{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:A4EEER7TQEIL4IE4NREALTBYQW","short_pith_number":"pith:A4EEER7T","canonical_record":{"source":{"id":"1303.5114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-20T22:44:36Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"49121887b9690f7760108b8480bcd0c313494d477b75ea9be9b0b4fdfa4c429d","abstract_canon_sha256":"cfc6e25e51c01d9eacdc06f1dbbe95000a31fbe23c6c3f1f29754dd1db47a913"},"schema_version":"1.0"},"canonical_sha256":"07084247f38110be209c6c4805cc3885927674f72a5748d3e8e250a71a4a881c","source":{"kind":"arxiv","id":"1303.5114","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5114","created_at":"2026-05-18T03:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5114v1","created_at":"2026-05-18T03:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5114","created_at":"2026-05-18T03:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"A4EEER7TQEIL","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A4EEER7TQEIL4IE4","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A4EEER7T","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:A4EEER7TQEIL4IE4NREALTBYQW","target":"record","payload":{"canonical_record":{"source":{"id":"1303.5114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-20T22:44:36Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"49121887b9690f7760108b8480bcd0c313494d477b75ea9be9b0b4fdfa4c429d","abstract_canon_sha256":"cfc6e25e51c01d9eacdc06f1dbbe95000a31fbe23c6c3f1f29754dd1db47a913"},"schema_version":"1.0"},"canonical_sha256":"07084247f38110be209c6c4805cc3885927674f72a5748d3e8e250a71a4a881c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:47.809951Z","signature_b64":"flsXu4QfU9tUzTNX47u7XTc5tb1R1AlFNqo8E4zL5I6fAlCcgZz0SeEYRS0DqdXu/JPmD23P7f/FJkNgwdSqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07084247f38110be209c6c4805cc3885927674f72a5748d3e8e250a71a4a881c","last_reissued_at":"2026-05-18T03:10:47.808949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:47.808949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.5114","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":"2026-05-18T03:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kEBRAJlmJQLlRP0e2uENsHmLPk688l5cIdojb+vSVkF4TeIwNMs+ikpdo97M/CezOGHsDxp1CL5izhQJvo2wCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T18:41:12.991757Z"},"content_sha256":"cbc2e26cf5cc5e5dce40ca7ffb9e2be46e73bc59aa19778774f5f9c68da96c2a","schema_version":"1.0","event_id":"sha256:cbc2e26cf5cc5e5dce40ca7ffb9e2be46e73bc59aa19778774f5f9c68da96c2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:A4EEER7TQEIL4IE4NREALTBYQW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The matrix sign function for solving surface wave problems in homogeneous and laterally periodic elastic half-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. A. Kutsenko, A. L. Shuvalov, A. N. Norris","submitted_at":"2013-03-20T22:44:36Z","abstract_excerpt":"The matrix sign function is shown to provide a simple and direct method to derive some fundamental results in the theory of surface waves in anisotropic materials. It is used to establish a shortcut to the basic formulas of the Barnett-Lothe integral formalism and to obtain an explicit solution of the algebraic matrix Riccati equation for the surface impedance. The matrix sign function allows the Barnett-Lothe formalism to be readily generalized for the problem of finding the surface wave speed in a periodically inhomogeneous half-space with material properties that are independent of depth. N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5114","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":"2026-05-18T03:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"edisfgV1XBf/Fw35aVmsgPtgZdjZ40tJdU7x/QTntx25Tbspqcvjk9KnO3+zgU8Z6ichA+TayqkPC9+9tmGEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T18:41:12.992126Z"},"content_sha256":"e8f242d201e13692bae98743ba66fcff343f00e3af327120545d02f101c8e089","schema_version":"1.0","event_id":"sha256:e8f242d201e13692bae98743ba66fcff343f00e3af327120545d02f101c8e089"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A4EEER7TQEIL4IE4NREALTBYQW/bundle.json","state_url":"https://pith.science