{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GRCHKJHM3DAOX7YA567FTNS7PM","short_pith_number":"pith:GRCHKJHM","canonical_record":{"source":{"id":"1703.03495","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2017-03-10T00:46:29Z","cross_cats_sorted":[],"title_canon_sha256":"e0ac27f13848f0b25c0b37aa424a7e92ebc167d2dbda06182367be2346196129","abstract_canon_sha256":"c56562b0ce1149cdbe7800d84335446771f0b7698b5ddf26e8cde68e56dbaf5e"},"schema_version":"1.0"},"canonical_sha256":"34447524ecd8c0ebff00efbe59b65f7b3e80e7d3ec06a96279b392007c102094","source":{"kind":"arxiv","id":"1703.03495","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03495","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03495v1","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03495","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"GRCHKJHM3DAO","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GRCHKJHM3DAOX7YA","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GRCHKJHM","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GRCHKJHM3DAOX7YA567FTNS7PM","target":"record","payload":{"canonical_record":{"source":{"id":"1703.03495","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2017-03-10T00:46:29Z","cross_cats_sorted":[],"title_canon_sha256":"e0ac27f13848f0b25c0b37aa424a7e92ebc167d2dbda06182367be2346196129","abstract_canon_sha256":"c56562b0ce1149cdbe7800d84335446771f0b7698b5ddf26e8cde68e56dbaf5e"},"schema_version":"1.0"},"canonical_sha256":"34447524ecd8c0ebff00efbe59b65f7b3e80e7d3ec06a96279b392007c102094","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:58.963172Z","signature_b64":"lXWWuCKX6ScwPZXti21rbTP9H49iBEQl8Upk0j9e8nm9gVlMe57nIzIZcYqs8cqecjKZbYg8H+D2pcCVCyMVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34447524ecd8c0ebff00efbe59b65f7b3e80e7d3ec06a96279b392007c102094","last_reissued_at":"2026-05-18T00:48:58.962421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:58.962421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.03495","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":"2026-05-18T00:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pi4BEhV8iE0KUEVaIJvTMkZT5DiWzDFtI+yrjbJXZo33UQi3fh1Sesmtykf3+fkvYkSWdgI73Kz7Del7aMBUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T17:31:21.565801Z"},"content_sha256":"bc9b540497ef048fe51ba6d602702d39a9e8d4087c8cbcd3c7c2a49d0f966af0","schema_version":"1.0","event_id":"sha256:bc9b540497ef048fe51ba6d602702d39a9e8d4087c8cbcd3c7c2a49d0f966af0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GRCHKJHM3DAOX7YA567FTNS7PM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wave propagation and homogenization in 2D and 3D lattices: a semi-analytical approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"A. A. Kutsenko, A. J. Nagy, A. L. Shuvalov, A. N. Norris, X. Su","submitted_at":"2017-03-10T00:46:29Z","abstract_excerpt":"Wave motion in two- and three-dimensional periodic lattices of beam members supporting longitudinal and flexural waves is considered. An analytic method for solving the Bloch wave spectrum is developed, characterized by a generalized eigenvalue equation obtained by enforcing the Floquet condition. The dynamic stiffness matrix is shown to be explicitly Hermitian and to admit positive eigenvalues. Lattices with hexagonal, rectangular, tetrahedral and cubic unit cells are analyzed. The semi-analytical method can be asymptotically expanded for low frequency yielding explicit forms for the Christof"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03495","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":"2026-05-18T00:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tSUB2pb/4iJo61X0nrAEnfj7NiViDAZR5X6pH+GiVwFTB4X74djmlfFhrjBNFnhFnY6ypfs5VaJB3n2H3SNHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T17:31:21.566150Z"},"content_sha256":"d600e2f0d08b99cad68e16ad43a8d44eff73a59d74c8ec91c7b22a0c6f81c48d","schema_version":"1.0","event_id":"sha256:d600e2f0d08b99cad68e16ad43a8d44eff73a59d74c8ec91c7b22a0c6f81c48d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GRCHKJHM3DAOX7YA567FTNS7PM/bundle.json","state_url":"https://pith.science