{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:E3WO2EJRDRBPJYNLLI6VFOXWAN","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":"b0a2fae606528f61e792cbc4e1e23c14348577d707926e100196272367f23c1f","cross_cats_sorted":["physics.gen-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-04T11:32:40Z","title_canon_sha256":"464369ecbdcec437ed9081ec2135927e17233d7899a0e242d4f1d1a669d20382"},"schema_version":"1.0","source":{"id":"1209.0611","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0611","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0611v2","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0611","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"E3WO2EJRDRBP","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E3WO2EJRDRBPJYNL","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E3WO2EJR","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:2e2e766e24b6b25312d0ee0bdfc198546f1945f50a34c9c72700adf8f6f17d9b","target":"graph","created_at":"2026-05-18T02:41:52Z","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 article we propose to add stress-energy tensor to the Einstein equations, assuming that the matter-energy and the metric space-time is nothing but a continuous medium with some elastic properties. We first give a general expression of the stress tensor which is linearly related to the strain tensor. Then, we give the particular expression of the stress tensor for a spatially homnogeneous and isotropic cosmological medium. After that we derive the modified Friedmann equations. In first approximation, we end up with the usual term $\\Lambda g_{\\mu\\nu}$ , where the cosmological constant $\\","authors_text":"Mathieu Beau (STP-DIAS)","cross_cats":["physics.gen-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-04T11:32:40Z","title":"Th\\'eorie des champs des contraintes et d\\'eformations en relativit\\'e g\\'en\\'erale et expansion cosmologique: Theory of stress and strain fields in general relativity and cosmological expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0611","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:a8d38de5f206820ec7ecf859e2b2bdc14f0a8d8c02cbef44b50ef3f2d32b1229","target":"record","created_at":"2026-05-18T02:41:52Z","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":"b0a2fae606528f61e792cbc4e1e23c14348577d707926e100196272367f23c1f","cross_cats_sorted":["physics.gen-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-04T11:32:40Z","title_canon_sha256":"464369ecbdcec437ed9081ec2135927e17233d7899a0e242d4f1d1a669d20382"},"schema_version":"1.0","source":{"id":"1209.0611","kind":"arxiv","version":2}},"canonical_sha256":"26eced11311c42f4e1ab5a3d52baf6036dc7d84ed2554e69a5f81d08afdba347","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26eced11311c42f4e1ab5a3d52baf6036dc7d84ed2554e69a5f81d08afdba347","first_computed_at":"2026-05-18T02:41:52.172906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:52.172906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IZYMyp/BtoTKXsMsY3Fmt2PIncklVAqrp4Iv+8IHdH1UwKbwy5oaInwBcPRCwBMUSYVbS81Y/VGYzmiyek1HBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:52.173515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0611","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8d38de5f206820ec7ecf859e2b2bdc14f0a8d8c02cbef44b50ef3f2d32b1229","sha256:2e2e766e24b6b25312d0ee0bdfc198546f1945f50a34c9c72700adf8f6f17d9b"],"state_sha256":"99a83f5d3a91d334a97485ed5045f3a14fc0c2ebd0339b89d662196a59635432"}