{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7HNWBAIKHGFVAA3VC2VRXIA4GU","short_pith_number":"pith:7HNWBAIK","canonical_record":{"source":{"id":"1303.1260","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-06T07:19:25Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"0d799598473419940b7218acd8b3253f11a78cdfdf739b74819b0d34f69998f1","abstract_canon_sha256":"bd4578f33c0302074513403e5994be65319a7c5ffd7a3815c4deef74d6614233"},"schema_version":"1.0"},"canonical_sha256":"f9db60810a398b50037516ab1ba01c35097f1584133365be18cc90aa2d3c4f50","source":{"kind":"arxiv","id":"1303.1260","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1260","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1260v3","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1260","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"pith_short_12","alias_value":"7HNWBAIKHGFV","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7HNWBAIKHGFVAA3V","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7HNWBAIK","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7HNWBAIKHGFVAA3VC2VRXIA4GU","target":"record","payload":{"canonical_record":{"source":{"id":"1303.1260","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-06T07:19:25Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"0d799598473419940b7218acd8b3253f11a78cdfdf739b74819b0d34f69998f1","abstract_canon_sha256":"bd4578f33c0302074513403e5994be65319a7c5ffd7a3815c4deef74d6614233"},"schema_version":"1.0"},"canonical_sha256":"f9db60810a398b50037516ab1ba01c35097f1584133365be18cc90aa2d3c4f50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:46.133214Z","signature_b64":"c19jvshh8gyTMpNmoj1Q3VG8ddxIr9h0m6xKkU1k9OeDnqIIDL1a3iygJLyYoddeRRvYSPDd220wXq+E0MVNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9db60810a398b50037516ab1ba01c35097f1584133365be18cc90aa2d3c4f50","last_reissued_at":"2026-05-18T01:04:46.132703Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:46.132703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.1260","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3GOChJF4gAyUtK1Zxh7VHlKpLGuh/QbToNNvoNrJFzWrtgGcN9UorGeT/cxcgDqbhyn/RsZp8oJTNp8dytiNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T16:19:11.831407Z"},"content_sha256":"9cfdb7f7dae1704091b39ba7f2cd05c8b6ad218d7dce93738d1386e950f67cf3","schema_version":"1.0","event_id":"sha256:9cfdb7f7dae1704091b39ba7f2cd05c8b6ad218d7dce93738d1386e950f67cf3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7HNWBAIKHGFVAA3VC2VRXIA4GU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Geometry of Null Cones to Infinity Under Curvature Flux Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.AP","authors_text":"Arick Shao, Spyros Alexakis","submitted_at":"2013-03-06T07:19:25Z","abstract_excerpt":"The main objective of this paper is to control the geometry of a future outgoing truncated null cone extending smoothly toward infinity in an Einstein-vacuum spacetime. In particular, we wish to do this under minimal regularity assumptions, namely, at the (weighted) L^2-curvature level. We show that if the curvature flux and the data on an initial sphere of the cone are sufficiently close to the corresponding values in a standard Minkowski or Schwarzschild null cone, then we can obtain quantitative bounds on the geometry of the entire infinite cone. The same bounds also imply the existence of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1260","kind":"arxiv","version":3},"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":"2026-05-18T01:04:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0uKasyjxCcmxkVvBK0gmjHxex7a8dnhDz6yBR2/+pvyBXxpOsRvTQnbUoTdzQ90b/Bhaq8sZppQPf/jIcN01CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T16:19:11.831769Z"},"content_sha256":"a16f868a08a40914d2a945aac1c46025f397e53202eeb32d9108e225726b48ca","schema_version":"1.0","event_id":"sha256:a16f868a08a40914d2a945aac1c46025f397e53202eeb32d9108e225726b48ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7HNWBAIKHGFVAA3VC2VRXIA4GU/bundle.json","state_url":"https://pith.science/pith/7HNWBAIKHGFVAA3VC2VRXIA4GU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7HNWBAIKHGFVAA3VC2VRXIA4GU/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":"2026-05-20T16:19:11Z","links":{"resolver":"https://pith.science/pith/7HNWBAIKHGFVAA3VC2VRXIA4GU","bundle":"https://pith.science/pith/7HNWBAIKHGFVAA3VC2VRXIA4GU/bundle.json","state":"https://pith.science/pith/7HNWBAIKHGFVAA3VC2VRXIA4GU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7HNWBAIKHGFVAA3VC2VRXIA4GU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7HNWBAIKHGFVAA3VC2VRXIA4GU","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":"bd4578f33c0302074513403e5994be65319a7c5ffd7a3815c4deef74d6614233","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-06T07:19:25Z","title_canon_sha256":"0d799598473419940b7218acd8b3253f11a78cdfdf739b74819b0d34f69998f1"},"schema_version":"1.0","source":{"id":"1303.1260","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1260","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1260v3","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1260","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"pith_short_12","alias_value":"7HNWBAIKHGFV","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7HNWBAIKHGFVAA3V","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7HNWBAIK","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:a16f868a08a40914d2a945aac1c46025f397e53202eeb32d9108e225726b48ca","target":"graph","created_at":"2026-05-18T01:04:46Z","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":"The main objective of this paper is to control the geometry of a future outgoing truncated null cone extending smoothly toward infinity in an Einstein-vacuum spacetime. In particular, we wish to do this under minimal regularity assumptions, namely, at the (weighted) L^2-curvature level. We show that if the curvature flux and the data on an initial sphere of the cone are sufficiently close to the corresponding values in a standard Minkowski or Schwarzschild null cone, then we can obtain quantitative bounds on the geometry of the entire infinite cone. The same bounds also imply the existence of ","authors_text":"Arick Shao, Spyros Alexakis","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-06T07:19:25Z","title":"On the Geometry of Null Cones to Infinity Under Curvature Flux Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1260","kind":"arxiv","version":3},"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":"sha256:9cfdb7f7dae1704091b39ba7f2cd05c8b6ad218d7dce93738d1386e950f67cf3","target":"record","created_at":"2026-05-18T01:04:46Z","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":"bd4578f33c0302074513403e5994be65319a7c5ffd7a3815c4deef74d6614233","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-06T07:19:25Z","title_canon_sha256":"0d799598473419940b7218acd8b3253f11a78cdfdf739b74819b0d34f69998f1"},"schema_version":"1.0","source":{"id":"1303.1260","kind":"arxiv","version":3}},"canonical_sha256":"f9db60810a398b50037516ab1ba01c35097f1584133365be18cc90aa2d3c4f50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9db60810a398b50037516ab1ba01c35097f1584133365be18cc90aa2d3c4f50","first_computed_at":"2026-05-18T01:04:46.132703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:46.132703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c19jvshh8gyTMpNmoj1Q3VG8ddxIr9h0m6xKkU1k9OeDnqIIDL1a3iygJLyYoddeRRvYSPDd220wXq+E0MVNAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:46.133214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1260","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cfdb7f7dae1704091b39ba7f2cd05c8b6ad218d7dce93738d1386e950f67cf3","sha256:a16f868a08a40914d2a945aac1c46025f397e53202eeb32d9108e225726b48ca"],"state_sha256":"0765f42a0946111168271c5c14dda110b8d53a3e1d6a4d01893c1384f955353c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VNsRmJzg5SJWiv09sIopplyzhJsHg4MOHLKAXk1ttugbipSQmM3HYuEUwfg8mTTVbIRkcUCUmOR7EYiRHpBhBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T16:19:11.834017Z","bundle_sha256":"3f2d27706ebb4b651ba1272b21e8d4c9a2c8ee8cf62e38cfbe5d3d6b710c4124"}}