{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:QJAGZKQA6532PUFVX7NVIZM7NG","short_pith_number":"pith:QJAGZKQA","canonical_record":{"source":{"id":"1011.4920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-22T19:56:42Z","cross_cats_sorted":["astro-ph.CO"],"title_canon_sha256":"6061f71bc9285143fb0904fd6a6ccb71d17a8e63ede6145d12b9feb90908433d","abstract_canon_sha256":"10259467a5fefec8a81ceb1a4894fc6fd10cbaaba82208eeef4f0a0dc02f07cf"},"schema_version":"1.0"},"canonical_sha256":"82406caa00f777a7d0b5bfdb54659f69b33954656e1cedee5c2e79cdb825b69b","source":{"kind":"arxiv","id":"1011.4920","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4920","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4920v2","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4920","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"pith_short_12","alias_value":"QJAGZKQA6532","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QJAGZKQA6532PUFV","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QJAGZKQA","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:QJAGZKQA6532PUFVX7NVIZM7NG","target":"record","payload":{"canonical_record":{"source":{"id":"1011.4920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-22T19:56:42Z","cross_cats_sorted":["astro-ph.CO"],"title_canon_sha256":"6061f71bc9285143fb0904fd6a6ccb71d17a8e63ede6145d12b9feb90908433d","abstract_canon_sha256":"10259467a5fefec8a81ceb1a4894fc6fd10cbaaba82208eeef4f0a0dc02f07cf"},"schema_version":"1.0"},"canonical_sha256":"82406caa00f777a7d0b5bfdb54659f69b33954656e1cedee5c2e79cdb825b69b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:35.040003Z","signature_b64":"yAK/BikdpubOW6g5xJP0MLXCz7ZVYeb9M7aAkAlJhFFiGDp1xrWdY4NFEyingFGucsHBnrYVnBp7Lc3Dk6FbBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82406caa00f777a7d0b5bfdb54659f69b33954656e1cedee5c2e79cdb825b69b","last_reissued_at":"2026-05-18T04:24:35.039601Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:35.039601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.4920","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":"2026-05-18T04:24:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QQFTiCugMVqKMMvFVfAbrKo3K6vu9gc2WrTl1v+5UDPYU7g79PONT9MrHOGW0yJcDpRgoN2iQ8duaYyfMb5sBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:48:32.210787Z"},"content_sha256":"32e0b77a52fec1544f7f0a305778fa263db9b7153aa8954c268a2a6b50b4ecf6","schema_version":"1.0","event_id":"sha256:32e0b77a52fec1544f7f0a305778fa263db9b7153aa8954c268a2a6b50b4ecf6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:QJAGZKQA6532PUFVX7NVIZM7NG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new framework for analyzing the effects of small scale inhomogeneities in cosmology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO"],"primary_cat":"gr-qc","authors_text":"Robert M. Wald, Stephen R. Green","submitted_at":"2010-11-22T19:56:42Z","abstract_excerpt":"We develop a new, mathematically precise framework for treating the effects of nonlinear phenomena occurring on small scales in general relativity. Our approach is an adaptation of Burnett's formulation of the \"shortwave approximation\", which we generalize to analyze the effects of matter inhomogeneities as well as gravitational radiation. Our framework requires the metric to be close to a \"background metric\", but allows arbitrarily large stress-energy fluctuations on small scales. We prove that, within our framework, if the matter stress-energy tensor satisfies the weak energy condition (i.e."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4920","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":""},"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":"2026-05-18T04:24:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zQZPxLSUBlMgPZXyZzSCV21sQEjQT8GQRK2nJn+ItRMgcLZivJjVBFEnVXmNErtJYgzLtnoj3YxXrczW/l2vBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:48:32.211164Z"},"content_sha256":"3c7a37e0df4128f45fa354bd86615110b226e8195ec416f67a5cd6b37f431ce8","schema_version":"1.0","event_id":"sha256:3c7a37e0df4128f45fa354bd86615110b226e8195ec416f67a5cd6b37f431ce8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJAGZKQA6532PUFVX7NVIZM7NG/bundle.json","state_url":"https://pith.science/pith/QJAGZKQA6532PUFVX7NVIZM7NG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJAGZKQA6532PUFVX7NVIZM7NG/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":"2026-06-05T00:48:32Z","links":{"resolver":"https://pith.science/pith/QJAGZKQA6532PUFVX7NVIZM7NG","bundle":"https://pith.science/pith/QJAGZKQA6532PUFVX7NVIZM7NG/bundle.json","state":"https://pith.science/pith/QJAGZKQA6532PUFVX7NVIZM7NG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJAGZKQA6532PUFVX7NVIZM7NG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QJAGZKQA6532PUFVX7NVIZM7NG","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":"10259467a5fefec8a81ceb1a4894fc6fd10cbaaba82208eeef4f0a0dc02f07cf","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-22T19:56:42Z","title_canon_sha256":"6061f71bc9285143fb0904fd6a6ccb71d17a8e63ede6145d12b9feb90908433d"},"schema_version":"1.0","source":{"id":"1011.4920","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4920","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4920v2","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4920","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"pith_short_12","alias_value":"QJAGZKQA6532","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QJAGZKQA6532PUFV","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QJAGZKQA","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:3c7a37e0df4128f45fa354bd86615110b226e8195ec416f67a5cd6b37f431ce8","target":"graph","created_at":"2026-05-18T04:24:35Z","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":"We develop a new, mathematically precise framework for treating the effects of nonlinear phenomena occurring on small scales in general relativity. Our approach is an adaptation of Burnett's formulation of the \"shortwave approximation\", which we generalize to analyze the effects of matter inhomogeneities as well as gravitational radiation. Our framework requires the metric to be close to a \"background metric\", but allows arbitrarily large stress-energy fluctuations on small scales. We prove that, within our framework, if the matter stress-energy tensor satisfies the weak energy condition (i.e.","authors_text":"Robert M. Wald, Stephen R. Green","cross_cats":["astro-ph.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-22T19:56:42Z","title":"A new framework for analyzing the effects of small scale inhomogeneities in cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4920","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":"sha256:32e0b77a52fec1544f7f0a305778fa263db9b7153aa8954c268a2a6b50b4ecf6","target":"record","created_at":"2026-05-18T04:24:35Z","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":"10259467a5fefec8a81ceb1a4894fc6fd10cbaaba82208eeef4f0a0dc02f07cf","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-22T19:56:42Z","title_canon_sha256":"6061f71bc9285143fb0904fd6a6ccb71d17a8e63ede6145d12b9feb90908433d"},"schema_version":"1.0","source":{"id":"1011.4920","kind":"arxiv","version":2}},"canonical_sha256":"82406caa00f777a7d0b5bfdb54659f69b33954656e1cedee5c2e79cdb825b69b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82406caa00f777a7d0b5bfdb54659f69b33954656e1cedee5c2e79cdb825b69b","first_computed_at":"2026-05-18T04:24:35.039601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:35.039601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yAK/BikdpubOW6g5xJP0MLXCz7ZVYeb9M7aAkAlJhFFiGDp1xrWdY4NFEyingFGucsHBnrYVnBp7Lc3Dk6FbBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:35.040003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.4920","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32e0b77a52fec1544f7f0a305778fa263db9b7153aa8954c268a2a6b50b4ecf6","sha256:3c7a37e0df4128f45fa354bd86615110b226e8195ec416f67a5cd6b37f431ce8"],"state_sha256":"4dcd8d27263abdfe6e194ad561d12f52ecc5176d502d2521d68e77df23ee3aba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mfqY3j7kzedXXV5BcUof5kBY2s+Y33ULBdWyetYGuoSkRTVpTJjAigGWNFsEgcL4XgiH0Nthr5X4m/N5xvT5AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:48:32.214467Z","bundle_sha256":"5bb28ec4ff08cb04f9352506230c12761a2b3eabb1bc37d8aabd8a4f4a848555"}}