{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:2OQX55JLPY6VQV5A63NCAF7CSO","short_pith_number":"pith:2OQX55JL","schema_version":"1.0","canonical_sha256":"d3a17ef52b7e3d5857a0f6da2017e293aecc2ccae42e9d9739cebcdf298f0d4a","source":{"kind":"arxiv","id":"1605.09561","version":2},"attestation_state":"computed","paper":{"title":"A minimal integrity basis for the elasticity tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Boris Kolev (I2M), Marc Olive (LMA ), Nicolas Auffray (MSME)","submitted_at":"2016-05-31T10:30:10Z","abstract_excerpt":"We definitively solve the old problem of finding a minimal integrity basis of polynomial invariants of the fourth-order elasticity tensor C. Decomposing C into its SO(3)-irreducible components we reduce this problem to finding joint invariants of a triplet (a, b, D), where a and b are second-order harmonic tensors, and D is a fourth-order harmonic tensor. Combining theorems of classical invariant theory and formal computations, a minimal integrity basis of 297 polynomial invariants for the elasticity tensor is obtained for the first time."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.09561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-31T10:30:10Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"129bf69ad575351d8da59a66ab18e574fd4dfadc265c6c526af905e674ce55ae","abstract_canon_sha256":"b31f9f51a7bb73ec2b14c88e20fd7b859a0b516b28a5cd9981922ac9a7425e16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:15.985031Z","signature_b64":"zK6Ay/WftJgkUY1BPVDQ2Qsyllfg++cLhrOAwAMXM+1a0sLphtEcAWgQYA+0IwHbjqe/aC4DOlwTL0QHEpCEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3a17ef52b7e3d5857a0f6da2017e293aecc2ccae42e9d9739cebcdf298f0d4a","last_reissued_at":"2026-05-17T23:57:15.984676Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:15.984676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A minimal integrity basis for the elasticity tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Boris Kolev (I2M), Marc Olive (LMA ), Nicolas Auffray (MSME)","submitted_at":"2016-05-31T10:30:10Z","abstract_excerpt":"We definitively solve the old problem of finding a minimal integrity basis of polynomial invariants of the fourth-order elasticity tensor C. Decomposing C into its SO(3)-irreducible components we reduce this problem to finding joint invariants of a triplet (a, b, D), where a and b are second-order harmonic tensors, and D is a fourth-order harmonic tensor. Combining theorems of classical invariant theory and formal computations, a minimal integrity basis of 297 polynomial invariants for the elasticity tensor is obtained for the first time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09561","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.09561","created_at":"2026-05-17T23:57:15.984730+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.09561v2","created_at":"2026-05-17T23:57:15.984730+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09561","created_at":"2026-05-17T23:57:15.984730+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OQX55JLPY6V","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OQX55JLPY6VQV5A","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OQX55JL","created_at":"2026-05-18T12:29:55.572404+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2OQX55JLPY6VQV5A63NCAF7CSO","json":"https://pith.science/pith/2OQX55JLPY6VQV5A63NCAF7CSO.json","graph_json":"https://pith.science/api/pith-number/2OQX55JLPY6VQV5A63NCAF7CSO/graph.json","events_json":"https://pith.science/api/pith-number/2OQX55JLPY6VQV5A63NCAF7CSO/events.json","paper":"https://pith.science/paper/2OQX55JL"},"agent_actions":{"view_html":"https://pith.science/pith/2OQX55JLPY6VQV5A63NCAF7CSO","download_json":"https://pith.science/pith/2OQX55JLPY6VQV5A63NCAF7CSO.json","view_paper":"https://pith.science/paper/2OQX55JL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.09561&json=true","fetch_graph":"https://pith.science/api/pith-number/2OQX55JLPY6VQV5A63NCAF7CSO/graph.json","fetch_events":"https://pith.science/api/pith-number/2OQX55JLPY6VQV5A63NCAF7CSO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OQX55JLPY6VQV5A63NCAF7CSO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OQX55JLPY6VQV5A63NCAF7CSO/action/storage_attestation","attest_author":"https://pith.science/pith/2OQX55JLPY6VQV5A63NCAF7CSO/action/author_attestation","sign_citation":"https://pith.science/pith/2OQX55JLPY6VQV5A63NCAF7CSO/action/citation_signature","submit_replication":"https://pith.science/pith/2OQX55JLPY6VQV5A63NCAF7CSO/action/replication_record"}},"created_at":"2026-05-17T23:57:15.984730+00:00","updated_at":"2026-05-17T23:57:15.984730+00:00"}