{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FKQCXNFPZUZZCNPNYIOF3LJHBY","short_pith_number":"pith:FKQCXNFP","canonical_record":{"source":{"id":"1709.09088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-26T15:26:49Z","cross_cats_sorted":[],"title_canon_sha256":"ede54037692c4634a85a6422e6aed067b8fe3fd6c609611b8826932427249464","abstract_canon_sha256":"abaca429c9c71e24060b1be2d041efc2470a2dc365a603ccbc24dcbacddd22f5"},"schema_version":"1.0"},"canonical_sha256":"2aa02bb4afcd339135edc21c5dad270e241d0af6aeaa6a0eef2f8c21f80d78e7","source":{"kind":"arxiv","id":"1709.09088","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09088","created_at":"2026-05-18T00:34:21Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09088v1","created_at":"2026-05-18T00:34:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09088","created_at":"2026-05-18T00:34:21Z"},{"alias_kind":"pith_short_12","alias_value":"FKQCXNFPZUZZ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FKQCXNFPZUZZCNPN","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FKQCXNFP","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FKQCXNFPZUZZCNPNYIOF3LJHBY","target":"record","payload":{"canonical_record":{"source":{"id":"1709.09088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-26T15:26:49Z","cross_cats_sorted":[],"title_canon_sha256":"ede54037692c4634a85a6422e6aed067b8fe3fd6c609611b8826932427249464","abstract_canon_sha256":"abaca429c9c71e24060b1be2d041efc2470a2dc365a603ccbc24dcbacddd22f5"},"schema_version":"1.0"},"canonical_sha256":"2aa02bb4afcd339135edc21c5dad270e241d0af6aeaa6a0eef2f8c21f80d78e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:21.188501Z","signature_b64":"J/AXPOPNX3nqgl/0j6ViWd4xwnDLFNxQefx9ny4Yf0IRR6JcJxh5LQxUJQhXGE4wiYg6HbeMficpwpqFLRTCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2aa02bb4afcd339135edc21c5dad270e241d0af6aeaa6a0eef2f8c21f80d78e7","last_reissued_at":"2026-05-18T00:34:21.188086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:21.188086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.09088","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":"2026-05-18T00:34:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AHx+tDe2ef5XK9CNrDvV5ONEVcizKVheITKmg7qlVx6k/xxrJOaGGLS4asJYrKesb+fYN6JY/vrf0wYlp7sYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:28:54.535818Z"},"content_sha256":"f9aa916d03b1f54fd228bf46e4befb1fe5012f7141fa1e34aeaf994c68a7256d","schema_version":"1.0","event_id":"sha256:f9aa916d03b1f54fd228bf46e4befb1fe5012f7141fa1e34aeaf994c68a7256d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FKQCXNFPZUZZCNPNYIOF3LJHBY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Threshold Theorem for the $(4+1)$-dimensional Yang--Mills equation: an overview of the proof","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":"2017-09-26T15:26:49Z","abstract_excerpt":"This article is devoted to the energy critical hyperbolic Yang--Mills system in the $(4+1)$ dimensional Minkowski space, which is considered by the authors in a sequence of four papers. The final outcome of these papers is twofold: (i) the Threshold Theorem, which asserts that global well-posedness and scattering hold for all topologically trivial initial data with energy below twice the ground state energy, and (ii) the Dichotomy Theorem, which for larger data in arbitrary topological classes provides a choice of two outcomes, either a global, scattering solution or a soliton bubbling off. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09088","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":"2026-05-18T00:34:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IsLXz9Fbx4LafMYY5PNW7CJa1OHp8dJegxFUtaOtRTFgjkkhXfebjBMUgiN4HiKpf3rhvITusbvDBML62vzRCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:28:54.536166Z"},"content_sha256":"e586c5ec1f7944e2f366c614e7b51572444535d77a0941058cc112a28e24128b","schema_version":"1.0","event_id":"sha256:e586c5ec1f7944e2f366c614e7b51572444535d77a0941058cc112a28e24128b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FKQCXNFPZUZZCNPNYIOF3LJHBY/bundle.json","state_url":"https://pith.science