{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SW4HKLDH7X6PIWHOL4QT53XTLB","short_pith_number":"pith:SW4HKLDH","canonical_record":{"source":{"id":"1509.03506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-09-11T13:46:46Z","cross_cats_sorted":[],"title_canon_sha256":"f6e734b12992d25595fd352843baf0b5b0ebdbf83a726d05f4c6004995b46b2f","abstract_canon_sha256":"965652ff8684b252f4203f3822e3a4cdc30e55c0565466bc510096825ecb1880"},"schema_version":"1.0"},"canonical_sha256":"95b8752c67fdfcf458ee5f213eeef3587915304aa3572b00f2614869e97a4c56","source":{"kind":"arxiv","id":"1509.03506","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03506","created_at":"2026-05-18T01:32:59Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03506v1","created_at":"2026-05-18T01:32:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03506","created_at":"2026-05-18T01:32:59Z"},{"alias_kind":"pith_short_12","alias_value":"SW4HKLDH7X6P","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SW4HKLDH7X6PIWHO","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SW4HKLDH","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SW4HKLDH7X6PIWHOL4QT53XTLB","target":"record","payload":{"canonical_record":{"source":{"id":"1509.03506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-09-11T13:46:46Z","cross_cats_sorted":[],"title_canon_sha256":"f6e734b12992d25595fd352843baf0b5b0ebdbf83a726d05f4c6004995b46b2f","abstract_canon_sha256":"965652ff8684b252f4203f3822e3a4cdc30e55c0565466bc510096825ecb1880"},"schema_version":"1.0"},"canonical_sha256":"95b8752c67fdfcf458ee5f213eeef3587915304aa3572b00f2614869e97a4c56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:59.012146Z","signature_b64":"cYDwPKSwlkWYbLnPGQwkHIQ7/CJfABXoAJBSz+L06NrCQYwRuH04KJ0TG2a4hEEW1Y7UaTPOu2b6oC9ocdPJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95b8752c67fdfcf458ee5f213eeef3587915304aa3572b00f2614869e97a4c56","last_reissued_at":"2026-05-18T01:32:59.011520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:59.011520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.03506","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":"2026-05-18T01:32:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kyQZMVfDKUrBEM9j7S/vj2G6vXwoU1JKrytK4Sn19uIBHNcype7AqBgQcruHQrP9NrWbxorkrNFFFzkXHQ1UDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:21:40.810166Z"},"content_sha256":"ad8b54d12da7bca35b745592df84acf81f3b87d239caf02d9c24593c7d41cbdb","schema_version":"1.0","event_id":"sha256:ad8b54d12da7bca35b745592df84acf81f3b87d239caf02d9c24593c7d41cbdb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SW4HKLDH7X6PIWHOL4QT53XTLB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Null-Field Radiationless Sources: Comment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Iver Brevik","submitted_at":"2015-09-11T13:46:46Z","abstract_excerpt":"We elaborate upon a recent paper of E. Hurwitz and G. Gbur [Opt. Lett. {\\bf 39}, 6529 (2014)], dealing with null-field sources. After commenting on their theory in Minkowski space, we show how the theory can be conveniently generalized to the case of curvilinear space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03506","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":"2026-05-18T01:32:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DO1d8loATkBSOXVAecUglOn4acTwZdrae7Jni75IHyTcsdJOIGUSHCFDFDm6Ey5RSpkiDn5rO9h+tPvgY+AECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:21:40.810847Z"},"content_sha256":"d19f0b1953b72c8f69a493009dd93de1677af7a1c1a7392e3fc86f58805e084b","schema_version":"1.0","event_id":"sha256:d19f0b1953b72c8f69a493009dd93de1677af7a1c1a7392e3fc86f58805e084b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SW4HKLDH7X6PIWHOL4QT53XTLB/bundle.json","state_url":"https://pith.science/pith/SW4HKLDH7X6PIWHOL4QT53XTLB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SW4HKLDH7X6PIWHOL4QT53XTLB/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":"2026-05-31T14:21:40Z","links":{"resolver":"https://pith.science/pith/SW4HKLDH7X6PIWHOL4QT53XTLB","bundle":"https://pith.science/pith/SW4HKLDH7X6PIWHOL4QT53XTLB/bundle.json","state":"https://pith.science/pith/SW4HKLDH7X6PIWHOL4QT53XTLB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SW4HKLDH7X6PIWHOL4QT53XTLB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SW4HKLDH7X6PIWHOL4QT53XTLB","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":"965652ff8684b252f4203f3822e3a4cdc30e55c0565466bc510096825ecb1880","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-09-11T13:46:46Z","title_canon_sha256":"f6e734b12992d25595fd352843baf0b5b0ebdbf83a726d05f4c6004995b46b2f"},"schema_version":"1.0","source":{"id":"1509.03506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03506","created_at":"2026-05-18T01:32:59Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03506v1","created_at":"2026-05-18T01:32:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03506","created_at":"2026-05-18T01:32:59Z"},{"alias_kind":"pith_short_12","alias_value":"SW4HKLDH7X6P","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SW4HKLDH7X6PIWHO","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SW4HKLDH","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:d19f0b1953b72c8f69a493009dd93de1677af7a1c1a7392e3fc86f58805e084b","target":"graph","created_at":"2026-05-18T01:32:59Z","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 elaborate upon a recent paper of E. Hurwitz and G. Gbur [Opt. Lett. {\\bf 39}, 6529 (2014)], dealing with null-field sources. After commenting on their theory in Minkowski space, we show how the theory can be conveniently generalized to the case of curvilinear space.","authors_text":"Iver Brevik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-09-11T13:46:46Z","title":"Null-Field Radiationless Sources: Comment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03506","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:ad8b54d12da7bca35b745592df84acf81f3b87d239caf02d9c24593c7d41cbdb","target":"record","created_at":"2026-05-18T01:32:59Z","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":"965652ff8684b252f4203f3822e3a4cdc30e55c0565466bc510096825ecb1880","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-09-11T13:46:46Z","title_canon_sha256":"f6e734b12992d25595fd352843baf0b5b0ebdbf83a726d05f4c6004995b46b2f"},"schema_version":"1.0","source":{"id":"1509.03506","kind":"arxiv","version":1}},"canonical_sha256":"95b8752c67fdfcf458ee5f213eeef3587915304aa3572b00f2614869e97a4c56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95b8752c67fdfcf458ee5f213eeef3587915304aa3572b00f2614869e97a4c56","first_computed_at":"2026-05-18T01:32:59.011520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:59.011520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cYDwPKSwlkWYbLnPGQwkHIQ7/CJfABXoAJBSz+L06NrCQYwRuH04KJ0TG2a4hEEW1Y7UaTPOu2b6oC9ocdPJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:59.012146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad8b54d12da7bca35b745592df84acf81f3b87d239caf02d9c24593c7d41cbdb","sha256:d19f0b1953b72c8f69a493009dd93de1677af7a1c1a7392e3fc86f58805e084b"],"state_sha256":"b7e5579c2682f96a2904c0cad78fb6b646f243a945214f264c84438ba69d283c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WFOrqNCnooUk4pXRjtB9VBCKpvixDMdJKRqIlKU6QMRklnZCqg3UpSdg684znly/mAz7XMdorJYRjaimHOToDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:21:40.814002Z","bundle_sha256":"234c9f4daafa061f612360be475db50ee61c91aeca090b175a115e8320a98eaf"}}