/pith/A4EEER7TQEIL4IE4NREALTBYQW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A4EEER7TQEIL4IE4NREALTBYQW/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":"2026-06-29T18:41:12Z","links":{"resolver":"https://pith.science/pith/A4EEER7TQEIL4IE4NREALTBYQW","bundle":"https://pith.science/pith/A4EEER7TQEIL4IE4NREALTBYQW/bundle.json","state":"https://pith.science/pith/A4EEER7TQEIL4IE4NREALTBYQW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A4EEER7TQEIL4IE4NREALTBYQW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:A4EEER7TQEIL4IE4NREALTBYQW","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":"cfc6e25e51c01d9eacdc06f1dbbe95000a31fbe23c6c3f1f29754dd1db47a913","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-20T22:44:36Z","title_canon_sha256":"49121887b9690f7760108b8480bcd0c313494d477b75ea9be9b0b4fdfa4c429d"},"schema_version":"1.0","source":{"id":"1303.5114","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5114","created_at":"2026-05-18T03:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5114v1","created_at":"2026-05-18T03:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5114","created_at":"2026-05-18T03:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"A4EEER7TQEIL","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"A4EEER7TQEIL4IE4","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"A4EEER7T","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:e8f242d201e13692bae98743ba66fcff343f00e3af327120545d02f101c8e089","target":"graph","created_at":"2026-05-18T03:10:47Z","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 matrix sign function is shown to provide a simple and direct method to derive some fundamental results in the theory of surface waves in anisotropic materials. It is used to establish a shortcut to the basic formulas of the Barnett-Lothe integral formalism and to obtain an explicit solution of the algebraic matrix Riccati equation for the surface impedance. The matrix sign function allows the Barnett-Lothe formalism to be readily generalized for the problem of finding the surface wave speed in a periodically inhomogeneous half-space with material properties that are independent of depth. N","authors_text":"A. A. Kutsenko, A. L. Shuvalov, A. N. Norris","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-20T22:44:36Z","title":"The matrix sign function for solving surface wave problems in homogeneous and laterally periodic elastic half-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5114","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:cbc2e26cf5cc5e5dce40ca7ffb9e2be46e73bc59aa19778774f5f9c68da96c2a","target":"record","created_at":"2026-05-18T03:10:47Z","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":"cfc6e25e51c01d9eacdc06f1dbbe95000a31fbe23c6c3f1f29754dd1db47a913","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-20T22:44:36Z","title_canon_sha256":"49121887b9690f7760108b8480bcd0c313494d477b75ea9be9b0b4fdfa4c429d"},"schema_version":"1.0","source":{"id":"1303.5114","kind":"arxiv","version":1}},"canonical_sha256":"07084247f38110be209c6c4805cc3885927674f72a5748d3e8e250a71a4a881c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07084247f38110be209c6c4805cc3885927674f72a5748d3e8e250a71a4a881c","first_computed_at":"2026-05-18T03:10:47.808949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:47.808949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"flsXu4QfU9tUzTNX47u7XTc5tb1R1AlFNqo8E4zL5I6fAlCcgZz0SeEYRS0DqdXu/JPmD23P7f/FJkNgwdSqCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:47.809951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.5114","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbc2e26cf5cc5e5dce40ca7ffb9e2be46e73bc59aa19778774f5f9c68da96c2a","sha256:e8f242d201e13692bae98743ba66fcff343f00e3af327120545d02f101c8e089"],"state_sha256":"4456378089be2d9a037ca8a64fa353ceae42e8831aafbe552e9dbdcb850226fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4RlcE8ctxZhb0sI5eoAW3xlWwDRpyNGlP0I0fKV2M2Cpg6dPG6NKOG1VvhpPVOL8MiuVrDagR3XnrZH1vrUgCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T18:41:12.993898Z","bundle_sha256":"ecd806a2909cb3795c51f800c21b2d43058e51027f046938b83e47697d54873e"}}