/qUkPIg/Udjr1ZBmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:14.693866Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.5476","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8986e9622fd6bfc7e92bd50fdaa86aa6f6d54f73ce53b731eb0f03795bc08a6","sha256:b550b2c409db7b79f8cdd562ff5a361286607ebd556f2c3647fda87db1da5c00"],"state_sha256":"dc530faeab3cbc369498b0b9bb9e1a2ef22ff0277367e8da04fafd475b955eca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O7q13cDc5e5H3tdzaNr+L0IkzWCoFNMxsDOUKuUrbt3XDN8YObMQmvMTso/i1qzch9ASLMgisHPv69Am0+yJAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T18:57:20.586854Z","bundle_sha256":"1b593c4141e8c6d9cd285b80ab8d859aeb1714f3d687925a240a816ad4cc8ba4"}}