{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:I3V6R3NHVF6UZ7KOTMVMGABLXF","short_pith_number":"pith:I3V6R3NH","schema_version":"1.0","canonical_sha256":"46ebe8eda7a97d4cfd4e9b2ac3002bb97e47e102f1d04e143fec59186aa08d5f","source":{"kind":"arxiv","id":"1608.07552","version":1},"attestation_state":"computed","paper":{"title":"Bloch Wave Homogenization Relative to a Microstructure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Muthusamy Vanninathan, Tuhin Ghosh","submitted_at":"2016-08-26T18:28:40Z","abstract_excerpt":"In this work, we study the aspect of Bloch wave homogenization of the new notion of convergence of microstructures represented by matrices $B^\\epsilon$ related to the classical $H$-convergence of $A^\\epsilon$ introduced in \\cite{TG-MV-1}. The new macro quantity $B^{#}$ appears to incorporate the interaction between the two microstructures $A^\\epsilon,B^\\epsilon$. Here we present its Bloch spectral representation along with the homogenization result."},"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":"1608.07552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-26T18:28:40Z","cross_cats_sorted":[],"title_canon_sha256":"6e6872204d6cf76abc2635dddaf28798f7c906503b6d6543ea982242a05ee99e","abstract_canon_sha256":"899133bd5facf6338476dbea9304c5a08f84d1655fa55e39ca2cba79fb749eeb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:52.779078Z","signature_b64":"jJtktqXvtj8KYlyO+0jdrxmSIKkbYy7V3yeW50GJHMjPddNJHRrtj0avSMMLEH5OQJ+sHjJCWkKIYKSIR3zeBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46ebe8eda7a97d4cfd4e9b2ac3002bb97e47e102f1d04e143fec59186aa08d5f","last_reissued_at":"2026-05-18T01:07:52.778532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:52.778532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bloch Wave Homogenization Relative to a Microstructure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Muthusamy Vanninathan, Tuhin Ghosh","submitted_at":"2016-08-26T18:28:40Z","abstract_excerpt":"In this work, we study the aspect of Bloch wave homogenization of the new notion of convergence of microstructures represented by matrices $B^\\epsilon$ related to the classical $H$-convergence of $A^\\epsilon$ introduced in \\cite{TG-MV-1}. The new macro quantity $B^{#}$ appears to incorporate the interaction between the two microstructures $A^\\epsilon,B^\\epsilon$. Here we present its Bloch spectral representation along with the homogenization result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07552","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":""},"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":"1608.07552","created_at":"2026-05-18T01:07:52.778609+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.07552v1","created_at":"2026-05-18T01:07:52.778609+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07552","created_at":"2026-05-18T01:07:52.778609+00:00"},{"alias_kind":"pith_short_12","alias_value":"I3V6R3NHVF6U","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"I3V6R3NHVF6UZ7KO","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"I3V6R3NH","created_at":"2026-05-18T12:30:22.444734+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/I3V6R3NHVF6UZ7KOTMVMGABLXF","json":"https://pith.science/pith/I3V6R3NHVF6UZ7KOTMVMGABLXF.json","graph_json":"https://pith.science/api/pith-number/I3V6R3NHVF6UZ7KOTMVMGABLXF/graph.json","events_json":"https://pith.science/api/pith-number/I3V6R3NHVF6UZ7KOTMVMGABLXF/events.json","paper":"https://pith.science/paper/I3V6R3NH"},"agent_actions":{"view_html":"https://pith.science/pith/I3V6R3NHVF6UZ7KOTMVMGABLXF","download_json":"https://pith.science/pith/I3V6R3NHVF6UZ7KOTMVMGABLXF.json","view_paper":"https://pith.science/paper/I3V6R3NH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.07552&json=true","fetch_graph":"https://pith.science/api/pith-number/I3V6R3NHVF6UZ7KOTMVMGABLXF/graph.json","fetch_events":"https://pith.science/api/pith-number/I3V6R3NHVF6UZ7KOTMVMGABLXF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I3V6R3NHVF6UZ7KOTMVMGABLXF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I3V6R3NHVF6UZ7KOTMVMGABLXF/action/storage_attestation","attest_author":"https://pith.science/pith/I3V6R3NHVF6UZ7KOTMVMGABLXF/action/author_attestation","sign_citation":"https://pith.science/pith/I3V6R3NHVF6UZ7KOTMVMGABLXF/action/citation_signature","submit_replication":"https://pith.science/pith/I3V6R3NHVF6UZ7KOTMVMGABLXF/action/replication_record"}},"created_at":"2026-05-18T01:07:52.778609+00:00","updated_at":"2026-05-18T01:07:52.778609+00:00"}