{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:J36R2WKWSIH65HEQZ2G3PG4PFL","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":"b2dd0dbf090578b367c292b37e446989f080c1e378d0a4dfe56328cab458c440","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-17T14:40:16Z","title_canon_sha256":"c0fdb446f4495be0bbcbf86978462efbedee7de31ebccb714c2d9a6133d2e55b"},"schema_version":"1.0","source":{"id":"2607.16005","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16005","created_at":"2026-07-20T02:19:25Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16005v1","created_at":"2026-07-20T02:19:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16005","created_at":"2026-07-20T02:19:25Z"},{"alias_kind":"pith_short_12","alias_value":"J36R2WKWSIH6","created_at":"2026-07-20T02:19:25Z"},{"alias_kind":"pith_short_16","alias_value":"J36R2WKWSIH65HEQ","created_at":"2026-07-20T02:19:25Z"},{"alias_kind":"pith_short_8","alias_value":"J36R2WKW","created_at":"2026-07-20T02:19:25Z"}],"graph_snapshots":[{"event_id":"sha256:8006662dac9c568fc2e04ee32b86d62aecf44ef4025bcd26c006a5e447aac2b4","target":"graph","created_at":"2026-07-20T02:19:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.16005/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This study aims to develop a numerical homogenization method that can be applied to a heterogeneous stratified medium. Traditional scale transition methods are inadequate in capturing the essential gradient properties of some materials. Therefore, the focus of this work is to construct a homogenized model that considers the material property gradient. To achieve this, a two-step homogenization scheme is proposed. Firstly, the 3D model is decomposed into multiple 2D heterogeneous layers, and the behavior of each layer is estimated using a micro-mechanical model such as the Hashin-Shtrikman boun","authors_text":"Azdine Nait-Ali, Sami Ben Elhaj Salah","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-17T14:40:16Z","title":"Variational modeling adapted to the medium with gradient properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16005","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":"sha256:98a00dc1154e953c28160a8f4909ca1460499f132fffeab075537b9de5c43562","target":"record","created_at":"2026-07-20T02:19:25Z","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":"b2dd0dbf090578b367c292b37e446989f080c1e378d0a4dfe56328cab458c440","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-17T14:40:16Z","title_canon_sha256":"c0fdb446f4495be0bbcbf86978462efbedee7de31ebccb714c2d9a6133d2e55b"},"schema_version":"1.0","source":{"id":"2607.16005","kind":"arxiv","version":1}},"canonical_sha256":"4efd1d5956920fee9c90ce8db79b8f2ae5ccd4182b29ed52eddf9a09c94ec607","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4efd1d5956920fee9c90ce8db79b8f2ae5ccd4182b29ed52eddf9a09c94ec607","first_computed_at":"2026-07-20T02:19:25.725699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-20T02:19:25.725699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Z4ErtXTdb4i7wW6NB6okde++0yN6V+gpaD/hmmQGy3un9mplvwgRggSaTfMZ99FYdZrtMfBfFPzrzeqJK68Dw==","signature_status":"signed_v1","signed_at":"2026-07-20T02:19:25.726595Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16005","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98a00dc1154e953c28160a8f4909ca1460499f132fffeab075537b9de5c43562","sha256:8006662dac9c568fc2e04ee32b86d62aecf44ef4025bcd26c006a5e447aac2b4"],"state_sha256":"d67d1a4727f2cf585cf3c7c88488eda585c26723863f99c16b4557d736c722b3"}