{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZWNE2PQID5J2J5U2RMZJGTBQAE","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":"85099bed3823c020593e8ddf09d562c9322077de6300cf6d743e8c462a964d96","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-18T10:58:30Z","title_canon_sha256":"077843d4716575dd424217f230c7f2990c81cec56eaeff9ee43eb9145a04279e"},"schema_version":"1.0","source":{"id":"1503.05337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05337","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05337v1","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05337","created_at":"2026-05-18T02:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZWNE2PQID5J2","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZWNE2PQID5J2J5U2","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZWNE2PQI","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:1f848119da2c50efe7a4389ec33a55012fee038e9abd9bb1063d2805d678bb43","target":"graph","created_at":"2026-05-18T02:21:50Z","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 note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude by mentioning some open problems.","authors_text":"Jos\\'e Matias, Marco Morandotti","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-18T10:58:30Z","title":"Homogenization problems in the Calculus of Variations: an overview"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05337","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":"sha256:6273a3be63b33eefdffd6734a7bc78e36e6d367c2f38318e933b28e655366a20","target":"record","created_at":"2026-05-18T02:21:50Z","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":"85099bed3823c020593e8ddf09d562c9322077de6300cf6d743e8c462a964d96","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-18T10:58:30Z","title_canon_sha256":"077843d4716575dd424217f230c7f2990c81cec56eaeff9ee43eb9145a04279e"},"schema_version":"1.0","source":{"id":"1503.05337","kind":"arxiv","version":1}},"canonical_sha256":"cd9a4d3e081f53a4f69a8b32934c3001299179d675dd8364d0d7dc9b586736ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd9a4d3e081f53a4f69a8b32934c3001299179d675dd8364d0d7dc9b586736ec","first_computed_at":"2026-05-18T02:21:50.734147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:50.734147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tWQotNdunb2dXuFspX+woq8g/YMkLvRsb5n2VJt8nf/AZIOqtrf+EASHepCa58ffp7Th/vDY/oyzTC+8P619AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:50.734882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6273a3be63b33eefdffd6734a7bc78e36e6d367c2f38318e933b28e655366a20","sha256:1f848119da2c50efe7a4389ec33a55012fee038e9abd9bb1063d2805d678bb43"],"state_sha256":"b2514086f4ef0b116d59763f7e871c93c88d3fc5b83f6a6bce2d3b1a7c26e7aa"}