{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:I3ZMTEQWRGW3SWDKHYXCU3STJY","short_pith_number":"pith:I3ZMTEQW","schema_version":"1.0","canonical_sha256":"46f2c9921689adb9586a3e2e2a6e534e36e2593bf6f6fa9aaeb3c201d83488fb","source":{"kind":"arxiv","id":"2505.07128","version":2},"attestation_state":"computed","paper":{"title":"Well-posed geometric boundary data in General Relativity, I: Dirichlet boundary data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","math.DG"],"primary_cat":"math.AP","authors_text":"Michael T. Anderson, Zhongshan An","submitted_at":"2025-05-11T21:43:22Z","abstract_excerpt":"In this first work in a series, we prove the local-in-time well-posedness of the IBVP for the vacuum Einstein equations with Dirichlet boundary data on a finite timelike boundary, provided the Brown- York stress tensor of the boundary is a Lorentz metric of the same signature (up to an overall sign) as the induced Lorentz metric on the boundary. This is a convexity-type assumption which is an exact analog of a similar result in the Riemannian setting. This assumption on the (extrinsic) Brown-York tensor cannot be dropped in general."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2505.07128","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-11T21:43:22Z","cross_cats_sorted":["gr-qc","math.DG"],"title_canon_sha256":"2a47e75969e565e30bf1c8d13a73939c5a7eb3198b9bdef3bea3584bb9305f65","abstract_canon_sha256":"a10dd6f352ef7b9ecc5f63b1f617f0092deb52f05731850b893c046a35d66cbe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:03:31.470597Z","signature_b64":"0oiEOUPQX5FGFJCVe1OIZwttL+0BwQwA6ApW0/vFdqznWbn3xVIKkl26GG6jZp29CESEuYKnywguic05E7R8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46f2c9921689adb9586a3e2e2a6e534e36e2593bf6f6fa9aaeb3c201d83488fb","last_reissued_at":"2026-06-02T01:03:31.470042Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:03:31.470042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Well-posed geometric boundary data in General Relativity, I: Dirichlet boundary data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","math.DG"],"primary_cat":"math.AP","authors_text":"Michael T. Anderson, Zhongshan An","submitted_at":"2025-05-11T21:43:22Z","abstract_excerpt":"In this first work in a series, we prove the local-in-time well-posedness of the IBVP for the vacuum Einstein equations with Dirichlet boundary data on a finite timelike boundary, provided the Brown- York stress tensor of the boundary is a Lorentz metric of the same signature (up to an overall sign) as the induced Lorentz metric on the boundary. This is a convexity-type assumption which is an exact analog of a similar result in the Riemannian setting. This assumption on the (extrinsic) Brown-York tensor cannot be dropped in general."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.07128","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/2505.07128/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2505.07128","created_at":"2026-06-02T01:03:31.470104+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.07128v2","created_at":"2026-06-02T01:03:31.470104+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.07128","created_at":"2026-06-02T01:03:31.470104+00:00"},{"alias_kind":"pith_short_12","alias_value":"I3ZMTEQWRGW3","created_at":"2026-06-02T01:03:31.470104+00:00"},{"alias_kind":"pith_short_16","alias_value":"I3ZMTEQWRGW3SWDK","created_at":"2026-06-02T01:03:31.470104+00:00"},{"alias_kind":"pith_short_8","alias_value":"I3ZMTEQW","created_at":"2026-06-02T01:03:31.470104+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":3,"sample":[{"citing_arxiv_id":"2604.19668","citing_title":"Abstract null hypersurfaces and characteristic initial value problems in General Relativity","ref_index":19,"is_internal_anchor":true},{"citing_arxiv_id":"2604.10267","citing_title":"The yes boundaries wavefunctions of the universe","ref_index":145,"is_internal_anchor":true},{"citing_arxiv_id":"2605.08058","citing_title":"Undulating Conformal Boundaries in 3D Gravity","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I3ZMTEQWRGW3SWDKHYXCU3STJY","json":"https://pith.science/pith/I3ZMTEQWRGW3SWDKHYXCU3STJY.json","graph_json":"https://pith.science/api/pith-number/I3ZMTEQWRGW3SWDKHYXCU3STJY/graph.json","events_json":"https://pith.science/api/pith-number/I3ZMTEQWRGW3SWDKHYXCU3STJY/events.json","paper":"https://pith.science/paper/I3ZMTEQW"},"agent_actions":{"view_html":"https://pith.science/pith/I3ZMTEQWRGW3SWDKHYXCU3STJY","download_json":"https://pith.science/pith/I3ZMTEQWRGW3SWDKHYXCU3STJY.json","view_paper":"https://pith.science/paper/I3ZMTEQW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.07128&json=true","fetch_graph":"https://pith.science/api/pith-number/I3ZMTEQWRGW3SWDKHYXCU3STJY/graph.json","fetch_events":"https://pith.science/api/pith-number/I3ZMTEQWRGW3SWDKHYXCU3STJY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I3ZMTEQWRGW3SWDKHYXCU3STJY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I3ZMTEQWRGW3SWDKHYXCU3STJY/action/storage_attestation","attest_author":"https://pith.science/pith/I3ZMTEQWRGW3SWDKHYXCU3STJY/action/author_attestation","sign_citation":"https://pith.science/pith/I3ZMTEQWRGW3SWDKHYXCU3STJY/action/citation_signature","submit_replication":"https://pith.science/pith/I3ZMTEQWRGW3SWDKHYXCU3STJY/action/replication_record"}},"created_at":"2026-06-02T01:03:31.470104+00:00","updated_at":"2026-06-02T01:03:31.470104+00:00"}