{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:55ZBSKXJL2XBEMH4NQI7572FKY","short_pith_number":"pith:55ZBSKXJ","canonical_record":{"source":{"id":"1709.00267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-01T12:11:20Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a1c0e29223963ed3c69ff0e2905fe1ef04ee3b048a6db6eca28bd09f79c4e012","abstract_canon_sha256":"f41f4e48cc884cbd1de8783184dd6f4b01677ebae1d8011e397382aa3096d546"},"schema_version":"1.0"},"canonical_sha256":"ef72192ae95eae1230fc6c11feff45563ae0b8bb896123199958b06c49d2a018","source":{"kind":"arxiv","id":"1709.00267","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00267","created_at":"2026-05-18T00:36:12Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00267v1","created_at":"2026-05-18T00:36:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00267","created_at":"2026-05-18T00:36:12Z"},{"alias_kind":"pith_short_12","alias_value":"55ZBSKXJL2XB","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"55ZBSKXJL2XBEMH4","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"55ZBSKXJ","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:55ZBSKXJL2XBEMH4NQI7572FKY","target":"record","payload":{"canonical_record":{"source":{"id":"1709.00267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-01T12:11:20Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a1c0e29223963ed3c69ff0e2905fe1ef04ee3b048a6db6eca28bd09f79c4e012","abstract_canon_sha256":"f41f4e48cc884cbd1de8783184dd6f4b01677ebae1d8011e397382aa3096d546"},"schema_version":"1.0"},"canonical_sha256":"ef72192ae95eae1230fc6c11feff45563ae0b8bb896123199958b06c49d2a018","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:12.917782Z","signature_b64":"LgiVGmeWdoMBkPPs+bvoMGvR6e+4mdgVdFyiG2d2HfS0xrkMhtQMjcLsvnV4hr9aVU8XJ+2DQ9cWUno3rIbzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef72192ae95eae1230fc6c11feff45563ae0b8bb896123199958b06c49d2a018","last_reissued_at":"2026-05-18T00:36:12.917248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:12.917248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.00267","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":"2026-05-18T00:36:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5FqWyOJp/SqMtTNUkzrstlfYnUwsKmsFqQlvAjLbbANMw3969gpjIp0xkEgn3HTSdOKFfM7zTuNN1O6vZ08rDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:24:34.168184Z"},"content_sha256":"dd2b1a00b10033da62e0096fbbfe5c763cde3ba779e33bd2926a8687c82e363f","schema_version":"1.0","event_id":"sha256:dd2b1a00b10033da62e0096fbbfe5c763cde3ba779e33bd2926a8687c82e363f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:55ZBSKXJL2XBEMH4NQI7572FKY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear stability of the Milne model with matter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"David Fajman, Lars Andersson","submitted_at":"2017-09-01T12:11:20Z","abstract_excerpt":"We show that any 3+1-dimensional Milne model is future nonlinearly, asymptotically stable in the set of solutions to the Einstein-Vlasov system. For the analysis of the Einstein equations we use the constant-mean-curvature-spatial-harmonic gauge. For the distribution function the proof makes use of geometric L^2-estimates based on the Sasaki-metric. The resulting estimates on the energy momentum tensor are then upgraded by employing the natural continuity equation for the energy density."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00267","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":"2026-05-18T00:36:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cuw6irEm5i5I5P22zbKP4pFnfQ1Twxzn/YjG7y9WT6yAj8H9dit4k8Rw0WTTTfIzX1iaSjoW0CV5wmsXUETzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:24:34.168863Z"},"content_sha256":"243c49b4e387dd5677bc5c609fe336abc75ca980d7bc3d7c2050c13ff7fa60e7","schema_version":"1.0","event_id":"sha256:243c49b4e387dd5677bc5c609fe336abc75ca980d7bc3d7c2050c13ff7fa60e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/55ZBSKXJL2XBEMH4NQI7572FKY/bundle.json","state_url":"https://pith.science