/pith/GRCHKJHM3DAOX7YA567FTNS7PM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GRCHKJHM3DAOX7YA567FTNS7PM/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":"2026-06-29T17:31:21Z","links":{"resolver":"https://pith.science/pith/GRCHKJHM3DAOX7YA567FTNS7PM","bundle":"https://pith.science/pith/GRCHKJHM3DAOX7YA567FTNS7PM/bundle.json","state":"https://pith.science/pith/GRCHKJHM3DAOX7YA567FTNS7PM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GRCHKJHM3DAOX7YA567FTNS7PM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GRCHKJHM3DAOX7YA567FTNS7PM","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":"c56562b0ce1149cdbe7800d84335446771f0b7698b5ddf26e8cde68e56dbaf5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2017-03-10T00:46:29Z","title_canon_sha256":"e0ac27f13848f0b25c0b37aa424a7e92ebc167d2dbda06182367be2346196129"},"schema_version":"1.0","source":{"id":"1703.03495","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03495","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03495v1","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03495","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"GRCHKJHM3DAO","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GRCHKJHM3DAOX7YA","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GRCHKJHM","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:d600e2f0d08b99cad68e16ad43a8d44eff73a59d74c8ec91c7b22a0c6f81c48d","target":"graph","created_at":"2026-05-18T00:48:58Z","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":"Wave motion in two- and three-dimensional periodic lattices of beam members supporting longitudinal and flexural waves is considered. An analytic method for solving the Bloch wave spectrum is developed, characterized by a generalized eigenvalue equation obtained by enforcing the Floquet condition. The dynamic stiffness matrix is shown to be explicitly Hermitian and to admit positive eigenvalues. Lattices with hexagonal, rectangular, tetrahedral and cubic unit cells are analyzed. The semi-analytical method can be asymptotically expanded for low frequency yielding explicit forms for the Christof","authors_text":"A. A. Kutsenko, A. J. Nagy, A. L. Shuvalov, A. N. Norris, X. Su","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2017-03-10T00:46:29Z","title":"Wave propagation and homogenization in 2D and 3D lattices: a semi-analytical approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03495","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:bc9b540497ef048fe51ba6d602702d39a9e8d4087c8cbcd3c7c2a49d0f966af0","target":"record","created_at":"2026-05-18T00:48:58Z","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":"c56562b0ce1149cdbe7800d84335446771f0b7698b5ddf26e8cde68e56dbaf5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2017-03-10T00:46:29Z","title_canon_sha256":"e0ac27f13848f0b25c0b37aa424a7e92ebc167d2dbda06182367be2346196129"},"schema_version":"1.0","source":{"id":"1703.03495","kind":"arxiv","version":1}},"canonical_sha256":"34447524ecd8c0ebff00efbe59b65f7b3e80e7d3ec06a96279b392007c102094","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34447524ecd8c0ebff00efbe59b65f7b3e80e7d3ec06a96279b392007c102094","first_computed_at":"2026-05-18T00:48:58.962421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:58.962421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lXWWuCKX6ScwPZXti21rbTP9H49iBEQl8Upk0j9e8nm9gVlMe57nIzIZcYqs8cqecjKZbYg8H+D2pcCVCyMVBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:58.963172Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.03495","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc9b540497ef048fe51ba6d602702d39a9e8d4087c8cbcd3c7c2a49d0f966af0","sha256:d600e2f0d08b99cad68e16ad43a8d44eff73a59d74c8ec91c7b22a0c6f81c48d"],"state_sha256":"64323bbf76695a361d06d983284eae4e319612933b43d30f94a1bc7ade306d36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C4zvEBzXR6I0GHClDPxF2uLlyeuK00l9tdFyXj/FdMDA/cboqrqinu7KrXeVjZTx7rBganRAhyGR+3JtMSoEAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T17:31:21.568013Z","bundle_sha256":"5702241e0094437e5864a9096cd7cf6640521db0300518906f4d6655d5f32308"}}