{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:OLH3JYEN6FBBK2BCKNKSXBIZGD","short_pith_number":"pith:OLH3JYEN","canonical_record":{"source":{"id":"2006.10423","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SP","submitted_at":"2020-06-18T10:57:49Z","cross_cats_sorted":["physics.app-ph"],"title_canon_sha256":"2d86e475ca5ce1fb278e3ce16f3c4754f25e29c824ce0c47afb7440e6fc5f119","abstract_canon_sha256":"30ffa4e413c4cdef980c6644474125c1137f01f0b4e37bed1b081135258921d3"},"schema_version":"1.0"},"canonical_sha256":"72cfb4e08df14215682253552b851930ea3b98cb6e427c40b34c3e14256cf40d","source":{"kind":"arxiv","id":"2006.10423","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.10423","created_at":"2026-07-05T01:11:21Z"},{"alias_kind":"arxiv_version","alias_value":"2006.10423v1","created_at":"2026-07-05T01:11:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.10423","created_at":"2026-07-05T01:11:21Z"},{"alias_kind":"pith_short_12","alias_value":"OLH3JYEN6FBB","created_at":"2026-07-05T01:11:21Z"},{"alias_kind":"pith_short_16","alias_value":"OLH3JYEN6FBBK2BC","created_at":"2026-07-05T01:11:21Z"},{"alias_kind":"pith_short_8","alias_value":"OLH3JYEN","created_at":"2026-07-05T01:11:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:OLH3JYEN6FBBK2BCKNKSXBIZGD","target":"record","payload":{"canonical_record":{"source":{"id":"2006.10423","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SP","submitted_at":"2020-06-18T10:57:49Z","cross_cats_sorted":["physics.app-ph"],"title_canon_sha256":"2d86e475ca5ce1fb278e3ce16f3c4754f25e29c824ce0c47afb7440e6fc5f119","abstract_canon_sha256":"30ffa4e413c4cdef980c6644474125c1137f01f0b4e37bed1b081135258921d3"},"schema_version":"1.0"},"canonical_sha256":"72cfb4e08df14215682253552b851930ea3b98cb6e427c40b34c3e14256cf40d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:11:21.389302Z","signature_b64":"G9WCLSv5+wNgEp+2XpYPWp/7M79MxxmQAmcGZgWiYdsTI899gbCsgA09kvoMjAKGlrRrwbUckIfJDxWLYHWhCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72cfb4e08df14215682253552b851930ea3b98cb6e427c40b34c3e14256cf40d","last_reissued_at":"2026-07-05T01:11:21.388876Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:11:21.388876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.10423","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":"2026-07-05T01:11:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n/5nSgJpxJj+dvBQKa9yfyn+8vvfT+dUmbXPPkkUMGkpQMtbjePbU+QdTG/ESy/bjY65Hs7OZjkKAsYQ2cfIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T03:42:38.616661Z"},"content_sha256":"6ae5433fc71405dc1a1b4d6ffce80edcb3f3c7546344c2956ecd4ef5dcb85e5e","schema_version":"1.0","event_id":"sha256:6ae5433fc71405dc1a1b4d6ffce80edcb3f3c7546344c2956ecd4ef5dcb85e5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:OLH3JYEN6FBBK2BCKNKSXBIZGD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some useful approximations for calculation of directivities of multibeam power patterns of large planar arrays","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.app-ph"],"primary_cat":"eess.SP","authors_text":"Homayoon Oraizi, Javad Shabanpour","submitted_at":"2020-06-18T10:57:49Z","abstract_excerpt":"In this paper, by adopting the superposition of terms with unequal coefficients, some useful closed-form formulas for the class of large planar arrays are presented for predicting the directivities of radiated beams. Despite the applied simplifying assumptions, the provided formulas may be used for designing a large multiple-beam planar array with a specified power pattern. Several illustrative examples are presented which are numerically demonstrate by the MATLAB software. The applicability of the proposed synthesis method verified by the achieved conformity between the simulations and theore"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.10423","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.10423/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:11:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hlqykN72rVZXmJsyo9OjVUIeEyCSDszfm/wgy5gG8jcm+3VfsGCQzdACE/qK7Y9kVUogWIJaaLqtXOVRmb3JDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T03:42:38.617126Z"},"content_sha256":"b58635625abe412c611fa3ee126c503f463d90cdfdf6324ba2ec3dadb972b712","schema_version":"1.0","event_id":"sha256:b58635625abe412c611fa3ee126c503f463d90cdfdf6324ba2ec3dadb972b712"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OLH3JYEN6FBBK2BCKNKSXBIZGD/bundle.json","state_url":"https://pith.science/pith/OLH3JYEN6FBBK2BCKNKSXBIZGD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OLH3JYEN6FBBK2BCKNKSXBIZGD/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":"2026-08-06T03:42:38Z","links":{"resolver":"https://pith.science/pith/OLH3JYEN6FBBK2BCKNKSXBIZGD","bundle":"https://pith.science/pith/OLH3JYEN6FBBK2BCKNKSXBIZGD/bundle.json","state":"https://pith.science/pith/OLH3JYEN6FBBK2BCKNKSXBIZGD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OLH3JYEN6FBBK2BCKNKSXBIZGD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:OLH3JYEN6FBBK2BCKNKSXBIZGD","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":"30ffa4e413c4cdef980c6644474125c1137f01f0b4e37bed1b081135258921d3","cross_cats_sorted":["physics.app-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SP","submitted_at":"2020-06-18T10:57:49Z","title_canon_sha256":"2d86e475ca5ce1fb278e3ce16f3c4754f25e29c824ce0c47afb7440e6fc5f119"},"schema_version":"1.0","source":{"id":"2006.10423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.10423","created_at":"2026-07-05T01:11:21Z"},{"alias_kind":"arxiv_version","alias_value":"2006.10423v1","created_at":"2026-07-05T01:11:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.10423","created_at":"2026-07-05T01:11:21Z"},{"alias_kind":"pith_short_12","alias_value":"OLH3JYEN6FBB","created_at":"2026-07-05T01:11:21Z"},{"alias_kind":"pith_short_16","alias_value":"OLH3JYEN6FBBK2BC","created_at":"2026-07-05T01:11:21Z"},{"alias_kind":"pith_short_8","alias_value":"OLH3JYEN","created_at":"2026-07-05T01:11:21Z"}],"graph_snapshots":[{"event_id":"sha256:b58635625abe412c611fa3ee126c503f463d90cdfdf6324ba2ec3dadb972b712","target":"graph","created_at":"2026-07-05T01:11:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2006.10423/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, by adopting the superposition of terms with unequal coefficients, some useful closed-form formulas for the class of large planar arrays are presented for predicting the directivities of radiated beams. Despite the applied simplifying assumptions, the provided formulas may be used for designing a large multiple-beam planar array with a specified power pattern. Several illustrative examples are presented which are numerically demonstrate by the MATLAB software. The applicability of the proposed synthesis method verified by the achieved conformity between the simulations and theore","authors_text":"Homayoon Oraizi, Javad Shabanpour","cross_cats":["physics.app-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SP","submitted_at":"2020-06-18T10:57:49Z","title":"Some useful approximations for calculation of directivities of multibeam power patterns of large planar arrays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.10423","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":"sha256:6ae5433fc71405dc1a1b4d6ffce80edcb3f3c7546344c2956ecd4ef5dcb85e5e","target":"record","created_at":"2026-07-05T01:11:21Z","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":"30ffa4e413c4cdef980c6644474125c1137f01f0b4e37bed1b081135258921d3","cross_cats_sorted":["physics.app-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SP","submitted_at":"2020-06-18T10:57:49Z","title_canon_sha256":"2d86e475ca5ce1fb278e3ce16f3c4754f25e29c824ce0c47afb7440e6fc5f119"},"schema_version":"1.0","source":{"id":"2006.10423","kind":"arxiv","version":1}},"canonical_sha256":"72cfb4e08df14215682253552b851930ea3b98cb6e427c40b34c3e14256cf40d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72cfb4e08df14215682253552b851930ea3b98cb6e427c40b34c3e14256cf40d","first_computed_at":"2026-07-05T01:11:21.388876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:11:21.388876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G9WCLSv5+wNgEp+2XpYPWp/7M79MxxmQAmcGZgWiYdsTI899gbCsgA09kvoMjAKGlrRrwbUckIfJDxWLYHWhCw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:11:21.389302Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.10423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ae5433fc71405dc1a1b4d6ffce80edcb3f3c7546344c2956ecd4ef5dcb85e5e","sha256:b58635625abe412c611fa3ee126c503f463d90cdfdf6324ba2ec3dadb972b712"],"state_sha256":"ac4e26b7c89c5549259a2be12c0a79c7ad63e4f9a38ff908c1c233b58fe9b607"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ClQfqKmuWFT+gJ+JENzzYvKvqrv6Sbvxr5lLA0ZoqDf3t5yx0PDqOawFHOJ7SJEdHZTp0BmX1gYTMkz9aPBOBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T03:42:38.620576Z","bundle_sha256":"440e18e25ca8a0305c07790e2577b311e9aad089172a3b87cc5434be799be9f0"}}