{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:CRREQ4N3YC4LHMRHNVNEYVICEV","short_pith_number":"pith:CRREQ4N3","schema_version":"1.0","canonical_sha256":"14624871bbc0b8b3b2276d5a4c5502256d156ed9f827b5a200af216082fdc780","source":{"kind":"arxiv","id":"2608.05524","version":1},"attestation_state":"computed","paper":{"title":"On the synthesis of complete two-dimensional second-gradient continua: Tri-pantographic fabrics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math.MP","physics.class-ph"],"primary_cat":"math-ph","authors_text":"Casey Rodriguez, Emilio Barchiesi, Francesco Dell'Isola, Ivan Giorgio, Simon R. Eugster","submitted_at":"2026-08-06T02:02:22Z","abstract_excerpt":"We introduce a notion of completeness for two-dimensional second-gradient elastic continua and propose a microstructural route toward its synthesis. A continuum is said to be complete if the Hessian of the stored energy with respect to the second-gradient variable is locally positive definite, so that every nonzero admissible increment of the placement second gradient is quadratically controlled in the highest-order part of the energy about each configuration. Starting from the Principle of Virtual Work, we derive the constitutive relations, equilibrium equations, and admissible boundary inter"},"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":"2608.05524","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-08-06T02:02:22Z","cross_cats_sorted":["cond-mat.mtrl-sci","math.MP","physics.class-ph"],"title_canon_sha256":"40a4d28ebc6babb9888e245783b866ecaeb70df776ad812127a9b5871d36c17d","abstract_canon_sha256":"c5ca449e5bf3baab52be868fe421fe6d14ac6964e87c1ec364e6bf394ff2391f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-07T00:48:01.506774Z","signature_b64":"MyBotwCkITv0jCTl/rjfZjjrZzR+RpWlqxCHiMyoAivZCXTUFeRWJZyxjocoIZtcfgvuWKcnnqkS3kwKncNTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14624871bbc0b8b3b2276d5a4c5502256d156ed9f827b5a200af216082fdc780","last_reissued_at":"2026-08-07T00:48:01.505125Z","signature_status":"signed_v1","first_computed_at":"2026-08-07T00:48:01.505125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the synthesis of complete two-dimensional second-gradient continua: Tri-pantographic fabrics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math.MP","physics.class-ph"],"primary_cat":"math-ph","authors_text":"Casey Rodriguez, Emilio Barchiesi, Francesco Dell'Isola, Ivan Giorgio, Simon R. Eugster","submitted_at":"2026-08-06T02:02:22Z","abstract_excerpt":"We introduce a notion of completeness for two-dimensional second-gradient elastic continua and propose a microstructural route toward its synthesis. A continuum is said to be complete if the Hessian of the stored energy with respect to the second-gradient variable is locally positive definite, so that every nonzero admissible increment of the placement second gradient is quadratically controlled in the highest-order part of the energy about each configuration. Starting from the Principle of Virtual Work, we derive the constitutive relations, equilibrium equations, and admissible boundary inter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05524","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.05524/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2608.05524","created_at":"2026-08-07T00:48:01.506566+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.05524v1","created_at":"2026-08-07T00:48:01.506566+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.05524","created_at":"2026-08-07T00:48:01.506566+00:00"},{"alias_kind":"pith_short_12","alias_value":"CRREQ4N3YC4L","created_at":"2026-08-07T00:48:01.506566+00:00"},{"alias_kind":"pith_short_16","alias_value":"CRREQ4N3YC4LHMRH","created_at":"2026-08-07T00:48:01.506566+00:00"},{"alias_kind":"pith_short_8","alias_value":"CRREQ4N3","created_at":"2026-08-07T00:48:01.506566+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/CRREQ4N3YC4LHMRHNVNEYVICEV","json":"https://pith.science/pith/CRREQ4N3YC4LHMRHNVNEYVICEV.json","graph_json":"https://pith.science/api/pith-number/CRREQ4N3YC4LHMRHNVNEYVICEV/graph.json","events_json":"https://pith.science/api/pith-number/CRREQ4N3YC4LHMRHNVNEYVICEV/events.json","paper":"https://pith.science/paper/CRREQ4N3"},"agent_actions":{"view_html":"https://pith.science/pith/CRREQ4N3YC4LHMRHNVNEYVICEV","download_json":"https://pith.science/pith/CRREQ4N3YC4LHMRHNVNEYVICEV.json","view_paper":"https://pith.science/paper/CRREQ4N3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.05524&json=true","fetch_graph":"https://pith.science/api/pith-number/CRREQ4N3YC4LHMRHNVNEYVICEV/graph.json","fetch_events":"https://pith.science/api/pith-number/CRREQ4N3YC4LHMRHNVNEYVICEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CRREQ4N3YC4LHMRHNVNEYVICEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CRREQ4N3YC4LHMRHNVNEYVICEV/action/storage_attestation","attest_author":"https://pith.science/pith/CRREQ4N3YC4LHMRHNVNEYVICEV/action/author_attestation","sign_citation":"https://pith.science/pith/CRREQ4N3YC4LHMRHNVNEYVICEV/action/citation_signature","submit_replication":"https://pith.science/pith/CRREQ4N3YC4LHMRHNVNEYVICEV/action/replication_record"}},"created_at":"2026-08-07T00:48:01.506566+00:00","updated_at":"2026-08-07T00:48:01.506566+00:00"}