{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UINM3BK6LK57DVNTC5QWRCBJIW","short_pith_number":"pith:UINM3BK6","canonical_record":{"source":{"id":"1603.05395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T09:13:27Z","cross_cats_sorted":[],"title_canon_sha256":"995080bc7d4cfd9036626f1f3b38a9b097cc72f293ff45fdd282acd9aa2093a9","abstract_canon_sha256":"deb82ab478467a87baf9a9d66a3f4808ad7e133a444f6ec583a4b58d0f13c0ae"},"schema_version":"1.0"},"canonical_sha256":"a21acd855e5abbf1d5b3176168882945aa096b9f435b2255c030c9cca46e103c","source":{"kind":"arxiv","id":"1603.05395","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05395","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05395v1","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05395","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"UINM3BK6LK57","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UINM3BK6LK57DVNT","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UINM3BK6","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UINM3BK6LK57DVNTC5QWRCBJIW","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T09:13:27Z","cross_cats_sorted":[],"title_canon_sha256":"995080bc7d4cfd9036626f1f3b38a9b097cc72f293ff45fdd282acd9aa2093a9","abstract_canon_sha256":"deb82ab478467a87baf9a9d66a3f4808ad7e133a444f6ec583a4b58d0f13c0ae"},"schema_version":"1.0"},"canonical_sha256":"a21acd855e5abbf1d5b3176168882945aa096b9f435b2255c030c9cca46e103c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:56.448202Z","signature_b64":"IfqM2V34Zi3s2R3wAFwUK/QkoomnUCtFdxi3qM0PcBnQqXNatouBrTx+CKnp5MtKj5Xi0E/B5WM02++bbpq+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a21acd855e5abbf1d5b3176168882945aa096b9f435b2255c030c9cca46e103c","last_reissued_at":"2026-05-18T01:18:56.447827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:56.447827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05395","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v3OdSnaSsamyjb+Mx+pdAqaUuXy7PfgcVb982y5bHmYZ4igkg2lIq3QkcH3RxmklYKV4WlPJvCtEcq+hvOwYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:55:29.195635Z"},"content_sha256":"12bcf9c0db479b312caefa742c2bef37444d4c0b45b349660ea09cf2fc0fa0ca","schema_version":"1.0","event_id":"sha256:12bcf9c0db479b312caefa742c2bef37444d4c0b45b349660ea09cf2fc0fa0ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UINM3BK6LK57DVNTC5QWRCBJIW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effective acoustic properties of a meta-material consisting of small Helmholtz resonators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnes Lamacz, Ben Schweizer","submitted_at":"2016-03-17T09:13:27Z","abstract_excerpt":"We investigate the acoustic properties of meta-materials that are inspired by sound-absorbing structures. We show that it is possible to construct meta-materials with frequency-dependent effective properties, with large and/or negative permittivities. Mathematically, we investigate solutions $u^\\varepsilon: \\Omega_\\varepsilon \\rightarrow \\mathbb{R}$ to a Helmholtz equation in the limit $\\varepsilon\\rightarrow 0$ with the help of two-scale convergence. The domain $\\Omega_\\varepsilon$ is obtained by removing from an open set $\\Omega\\subset \\mathbb{R}^n$ in a periodic fashion a large number (orde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05395","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VwBEl5c8h43qEOmEdg+cLiETjs+y1iHtmGpl2WGDnv4FwXHHBaTHRSOcfQZb3xLb3rBOuqCXFOSzn/4h1X9tAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:55:29.195985Z"},"content_sha256":"7f5fe16943d7b3e0383ee4defdc1fc4d07bef1ed65385f73d1d24edc963749e8","schema_version":"1.0","event_id":"sha256:7f5fe16943d7b3e0383ee4defdc1fc4d07bef1ed65385f73d1d24edc963749e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UINM3BK6LK57DVNTC5QWRCBJIW/bundle.json","state_url":"https://pith.science/pith/UINM3BK6LK57DVNTC5QWRCBJIW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UINM3BK6LK57DVNTC5QWRCBJIW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T12:55:29Z","links":{"resolver":"https://pith.science/pith/UINM3BK6LK57DVNTC5QWRCBJIW","bundle":"https://pith.science/pith/UINM3BK6LK57DVNTC5QWRCBJIW/bundle.json","state":"https://pith.science/pith/UINM3BK6LK57DVNTC5QWRCBJIW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UINM3BK6LK57DVNTC5QWRCBJIW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UINM3BK6LK57DVNTC5QWRCBJIW","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":"deb82ab478467a87baf9a9d66a3f4808ad7e133a444f6ec583a4b58d0f13c0ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T09:13:27Z","title_canon_sha256":"995080bc7d4cfd9036626f1f3b38a9b097cc72f293ff45fdd282acd9aa2093a9"},"schema_version":"1.0","source":{"id":"1603.05395","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05395","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05395v1","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05395","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"UINM3BK6LK57","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UINM3BK6LK57DVNT","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UINM3BK6","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:7f5fe16943d7b3e0383ee4defdc1fc4d07bef1ed65385f73d1d24edc963749e8","target":"graph","created_at":"2026-05-18T01:18:56Z","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":"We investigate the acoustic properties of meta-materials that are inspired by sound-absorbing structures. We show that it is possible to construct meta-materials with frequency-dependent effective properties, with large and/or negative permittivities. Mathematically, we investigate solutions $u^\\varepsilon: \\Omega_\\varepsilon \\rightarrow \\mathbb{R}$ to a Helmholtz equation in the limit $\\varepsilon\\rightarrow 0$ with the help of two-scale convergence. The domain $\\Omega_\\varepsilon$ is obtained by removing from an open set $\\Omega\\subset \\mathbb{R}^n$ in a periodic fashion a large number (orde","authors_text":"Agnes Lamacz, Ben Schweizer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T09:13:27Z","title":"Effective acoustic properties of a meta-material consisting of small Helmholtz resonators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05395","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":"sha256:12bcf9c0db479b312caefa742c2bef37444d4c0b45b349660ea09cf2fc0fa0ca","target":"record","created_at":"2026-05-18T01:18:56Z","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":"deb82ab478467a87baf9a9d66a3f4808ad7e133a444f6ec583a4b58d0f13c0ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T09:13:27Z","title_canon_sha256":"995080bc7d4cfd9036626f1f3b38a9b097cc72f293ff45fdd282acd9aa2093a9"},"schema_version":"1.0","source":{"id":"1603.05395","kind":"arxiv","version":1}},"canonical_sha256":"a21acd855e5abbf1d5b3176168882945aa096b9f435b2255c030c9cca46e103c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a21acd855e5abbf1d5b3176168882945aa096b9f435b2255c030c9cca46e103c","first_computed_at":"2026-05-18T01:18:56.447827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:56.447827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IfqM2V34Zi3s2R3wAFwUK/QkoomnUCtFdxi3qM0PcBnQqXNatouBrTx+CKnp5MtKj5Xi0E/B5WM02++bbpq+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:56.448202Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05395","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12bcf9c0db479b312caefa742c2bef37444d4c0b45b349660ea09cf2fc0fa0ca","sha256:7f5fe16943d7b3e0383ee4defdc1fc4d07bef1ed65385f73d1d24edc963749e8"],"state_sha256":"bb3f253a63f8844c081cc674222a35f85fd246ad45fb4b7ecc2ed9046812416c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7eJsRN8Le041YBiIfvf+LpuhPfI7EIMUvDuhWDa77BGlEDkOO5YP2bE7KmzsJCXowxhlI0xXO03u10xWWNJfAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:55:29.197918Z","bundle_sha256":"4f00efa228727dc7a000092775cb71a140cfaee1b1d1b136353803ec5902932f"}}