{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:MKUACNTDCHXQVBF3EDNLQVMQJP","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":"afda75667464ea5b2ac7404f4d0ea368cd39ca71c4174b60ea8636ee3cfa7ef9","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-02-14T09:02:49Z","title_canon_sha256":"bbe3d5cb26ed4c947684a587ad3f1d11a6b5358df027e3bea8297627436ce013"},"schema_version":"1.0","source":{"id":"2302.06915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.06915","created_at":"2026-07-05T05:41:45Z"},{"alias_kind":"arxiv_version","alias_value":"2302.06915v1","created_at":"2026-07-05T05:41:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.06915","created_at":"2026-07-05T05:41:45Z"},{"alias_kind":"pith_short_12","alias_value":"MKUACNTDCHXQ","created_at":"2026-07-05T05:41:45Z"},{"alias_kind":"pith_short_16","alias_value":"MKUACNTDCHXQVBF3","created_at":"2026-07-05T05:41:45Z"},{"alias_kind":"pith_short_8","alias_value":"MKUACNTD","created_at":"2026-07-05T05:41:45Z"}],"graph_snapshots":[{"event_id":"sha256:b8b7693e589999d98a9943a63261f4b62a5d39d4f3134f5254c608f6bfc771ce","target":"graph","created_at":"2026-07-05T05:41:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2302.06915/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a scale-invariant, semi-global existence result and a trapped surface formation result in the context of coupled Einstein-Yang-Mills theory, without symmetry assumptions. More precisely, we prove a scale-invariant semi-global existence theorem from past null-infinity and show that the focusing of the gravitational and/or chromoelectric-chromomagnetic waves could lead to the formation of a trapped surface. Adopting the signature for decay rates approach introduced in \\cite{A19}, we develop a novel gauge (and scale) invariant hierarchy of non-linear estimates for the Yang-Mills curvatur","authors_text":"Nikolaos Athanasiou, Puskar Mondal, Shing-Tung Yau","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-02-14T09:02:49Z","title":"Formation of trapped surfaces in the Einstein-Yang-Mills system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.06915","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:e577abb0e3a0d9c85d44d1dac3286e0a677f2d81221a73b1aa0bf1544b5fb0bd","target":"record","created_at":"2026-07-05T05:41:45Z","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":"afda75667464ea5b2ac7404f4d0ea368cd39ca71c4174b60ea8636ee3cfa7ef9","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-02-14T09:02:49Z","title_canon_sha256":"bbe3d5cb26ed4c947684a587ad3f1d11a6b5358df027e3bea8297627436ce013"},"schema_version":"1.0","source":{"id":"2302.06915","kind":"arxiv","version":1}},"canonical_sha256":"62a801366311ef0a84bb20dab855904bd8adc51479fe0d2e6102d589fd6e9833","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62a801366311ef0a84bb20dab855904bd8adc51479fe0d2e6102d589fd6e9833","first_computed_at":"2026-07-05T05:41:45.047904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:41:45.047904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xvvuHsk3V+92kM3e3nnD6stOlNdzc5PSjmIEbZbry2q/iq+N8+XFI5Qx1mYx6f+KCgDFsOfqgXj3/FeAVVU+Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:41:45.048349Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.06915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e577abb0e3a0d9c85d44d1dac3286e0a677f2d81221a73b1aa0bf1544b5fb0bd","sha256:b8b7693e589999d98a9943a63261f4b62a5d39d4f3134f5254c608f6bfc771ce"],"state_sha256":"1d512eb591c476718f6f1ce4ead352890cff254fcd986c62efabb02b3a5dc137"}