{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:7DNAKKA3CK76O72XCGSDXBXSDA","short_pith_number":"pith:7DNAKKA3","canonical_record":{"source":{"id":"2210.00512","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-10-02T13:17:40Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"115fd170c3677b1ed016050b914f7069e7b8c299b49129b94c230003b9669446","abstract_canon_sha256":"f92f4728219b50bc3d3c6b7b9f4c2f0eb2fd11dad3b7f74e6dc6c082ddda23e9"},"schema_version":"1.0"},"canonical_sha256":"f8da05281b12bfe77f5711a43b86f2183c0c930adb7ee3b6809c00268cda1fe5","source":{"kind":"arxiv","id":"2210.00512","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.00512","created_at":"2026-07-05T05:04:15Z"},{"alias_kind":"arxiv_version","alias_value":"2210.00512v2","created_at":"2026-07-05T05:04:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.00512","created_at":"2026-07-05T05:04:15Z"},{"alias_kind":"pith_short_12","alias_value":"7DNAKKA3CK76","created_at":"2026-07-05T05:04:15Z"},{"alias_kind":"pith_short_16","alias_value":"7DNAKKA3CK76O72X","created_at":"2026-07-05T05:04:15Z"},{"alias_kind":"pith_short_8","alias_value":"7DNAKKA3","created_at":"2026-07-05T05:04:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:7DNAKKA3CK76O72XCGSDXBXSDA","target":"record","payload":{"canonical_record":{"source":{"id":"2210.00512","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-10-02T13:17:40Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"115fd170c3677b1ed016050b914f7069e7b8c299b49129b94c230003b9669446","abstract_canon_sha256":"f92f4728219b50bc3d3c6b7b9f4c2f0eb2fd11dad3b7f74e6dc6c082ddda23e9"},"schema_version":"1.0"},"canonical_sha256":"f8da05281b12bfe77f5711a43b86f2183c0c930adb7ee3b6809c00268cda1fe5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:04:15.254830Z","signature_b64":"iWn7xq7J/P0ZXkA/ddtjATKnW5pl88+Pi/eEqGPFWTGwqOojyS94Kp2OYPrP5biKNl5Lricvt0d57rOPfbW5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8da05281b12bfe77f5711a43b86f2183c0c930adb7ee3b6809c00268cda1fe5","last_reissued_at":"2026-07-05T05:04:15.254438Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:04:15.254438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.00512","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":"2026-07-05T05:04:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GH/YEya2WUcjJwDtl5QRfuM0BLv5B+94CxeqG2UY5P2mMTZZ8GyRqG/Oo0p816znj1D4UTG/jyhITR+Ifv5GAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:06:33.991503Z"},"content_sha256":"56900fd774f92c2f5a52f4eadf0f9c3463dd800dafb9b4afeab5b965f241cad1","schema_version":"1.0","event_id":"sha256:56900fd774f92c2f5a52f4eadf0f9c3463dd800dafb9b4afeab5b965f241cad1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:7DNAKKA3CK76O72XCGSDXBXSDA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global stability of the Minkowski spacetime for the Einstein-Vlasov system","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.AP","authors_text":"Xuecheng Wang","submitted_at":"2022-10-02T13:17:40Z","abstract_excerpt":"We prove global stability of the Minkowski spacetime in the wave coordinates system for the massive Einstein-Vlasov system. In particular, compared with previous results by Lindblad-Taylor, in which the Vlasov part is assumed to have compact support assumption, and Fajman-Joudioux-Smulevci, in which the spacetime is assumed to be exact Schwarzschild in the exterior region, we do not impose any compact support condition for the Vlasov part and allow a large class of non-isotropic perturbations for the metric part, which decay at rate $\\langle r\\rangle^{-1+}$ towards space infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.00512","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.00512/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:04:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"45LHv0XKcwy8PyipEHKdFvRF/k6nWMfei1VI87nwhryMQz3d4IAfY6aJQORj7s3GRTvM1ygByA7kYed9e9ByBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:06:33.991873Z"},"content_sha256":"9f9911082cf59b39bc1bbf13426876f296add34593531178ae3a3e37c53b2e83","schema_version":"1.0","event_id":"sha256:9f9911082cf59b39bc1bbf13426876f296add34593531178ae3a3e37c53b2e83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7DNAKKA3CK76O72XCGSDXBXSDA/bundle.json","state_url":"https://pith.science/pith