/pith/FKQCXNFPZUZZCNPNYIOF3LJHBY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FKQCXNFPZUZZCNPNYIOF3LJHBY/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":"2026-06-02T23:28:54Z","links":{"resolver":"https://pith.science/pith/FKQCXNFPZUZZCNPNYIOF3LJHBY","bundle":"https://pith.science/pith/FKQCXNFPZUZZCNPNYIOF3LJHBY/bundle.json","state":"https://pith.science/pith/FKQCXNFPZUZZCNPNYIOF3LJHBY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FKQCXNFPZUZZCNPNYIOF3LJHBY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FKQCXNFPZUZZCNPNYIOF3LJHBY","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":"abaca429c9c71e24060b1be2d041efc2470a2dc365a603ccbc24dcbacddd22f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-26T15:26:49Z","title_canon_sha256":"ede54037692c4634a85a6422e6aed067b8fe3fd6c609611b8826932427249464"},"schema_version":"1.0","source":{"id":"1709.09088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09088","created_at":"2026-05-18T00:34:21Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09088v1","created_at":"2026-05-18T00:34:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09088","created_at":"2026-05-18T00:34:21Z"},{"alias_kind":"pith_short_12","alias_value":"FKQCXNFPZUZZ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FKQCXNFPZUZZCNPN","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FKQCXNFP","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:e586c5ec1f7944e2f366c614e7b51572444535d77a0941058cc112a28e24128b","target":"graph","created_at":"2026-05-18T00:34:21Z","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 is devoted to the energy critical hyperbolic Yang--Mills system in the $(4+1)$ dimensional Minkowski space, which is considered by the authors in a sequence of four papers. The final outcome of these papers is twofold: (i) the Threshold Theorem, which asserts that global well-posedness and scattering hold for all topologically trivial initial data with energy below twice the ground state energy, and (ii) the Dichotomy Theorem, which for larger data in arbitrary topological classes provides a choice of two outcomes, either a global, scattering solution or a soliton bubbling off. In","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":"2017-09-26T15:26:49Z","title":"The Threshold Theorem for the $(4+1)$-dimensional Yang--Mills equation: an overview of the proof"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09088","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:f9aa916d03b1f54fd228bf46e4befb1fe5012f7141fa1e34aeaf994c68a7256d","target":"record","created_at":"2026-05-18T00:34:21Z","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":"abaca429c9c71e24060b1be2d041efc2470a2dc365a603ccbc24dcbacddd22f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-26T15:26:49Z","title_canon_sha256":"ede54037692c4634a85a6422e6aed067b8fe3fd6c609611b8826932427249464"},"schema_version":"1.0","source":{"id":"1709.09088","kind":"arxiv","version":1}},"canonical_sha256":"2aa02bb4afcd339135edc21c5dad270e241d0af6aeaa6a0eef2f8c21f80d78e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2aa02bb4afcd339135edc21c5dad270e241d0af6aeaa6a0eef2f8c21f80d78e7","first_computed_at":"2026-05-18T00:34:21.188086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:21.188086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J/AXPOPNX3nqgl/0j6ViWd4xwnDLFNxQefx9ny4Yf0IRR6JcJxh5LQxUJQhXGE4wiYg6HbeMficpwpqFLRTCAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:21.188501Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.09088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9aa916d03b1f54fd228bf46e4befb1fe5012f7141fa1e34aeaf994c68a7256d","sha256:e586c5ec1f7944e2f366c614e7b51572444535d77a0941058cc112a28e24128b"],"state_sha256":"f43df8f2a3bae7e771a93cc955917588c219369dd27ff36c820bb774d312b910"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lr9GJlIu0qODr4ADPNu97MXkvolTM4tYONps9y/9p7OEGcyIqz77y90uVDgKrJoCvENzVCnKfUWLaLb+V3CfAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:28:54.538094Z","bundle_sha256":"c11f8e276f55d2f43be5fc0470a4d25cd33039a12cc546549cb684c098d03019"}}