{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JHICAQUAQULWHPZT263ILTZBVN","short_pith_number":"pith:JHICAQUA","canonical_record":{"source":{"id":"1310.6561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2013-10-24T10:52:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5c53f5758f825215fe05320ad33e51ce0e0c1deaf547131e153d5d4a80c4973f","abstract_canon_sha256":"bab78a360c411f73cd3108ecae7a3d39c4336eb0425d03a208ba382a36593061"},"schema_version":"1.0"},"canonical_sha256":"49d0204280851763bf33d7b685cf21ab41c9b9ae7d70826c3dc7ac88bd9daa8f","source":{"kind":"arxiv","id":"1310.6561","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6561","created_at":"2026-05-18T03:09:09Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6561v1","created_at":"2026-05-18T03:09:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6561","created_at":"2026-05-18T03:09:09Z"},{"alias_kind":"pith_short_12","alias_value":"JHICAQUAQULW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JHICAQUAQULWHPZT","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JHICAQUA","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JHICAQUAQULWHPZT263ILTZBVN","target":"record","payload":{"canonical_record":{"source":{"id":"1310.6561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2013-10-24T10:52:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5c53f5758f825215fe05320ad33e51ce0e0c1deaf547131e153d5d4a80c4973f","abstract_canon_sha256":"bab78a360c411f73cd3108ecae7a3d39c4336eb0425d03a208ba382a36593061"},"schema_version":"1.0"},"canonical_sha256":"49d0204280851763bf33d7b685cf21ab41c9b9ae7d70826c3dc7ac88bd9daa8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:09.346436Z","signature_b64":"NQkOQMWtofBSdGrc79NP1uTZZ/QmT7w5qZoZzrCoVsz46Y5do7tBqSkLxknERz6aAVfpdFG3EJu0/mdGH6qJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49d0204280851763bf33d7b685cf21ab41c9b9ae7d70826c3dc7ac88bd9daa8f","last_reissued_at":"2026-05-18T03:09:09.345670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:09.345670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.6561","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":"2026-05-18T03:09:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UNpvqGR/TJBq2nQn0//qNfojuiMmKVDxVgF1OWnkX2Fpqmtv3Yg+pv8tBkgZyFfvw+8kOSfM7b/NZTUT10JvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:47:35.014860Z"},"content_sha256":"c86a7c3d04549dd4e06ac6010531ec59404eb727cbc8d0e6458be2cec35c7505","schema_version":"1.0","event_id":"sha256:c86a7c3d04549dd4e06ac6010531ec59404eb727cbc8d0e6458be2cec35c7505"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JHICAQUAQULWHPZT263ILTZBVN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A study of obliquely propagating longitudinal shear waves in a periodic laminate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"John Willis","submitted_at":"2013-10-24T10:52:28Z","abstract_excerpt":"The basic purpose of this work is to demonstrate, by quite simple and explicit calculation, the possibility that a simple laminate composed of ordinary materials can display the kind of response associated with a \"metamaterial\". Specifically, a wave of Floquet--Bloch type is analyzed, taking careful account of the requirements of causality and passivity. Then, the generation of such a wave by transmission, from ordinary homogeneous material, into a half-space composed of the laminate is considered. As is well-known for any dispersive material, phase velocity is distinct from group velocity, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6561","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":"2026-05-18T03:09:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZMS+CWWbVgqAieFq6ugQ+MEZHoR/YimsOi+/7sflR2+dHvT6UPaem44yV2cRgMMrza7TX+q+mP+60Ii5mXREAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:47:35.015629Z"},"content_sha256":"790ff5595c819b99cd2b9a1a7a95a1c2512e215fac6ae5832a793c30db8b647a","schema_version":"1.0","event_id":"sha256:790ff5595c819b99cd2b9a1a7a95a1c2512e215fac6ae5832a793c30db8b647a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JHICAQUAQULWHPZT263ILTZBVN/bundle.json","state_url":"https://pith.science/