/pith/55ZBSKXJL2XBEMH4NQI7572FKY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/55ZBSKXJL2XBEMH4NQI7572FKY/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":"2026-05-27T19:24:34Z","links":{"resolver":"https://pith.science/pith/55ZBSKXJL2XBEMH4NQI7572FKY","bundle":"https://pith.science/pith/55ZBSKXJL2XBEMH4NQI7572FKY/bundle.json","state":"https://pith.science/pith/55ZBSKXJL2XBEMH4NQI7572FKY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/55ZBSKXJL2XBEMH4NQI7572FKY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:55ZBSKXJL2XBEMH4NQI7572FKY","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":"f41f4e48cc884cbd1de8783184dd6f4b01677ebae1d8011e397382aa3096d546","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-01T12:11:20Z","title_canon_sha256":"a1c0e29223963ed3c69ff0e2905fe1ef04ee3b048a6db6eca28bd09f79c4e012"},"schema_version":"1.0","source":{"id":"1709.00267","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00267","created_at":"2026-05-18T00:36:12Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00267v1","created_at":"2026-05-18T00:36:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00267","created_at":"2026-05-18T00:36:12Z"},{"alias_kind":"pith_short_12","alias_value":"55ZBSKXJL2XB","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"55ZBSKXJL2XBEMH4","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"55ZBSKXJ","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:243c49b4e387dd5677bc5c609fe336abc75ca980d7bc3d7c2050c13ff7fa60e7","target":"graph","created_at":"2026-05-18T00:36:12Z","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":"We show that any 3+1-dimensional Milne model is future nonlinearly, asymptotically stable in the set of solutions to the Einstein-Vlasov system. For the analysis of the Einstein equations we use the constant-mean-curvature-spatial-harmonic gauge. For the distribution function the proof makes use of geometric L^2-estimates based on the Sasaki-metric. The resulting estimates on the energy momentum tensor are then upgraded by employing the natural continuity equation for the energy density.","authors_text":"David Fajman, Lars Andersson","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-01T12:11:20Z","title":"Nonlinear stability of the Milne model with matter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00267","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:dd2b1a00b10033da62e0096fbbfe5c763cde3ba779e33bd2926a8687c82e363f","target":"record","created_at":"2026-05-18T00:36:12Z","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":"f41f4e48cc884cbd1de8783184dd6f4b01677ebae1d8011e397382aa3096d546","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-01T12:11:20Z","title_canon_sha256":"a1c0e29223963ed3c69ff0e2905fe1ef04ee3b048a6db6eca28bd09f79c4e012"},"schema_version":"1.0","source":{"id":"1709.00267","kind":"arxiv","version":1}},"canonical_sha256":"ef72192ae95eae1230fc6c11feff45563ae0b8bb896123199958b06c49d2a018","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef72192ae95eae1230fc6c11feff45563ae0b8bb896123199958b06c49d2a018","first_computed_at":"2026-05-18T00:36:12.917248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:12.917248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LgiVGmeWdoMBkPPs+bvoMGvR6e+4mdgVdFyiG2d2HfS0xrkMhtQMjcLsvnV4hr9aVU8XJ+2DQ9cWUno3rIbzCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:12.917782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.00267","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd2b1a00b10033da62e0096fbbfe5c763cde3ba779e33bd2926a8687c82e363f","sha256:243c49b4e387dd5677bc5c609fe336abc75ca980d7bc3d7c2050c13ff7fa60e7"],"state_sha256":"29b180bf45ace307fe4f7d788d0bdfffa15b8642f49ddb64bf24904cbeebd999"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qXMTjMHLphmHzL80nuk8PEoxQ8mIiPuMb3f71gEnAnFr7zz3lvCoJTg+FUosdy1PmjEpxGctlWQwDOSP8jaWBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:24:34.172572Z","bundle_sha256":"39656fe870fa5bd1ded2b0091264437a3b900177948cc6812ead099bb71c5b79"}}