{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:C7VFBGXQLXPXHBUDS5KE2J3ZBE","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":"c9ca233d3722c5442c243447af3bd31cba0292039b6fa58f0e6499a28b53f9d9","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-20T02:56:15Z","title_canon_sha256":"94013830f472420307d1d6facc107fc17a7792bfb0c44688b9c097f3124320a7"},"schema_version":"1.0","source":{"id":"1701.05661","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05661","created_at":"2026-05-18T00:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05661v4","created_at":"2026-05-18T00:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05661","created_at":"2026-05-18T00:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"C7VFBGXQLXPX","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"C7VFBGXQLXPXHBUD","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"C7VFBGXQ","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:0d2460e27f87bbbdb3cf96610faeb2ef6f7567f59e374dea6c50cd7a8f59f771","target":"graph","created_at":"2026-05-18T00:22:48Z","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":"The convergence of spectra via two-scale convergence for double-porosity models is well known. A crucial assumption in these works is that the stiff component of the body forms a connected set. We show that under a relaxation of this assumption the (periodic) two-scale limit of the operator is insufficient to capture the full asymptotic spectral properties of high-contrast periodic media. Asymptotically, waves of all periods (or quasi-momenta) are shown to persist and an appropriate extension of the notion of two-scale convergence is introduced. As a result, homogenised limit equations with no","authors_text":"Shane Cooper","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-20T02:56:15Z","title":"Quasi-periodic two-scale homogenisation and effective spatial dispersion in high-contrast media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05661","kind":"arxiv","version":4},"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":"sha256:9fe1bcea617dafcf94b29fe87ad97e5ee1c30862552a1be7841d0c330f6326c8","target":"record","created_at":"2026-05-18T00:22:48Z","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":"c9ca233d3722c5442c243447af3bd31cba0292039b6fa58f0e6499a28b53f9d9","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-20T02:56:15Z","title_canon_sha256":"94013830f472420307d1d6facc107fc17a7792bfb0c44688b9c097f3124320a7"},"schema_version":"1.0","source":{"id":"1701.05661","kind":"arxiv","version":4}},"canonical_sha256":"17ea509af05ddf73868397544d27790938428d32c80a26da1706772a2cf4ef81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17ea509af05ddf73868397544d27790938428d32c80a26da1706772a2cf4ef81","first_computed_at":"2026-05-18T00:22:48.341171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:48.341171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gJv5iPNQIAHlxJCuGl0W0jZYfOyOzgnUUyct8K5a7udQmCMbqr1KR3/DKwiXQ3cyIiL5nlTCvQ5GHghGuIklBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:48.341814Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05661","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fe1bcea617dafcf94b29fe87ad97e5ee1c30862552a1be7841d0c330f6326c8","sha256:0d2460e27f87bbbdb3cf96610faeb2ef6f7567f59e374dea6c50cd7a8f59f771"],"state_sha256":"ea4c3c27389b504046641efd63682202c52fb51910fc49ff570103a93687c013"}