pith/JHICAQUAQULWHPZT263ILTZBVN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JHICAQUAQULWHPZT263ILTZBVN/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":"2026-05-30T16:47:35Z","links":{"resolver":"https://pith.science/pith/JHICAQUAQULWHPZT263ILTZBVN","bundle":"https://pith.science/pith/JHICAQUAQULWHPZT263ILTZBVN/bundle.json","state":"https://pith.science/pith/JHICAQUAQULWHPZT263ILTZBVN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JHICAQUAQULWHPZT263ILTZBVN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JHICAQUAQULWHPZT263ILTZBVN","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":"bab78a360c411f73cd3108ecae7a3d39c4336eb0425d03a208ba382a36593061","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2013-10-24T10:52:28Z","title_canon_sha256":"5c53f5758f825215fe05320ad33e51ce0e0c1deaf547131e153d5d4a80c4973f"},"schema_version":"1.0","source":{"id":"1310.6561","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6561","created_at":"2026-05-18T03:09:09Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6561v1","created_at":"2026-05-18T03:09:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6561","created_at":"2026-05-18T03:09:09Z"},{"alias_kind":"pith_short_12","alias_value":"JHICAQUAQULW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JHICAQUAQULWHPZT","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JHICAQUA","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:790ff5595c819b99cd2b9a1a7a95a1c2512e215fac6ae5832a793c30db8b647a","target":"graph","created_at":"2026-05-18T03:09:09Z","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 basic purpose of this work is to demonstrate, by quite simple and explicit calculation, the possibility that a simple laminate composed of ordinary materials can display the kind of response associated with a \"metamaterial\". Specifically, a wave of Floquet--Bloch type is analyzed, taking careful account of the requirements of causality and passivity. Then, the generation of such a wave by transmission, from ordinary homogeneous material, into a half-space composed of the laminate is considered. As is well-known for any dispersive material, phase velocity is distinct from group velocity, an","authors_text":"John Willis","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2013-10-24T10:52:28Z","title":"A study of obliquely propagating longitudinal shear waves in a periodic laminate"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6561","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:c86a7c3d04549dd4e06ac6010531ec59404eb727cbc8d0e6458be2cec35c7505","target":"record","created_at":"2026-05-18T03:09:09Z","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":"bab78a360c411f73cd3108ecae7a3d39c4336eb0425d03a208ba382a36593061","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2013-10-24T10:52:28Z","title_canon_sha256":"5c53f5758f825215fe05320ad33e51ce0e0c1deaf547131e153d5d4a80c4973f"},"schema_version":"1.0","source":{"id":"1310.6561","kind":"arxiv","version":1}},"canonical_sha256":"49d0204280851763bf33d7b685cf21ab41c9b9ae7d70826c3dc7ac88bd9daa8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49d0204280851763bf33d7b685cf21ab41c9b9ae7d70826c3dc7ac88bd9daa8f","first_computed_at":"2026-05-18T03:09:09.345670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:09.345670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NQkOQMWtofBSdGrc79NP1uTZZ/QmT7w5qZoZzrCoVsz46Y5do7tBqSkLxknERz6aAVfpdFG3EJu0/mdGH6qJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:09.346436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6561","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c86a7c3d04549dd4e06ac6010531ec59404eb727cbc8d0e6458be2cec35c7505","sha256:790ff5595c819b99cd2b9a1a7a95a1c2512e215fac6ae5832a793c30db8b647a"],"state_sha256":"ac8d24ebc540eaa29c6516f2100334e3f2166328ac99f078576e377dcd7b3d5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2MHgv7gctRIvSiwsvY0vH746I8CFzfWSTspH8GTMHkC2W3bBsVb1upYr4lyL7hnWZduTqWML5SH7Bq2bV//IDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:47:35.019742Z","bundle_sha256":"80634eaaa1e04491edc0cf2abba5e4d83372e1de4dca7f7882303fe8646b3c21"}}