/7DNAKKA3CK76O72XCGSDXBXSDA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7DNAKKA3CK76O72XCGSDXBXSDA/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":"2026-07-07T08:06:33Z","links":{"resolver":"https://pith.science/pith/7DNAKKA3CK76O72XCGSDXBXSDA","bundle":"https://pith.science/pith/7DNAKKA3CK76O72XCGSDXBXSDA/bundle.json","state":"https://pith.science/pith/7DNAKKA3CK76O72XCGSDXBXSDA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7DNAKKA3CK76O72XCGSDXBXSDA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:7DNAKKA3CK76O72XCGSDXBXSDA","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":"f92f4728219b50bc3d3c6b7b9f4c2f0eb2fd11dad3b7f74e6dc6c082ddda23e9","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-10-02T13:17:40Z","title_canon_sha256":"115fd170c3677b1ed016050b914f7069e7b8c299b49129b94c230003b9669446"},"schema_version":"1.0","source":{"id":"2210.00512","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.00512","created_at":"2026-07-05T05:04:15Z"},{"alias_kind":"arxiv_version","alias_value":"2210.00512v2","created_at":"2026-07-05T05:04:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.00512","created_at":"2026-07-05T05:04:15Z"},{"alias_kind":"pith_short_12","alias_value":"7DNAKKA3CK76","created_at":"2026-07-05T05:04:15Z"},{"alias_kind":"pith_short_16","alias_value":"7DNAKKA3CK76O72X","created_at":"2026-07-05T05:04:15Z"},{"alias_kind":"pith_short_8","alias_value":"7DNAKKA3","created_at":"2026-07-05T05:04:15Z"}],"graph_snapshots":[{"event_id":"sha256:9f9911082cf59b39bc1bbf13426876f296add34593531178ae3a3e37c53b2e83","target":"graph","created_at":"2026-07-05T05:04:15Z","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/2210.00512/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove global stability of the Minkowski spacetime in the wave coordinates system for the massive Einstein-Vlasov system. In particular, compared with previous results by Lindblad-Taylor, in which the Vlasov part is assumed to have compact support assumption, and Fajman-Joudioux-Smulevci, in which the spacetime is assumed to be exact Schwarzschild in the exterior region, we do not impose any compact support condition for the Vlasov part and allow a large class of non-isotropic perturbations for the metric part, which decay at rate $\\langle r\\rangle^{-1+}$ towards space infinity.","authors_text":"Xuecheng Wang","cross_cats":["gr-qc"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-10-02T13:17:40Z","title":"Global stability of the Minkowski spacetime for the Einstein-Vlasov system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.00512","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":"sha256:56900fd774f92c2f5a52f4eadf0f9c3463dd800dafb9b4afeab5b965f241cad1","target":"record","created_at":"2026-07-05T05:04:15Z","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":"f92f4728219b50bc3d3c6b7b9f4c2f0eb2fd11dad3b7f74e6dc6c082ddda23e9","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-10-02T13:17:40Z","title_canon_sha256":"115fd170c3677b1ed016050b914f7069e7b8c299b49129b94c230003b9669446"},"schema_version":"1.0","source":{"id":"2210.00512","kind":"arxiv","version":2}},"canonical_sha256":"f8da05281b12bfe77f5711a43b86f2183c0c930adb7ee3b6809c00268cda1fe5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8da05281b12bfe77f5711a43b86f2183c0c930adb7ee3b6809c00268cda1fe5","first_computed_at":"2026-07-05T05:04:15.254438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:04:15.254438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iWn7xq7J/P0ZXkA/ddtjATKnW5pl88+Pi/eEqGPFWTGwqOojyS94Kp2OYPrP5biKNl5Lricvt0d57rOPfbW5AA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:04:15.254830Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.00512","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56900fd774f92c2f5a52f4eadf0f9c3463dd800dafb9b4afeab5b965f241cad1","sha256:9f9911082cf59b39bc1bbf13426876f296add34593531178ae3a3e37c53b2e83"],"state_sha256":"636a389be0e9b517d2e0ef47fd7d693bffdbf5aa37d97d626b458e2aa304dba3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9LbkHtDFL6eXOguhq+hkiiU6En0lUTpUPYccbFiG3pOZ8CWGyX6Etcc+sMIk26GbvHBHpesmshK+10ALo3HgCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T08:06:33.993820Z","bundle_sha256":"b93bb045cab66b399b369527a85715ebe30160c5631c11a7a007bfbd385e85ec"}}