{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RILYU7SGBBPIQNXJBVW673NK6Q","short_pith_number":"pith:RILYU7SG","canonical_record":{"source":{"id":"1507.01913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-07T18:34:07Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"9773e052ce78ac20b6d8c1ae16099cfe1e845532f7e5a28d3712e160b2d06612","abstract_canon_sha256":"0c258efa8f80126610ad7e49bb867f9877ef9504818c2b816ab6e70f3a65c678"},"schema_version":"1.0"},"canonical_sha256":"8a178a7e46085e8836e90d6defedaaf413fb5079518fa69d5c8ab1282f0720c8","source":{"kind":"arxiv","id":"1507.01913","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01913","created_at":"2026-05-18T01:37:12Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01913v1","created_at":"2026-05-18T01:37:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01913","created_at":"2026-05-18T01:37:12Z"},{"alias_kind":"pith_short_12","alias_value":"RILYU7SGBBPI","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RILYU7SGBBPIQNXJ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RILYU7SG","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RILYU7SGBBPIQNXJBVW673NK6Q","target":"record","payload":{"canonical_record":{"source":{"id":"1507.01913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-07T18:34:07Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"9773e052ce78ac20b6d8c1ae16099cfe1e845532f7e5a28d3712e160b2d06612","abstract_canon_sha256":"0c258efa8f80126610ad7e49bb867f9877ef9504818c2b816ab6e70f3a65c678"},"schema_version":"1.0"},"canonical_sha256":"8a178a7e46085e8836e90d6defedaaf413fb5079518fa69d5c8ab1282f0720c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:12.053066Z","signature_b64":"CY9o1M9AhCNK07ETobb0lvaSWpkyvtxGCV0pQNd+MmQOnNtPSyV1n9Fb+eUkP0pBZtmx5zd+rdROBETo5+kyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a178a7e46085e8836e90d6defedaaf413fb5079518fa69d5c8ab1282f0720c8","last_reissued_at":"2026-05-18T01:37:12.052394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:12.052394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.01913","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":"2026-05-18T01:37:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8jIXCaPkKqhJ2elJpuqtDWjoIO7I5qTGre87IzFjFnTrGiDOkETirC3upovvPEArV3scLB0e6g4REzbngnb8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:52:19.275013Z"},"content_sha256":"a195ff3482932c093a4491c6ab24bd9cc1573df7a8c6501bca9cfe66e97f447e","schema_version":"1.0","event_id":"sha256:a195ff3482932c093a4491c6ab24bd9cc1573df7a8c6501bca9cfe66e97f447e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RILYU7SGBBPIQNXJBVW673NK6Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Einstein Constraint Equations on Asymptotically Euclidean Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"gr-qc","authors_text":"James Dilts","submitted_at":"2015-07-07T18:34:07Z","abstract_excerpt":"In this dissertation, we prove a number of results regarding the conformal method of finding solutions to the Einstein constraint equations. These results include necessary and sufficient conditions for the Lichnerowicz equation to have solutions, global supersolutions which guarantee solutions to the conformal constraint equations for near-constant-mean-curvature (near-CMC) data as well as for far-from-CMC data, a proof of the limit equation criterion in the near-CMC case, as well as a model problem on the relationship between the asymptotic constants of solutions and the ADM mass. We also pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01913","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":"2026-05-18T01:37:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S7LlAJip2H01SRydRWI3sguifU5jgcMHI+fyjtKDlcnxb8u4EmqmfQz95xlyiK0GfuMEmnMS0bCYp8CYjQkeBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:52:19.275393Z"},"content_sha256":"c7eb5d1337dd50a24a74a1d584ebcfaa79924fb8b304c182ce1128ce039bfa8a","schema_version":"1.0","event_id":"sha256:c7eb5d1337dd50a24a74a1d584ebcfaa79924fb8b304c182ce1128ce039bfa8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RILYU7SGBBPIQNXJBVW673NK6Q/bundle.json","state_url":"https://pith.science/pith/RILYU7SGBBPIQNXJBVW673NK6Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RILYU7SGBBPIQNXJBVW673NK6Q/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":"2026-06-23T16:52:19Z","links":{"resolver":"https://pith.science/pith/RILYU7SGBBPIQNXJBVW673NK6Q","bundle":"https://pith.science/pith/RILYU7SGBBPIQNXJBVW673NK6Q/bundle.json","state":"https://pith.science/pith/RILYU7SGBBPIQNXJBVW673NK6Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RILYU7SGBBPIQNXJBVW673NK6Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RILYU7SGBBPIQNXJBVW673NK6Q","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":"0c258efa8f80126610ad7e49bb867f9877ef9504818c2b816ab6e70f3a65c678","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-07T18:34:07Z","title_canon_sha256":"9773e052ce78ac20b6d8c1ae16099cfe1e845532f7e5a28d3712e160b2d06612"},"schema_version":"1.0","source":{"id":"1507.01913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01913","created_at":"2026-05-18T01:37:12Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01913v1","created_at":"2026-05-18T01:37:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01913","created_at":"2026-05-18T01:37:12Z"},{"alias_kind":"pith_short_12","alias_value":"RILYU7SGBBPI","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RILYU7SGBBPIQNXJ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RILYU7SG","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:c7eb5d1337dd50a24a74a1d584ebcfaa79924fb8b304c182ce1128ce039bfa8a","target":"graph","created_at":"2026-05-18T01:37:12Z","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":"In this dissertation, we prove a number of results regarding the conformal method of finding solutions to the Einstein constraint equations. These results include necessary and sufficient conditions for the Lichnerowicz equation to have solutions, global supersolutions which guarantee solutions to the conformal constraint equations for near-constant-mean-curvature (near-CMC) data as well as for far-from-CMC data, a proof of the limit equation criterion in the near-CMC case, as well as a model problem on the relationship between the asymptotic constants of solutions and the ADM mass. We also pr","authors_text":"James Dilts","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-07T18:34:07Z","title":"The Einstein Constraint Equations on Asymptotically Euclidean Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01913","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:a195ff3482932c093a4491c6ab24bd9cc1573df7a8c6501bca9cfe66e97f447e","target":"record","created_at":"2026-05-18T01:37:12Z","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":"0c258efa8f80126610ad7e49bb867f9877ef9504818c2b816ab6e70f3a65c678","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-07T18:34:07Z","title_canon_sha256":"9773e052ce78ac20b6d8c1ae16099cfe1e845532f7e5a28d3712e160b2d06612"},"schema_version":"1.0","source":{"id":"1507.01913","kind":"arxiv","version":1}},"canonical_sha256":"8a178a7e46085e8836e90d6defedaaf413fb5079518fa69d5c8ab1282f0720c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a178a7e46085e8836e90d6defedaaf413fb5079518fa69d5c8ab1282f0720c8","first_computed_at":"2026-05-18T01:37:12.052394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:12.052394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CY9o1M9AhCNK07ETobb0lvaSWpkyvtxGCV0pQNd+MmQOnNtPSyV1n9Fb+eUkP0pBZtmx5zd+rdROBETo5+kyDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:12.053066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a195ff3482932c093a4491c6ab24bd9cc1573df7a8c6501bca9cfe66e97f447e","sha256:c7eb5d1337dd50a24a74a1d584ebcfaa79924fb8b304c182ce1128ce039bfa8a"],"state_sha256":"bd6ee373e58e590efa89272cc4baa7c538370a0fa7ed4be27f1afdfcabd40ed7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BfN+i1rD0TfsXysgaT1Y3oSMgYrwlRwGn+kMDHiJ2B/7GM8XRObUKblY1s0o55/mML1sxpOsgdEXRMLrAWFMCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:52:19.277398Z","bundle_sha256":"c5dd09d9791b6a6d5d1e8e7f37579f4aefc24884bfa00331151c325b9378c4b7"}}