{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2LJ3MSFXXD2TNTU3W6XSWOON5Y","short_pith_number":"pith:2LJ3MSFX","canonical_record":{"source":{"id":"1602.09066","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-25T10:36:01Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"95b91618ae9f9c117514cf2c45f7ea2173cb25223fce3d2e04d6d4befff0773a","abstract_canon_sha256":"e35d133f281d6ff5d0af61b68fdc97f0aa04babfa81b9ab3bf80142f5c18542f"},"schema_version":"1.0"},"canonical_sha256":"d2d3b648b7b8f536ce9bb7af2b39cdee2142099f5fe14a3a0e3795d4f6bd9270","source":{"kind":"arxiv","id":"1602.09066","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.09066","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1602.09066v2","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.09066","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"2LJ3MSFXXD2T","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2LJ3MSFXXD2TNTU3","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2LJ3MSFX","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2LJ3MSFXXD2TNTU3W6XSWOON5Y","target":"record","payload":{"canonical_record":{"source":{"id":"1602.09066","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-25T10:36:01Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"95b91618ae9f9c117514cf2c45f7ea2173cb25223fce3d2e04d6d4befff0773a","abstract_canon_sha256":"e35d133f281d6ff5d0af61b68fdc97f0aa04babfa81b9ab3bf80142f5c18542f"},"schema_version":"1.0"},"canonical_sha256":"d2d3b648b7b8f536ce9bb7af2b39cdee2142099f5fe14a3a0e3795d4f6bd9270","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:13.253736Z","signature_b64":"rXn4xsTC7KZ/+RvZKL8d51hvkQXfyLMQqSAQ4STh2J3524xJ3Q8w1RIpGBaXj+4EuXw7dZl1C+a2F59SJGT+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2d3b648b7b8f536ce9bb7af2b39cdee2142099f5fe14a3a0e3795d4f6bd9270","last_reissued_at":"2026-05-18T00:42:13.253020Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:13.253020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.09066","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":"2026-05-18T00:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VWuAH8ihXY2104D/Uj0eW/QIkrd0klla5EncR8EWUxS3/LytDgi9BNkZ1c6KL1rkuYS90jApHKBft0ZDcD5oCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:45:35.989604Z"},"content_sha256":"17734a178ed8d40844420c1da3d52ab7912d4d135174e74890ef11fc6b813b82","schema_version":"1.0","event_id":"sha256:17734a178ed8d40844420c1da3d52ab7912d4d135174e74890ef11fc6b813b82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2LJ3MSFXXD2TNTU3W6XSWOON5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A random field formulation of Hooke's law in all elasticity classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Anatoliy Malyarenko, Martin Ostoja-Starzewski","submitted_at":"2016-02-25T10:36:01Z","abstract_excerpt":"For each of the $8$ isotropy classes of elastic materials, we consider a homogeneous random field taking values in the fixed point set $\\mathsf{V}$ of the corresponding class, that is isotropic with respect to the natural orthogonal representation of a group lying between the isotropy group of the class and its normaliser. We find the general form of the correlation tensors of orders $1$ and $2$ of such a field, and the field's spectral expansion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.09066","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":"2026-05-18T00:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TQA9JJOdrjbee+nY+NYHs5Ywu2n4JWpOK3U4V1Nxp6gN6Jhv3V/kjW3x/5tsWbhmCRwvgmu76n3eAXqjRyjWCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:45:35.990089Z"},"content_sha256":"3c85658d962cc5592d47bda27a665997702c7b030dc5849b1e76d2a7c96d204e","schema_version":"1.0","event_id":"sha256:3c85658d962cc5592d47bda27a665997702c7b030dc5849b1e76d2a7c96d204e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2LJ3MSFXXD2TNTU3W6XSWOON5Y/bundle.json","state_url":"https://pith.science/pith/2LJ3MSFXXD2TNTU3W6XSWOON5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2LJ3MSFXXD2TNTU3W6XSWOON5Y/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":"2026-06-26T00:45:35Z","links":{"resolver":"https://pith.science/pith/2LJ3MSFXXD2TNTU3W6XSWOON5Y","bundle":"https://pith.science/pith/2LJ3MSFXXD2TNTU3W6XSWOON5Y/bundle.json","state":"https://pith.science/pith/2LJ3MSFXXD2TNTU3W6XSWOON5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2LJ3MSFXXD2TNTU3W6XSWOON5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2LJ3MSFXXD2TNTU3W6XSWOON5Y","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":"e35d133f281d6ff5d0af61b68fdc97f0aa04babfa81b9ab3bf80142f5c18542f","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-25T10:36:01Z","title_canon_sha256":"95b91618ae9f9c117514cf2c45f7ea2173cb25223fce3d2e04d6d4befff0773a"},"schema_version":"1.0","source":{"id":"1602.09066","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.09066","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1602.09066v2","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.09066","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"2LJ3MSFXXD2T","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2LJ3MSFXXD2TNTU3","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2LJ3MSFX","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:3c85658d962cc5592d47bda27a665997702c7b030dc5849b1e76d2a7c96d204e","target":"graph","created_at":"2026-05-18T00:42:13Z","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":"For each of the $8$ isotropy classes of elastic materials, we consider a homogeneous random field taking values in the fixed point set $\\mathsf{V}$ of the corresponding class, that is isotropic with respect to the natural orthogonal representation of a group lying between the isotropy group of the class and its normaliser. We find the general form of the correlation tensors of orders $1$ and $2$ of such a field, and the field's spectral expansion.","authors_text":"Anatoliy Malyarenko, Martin Ostoja-Starzewski","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-25T10:36:01Z","title":"A random field formulation of Hooke's law in all elasticity classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.09066","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":"sha256:17734a178ed8d40844420c1da3d52ab7912d4d135174e74890ef11fc6b813b82","target":"record","created_at":"2026-05-18T00:42:13Z","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":"e35d133f281d6ff5d0af61b68fdc97f0aa04babfa81b9ab3bf80142f5c18542f","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-25T10:36:01Z","title_canon_sha256":"95b91618ae9f9c117514cf2c45f7ea2173cb25223fce3d2e04d6d4befff0773a"},"schema_version":"1.0","source":{"id":"1602.09066","kind":"arxiv","version":2}},"canonical_sha256":"d2d3b648b7b8f536ce9bb7af2b39cdee2142099f5fe14a3a0e3795d4f6bd9270","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2d3b648b7b8f536ce9bb7af2b39cdee2142099f5fe14a3a0e3795d4f6bd9270","first_computed_at":"2026-05-18T00:42:13.253020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:13.253020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rXn4xsTC7KZ/+RvZKL8d51hvkQXfyLMQqSAQ4STh2J3524xJ3Q8w1RIpGBaXj+4EuXw7dZl1C+a2F59SJGT+AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:13.253736Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.09066","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17734a178ed8d40844420c1da3d52ab7912d4d135174e74890ef11fc6b813b82","sha256:3c85658d962cc5592d47bda27a665997702c7b030dc5849b1e76d2a7c96d204e"],"state_sha256":"c76437a9e2600329961d182cb5f4088dad2625c8c3e9b36f5af9c25e6f5dca14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aZVWjdFCZi+Q7egw1jisdpgusRpKa7//b2BiacvCXE7LcWkNB0S20bwpZULKS8zpbi5DI2B8aCBjsHnxroPSAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:45:35.992554Z","bundle_sha256":"26116e59213d7de6524e6ae4891df028cbd63b654f1d9dc3e1d98fa1a7684928"}}