{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:TP4BQYPBMZYKF2XHLAW4C6FP42","short_pith_number":"pith:TP4BQYPB","schema_version":"1.0","canonical_sha256":"9bf81861e16670a2eae7582dc178afe6bd1cffa79fe1ee3b50ac4c4c3fc0c890","source":{"kind":"arxiv","id":"math/0612647","version":4},"attestation_state":"computed","paper":{"title":"On boundary value problems for Einstein metrics","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Michael T. Anderson","submitted_at":"2006-12-21T15:05:52Z","abstract_excerpt":"On any given compact (n+1)-manifold M with non-empty boundary, it is proved that the moduli space of Einstein metrics on M is a smooth, infinite dimensional Banach manifold under a mild condition on the fundamental group. Thus, the Einstein moduli space is unobstructed. The Dirichlet and Neumann boundary maps to data on the boundary are smooth, but not Fredholm. Instead, one has natural mixed boundary-value problems which give Fredholm boundary maps.\n  These results also hold for manifolds with compact boundary which have a finite number of locally asymptotically flat ends, as well as for the "},"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":"math/0612647","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2006-12-21T15:05:52Z","cross_cats_sorted":[],"title_canon_sha256":"5ede8fe6be05303ce27a9d2e5f4d01cf0e35cc04801385a269b210053b079d51","abstract_canon_sha256":"d191e112a87557e72fad6176d41800097b049baaea516f03b332ee07d55aad81"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:59.437411Z","signature_b64":"ufoTFGjFKtR1ri5MnMFV+E0Rp7YIRONUyvYZ0tcxAEfUybZtMSK6gQPiCP2tx+x8ZT5v0v7BtHZvqMBFb89LCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bf81861e16670a2eae7582dc178afe6bd1cffa79fe1ee3b50ac4c4c3fc0c890","last_reissued_at":"2026-05-18T02:37:59.436974Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:59.436974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On boundary value problems for Einstein metrics","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Michael T. Anderson","submitted_at":"2006-12-21T15:05:52Z","abstract_excerpt":"On any given compact (n+1)-manifold M with non-empty boundary, it is proved that the moduli space of Einstein metrics on M is a smooth, infinite dimensional Banach manifold under a mild condition on the fundamental group. Thus, the Einstein moduli space is unobstructed. The Dirichlet and Neumann boundary maps to data on the boundary are smooth, but not Fredholm. Instead, one has natural mixed boundary-value problems which give Fredholm boundary maps.\n  These results also hold for manifolds with compact boundary which have a finite number of locally asymptotically flat ends, as well as for the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612647","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0612647","created_at":"2026-05-18T02:37:59.437038+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0612647v4","created_at":"2026-05-18T02:37:59.437038+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612647","created_at":"2026-05-18T02:37:59.437038+00:00"},{"alias_kind":"pith_short_12","alias_value":"TP4BQYPBMZYK","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"TP4BQYPBMZYKF2XH","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"TP4BQYPB","created_at":"2026-05-18T12:25:54.717736+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":8,"internal_anchor_count":6,"sample":[{"citing_arxiv_id":"2605.28753","citing_title":"GR from RG, $2d$ Example: JT-Gravity Induced from Renormalization Group Flow","ref_index":74,"is_internal_anchor":true},{"citing_arxiv_id":"2606.22810","citing_title":"A Linearized Obstruction to the Supersymmetric Extension of Conformal Boundary Conditions in Euclidean Gravity","ref_index":2,"is_internal_anchor":true},{"citing_arxiv_id":"2602.05130","citing_title":"Holographic pressure and volume for black holes","ref_index":61,"is_internal_anchor":true},{"citing_arxiv_id":"2508.03236","citing_title":"Timelike Liouville theory and AdS$_3$ gravity at finite cutoff","ref_index":5,"is_internal_anchor":true},{"citing_arxiv_id":"2512.15969","citing_title":"Quantum Liouville Cosmology","ref_index":59,"is_internal_anchor":true},{"citing_arxiv_id":"2602.19812","citing_title":"dS$^4$ Metamorphosis","ref_index":54,"is_internal_anchor":true},{"citing_arxiv_id":"2604.10267","citing_title":"The yes boundaries wavefunctions of the universe","ref_index":136,"is_internal_anchor":false},{"citing_arxiv_id":"2605.08058","citing_title":"Undulating Conformal Boundaries in 3D Gravity","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TP4BQYPBMZYKF2XHLAW4C6FP42","json":"https://pith.science/pith/TP4BQYPBMZYKF2XHLAW4C6FP42.json","graph_json":"https://pith.science/api/pith-number/TP4BQYPBMZYKF2XHLAW4C6FP42/graph.json","events_json":"https://pith.science/api/pith-number/TP4BQYPBMZYKF2XHLAW4C6FP42/events.json","paper":"https://pith.science/paper/TP4BQYPB"},"agent_actions":{"view_html":"https://pith.science/pith/TP4BQYPBMZYKF2XHLAW4C6FP42","download_json":"https://pith.science/pith/TP4BQYPBMZYKF2XHLAW4C6FP42.json","view_paper":"https://pith.science/paper/TP4BQYPB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0612647&json=true","fetch_graph":"https://pith.science/api/pith-number/TP4BQYPBMZYKF2XHLAW4C6FP42/graph.json","fetch_events":"https://pith.science/api/pith-number/TP4BQYPBMZYKF2XHLAW4C6FP42/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TP4BQYPBMZYKF2XHLAW4C6FP42/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TP4BQYPBMZYKF2XHLAW4C6FP42/action/storage_attestation","attest_author":"https://pith.science/pith/TP4BQYPBMZYKF2XHLAW4C6FP42/action/author_attestation","sign_citation":"https://pith.science/pith/TP4BQYPBMZYKF2XHLAW4C6FP42/action/citation_signature","submit_replication":"https://pith.science/pith/TP4BQYPBMZYKF2XHLAW4C6FP42/action/replication_record"}},"created_at":"2026-05-18T02:37:59.437038+00:00","updated_at":"2026-05-18T02:37:59.437038+00:00"}