{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SXROOFN4LH5XRRV5YGTMYFC53T","short_pith_number":"pith:SXROOFN4","canonical_record":{"source":{"id":"1503.00639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-03-02T17:51:46Z","cross_cats_sorted":[],"title_canon_sha256":"8314f2001e2cd807ae2295add917dc5a7854721e8f34f51aac73bbe5c24fe227","abstract_canon_sha256":"932243390ac61fa8d6f07380531541c02eb29147a76f4f6ae48d88c311540bb1"},"schema_version":"1.0"},"canonical_sha256":"95e2e715bc59fb78c6bdc1a6cc145ddccd1e9670d628097598fc5a1744edd622","source":{"kind":"arxiv","id":"1503.00639","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00639","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00639v1","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00639","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"pith_short_12","alias_value":"SXROOFN4LH5X","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SXROOFN4LH5XRRV5","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SXROOFN4","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SXROOFN4LH5XRRV5YGTMYFC53T","target":"record","payload":{"canonical_record":{"source":{"id":"1503.00639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-03-02T17:51:46Z","cross_cats_sorted":[],"title_canon_sha256":"8314f2001e2cd807ae2295add917dc5a7854721e8f34f51aac73bbe5c24fe227","abstract_canon_sha256":"932243390ac61fa8d6f07380531541c02eb29147a76f4f6ae48d88c311540bb1"},"schema_version":"1.0"},"canonical_sha256":"95e2e715bc59fb78c6bdc1a6cc145ddccd1e9670d628097598fc5a1744edd622","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:49.614263Z","signature_b64":"o8WUUNQjFTJk8tEDlWKDDa3K6S+TUw65radOeTBXICLPbnvhS48PsmBR/H6z5U31JCL29Z7+7hIVhuLFGSttBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95e2e715bc59fb78c6bdc1a6cc145ddccd1e9670d628097598fc5a1744edd622","last_reissued_at":"2026-05-18T02:25:49.613717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:49.613717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.00639","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":"2026-05-18T02:25:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JgLInwOgEXG3rHtWDngmezccdcbdr12U6Kpb3oIuvoazZB88I2xDxDJZAuVMDnA29eCEBoUSYvH0HSGtM5xADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:55:48.726173Z"},"content_sha256":"d4b0614b51f713be905c477de25215d7633da00fcf83721aa9331b653dc1e083","schema_version":"1.0","event_id":"sha256:d4b0614b51f713be905c477de25215d7633da00fcf83721aa9331b653dc1e083"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SXROOFN4LH5XRRV5YGTMYFC53T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scattering of electromagnetic waves by small impedance particles of an arbitrary shape","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Alexander G. Ramm","submitted_at":"2015-03-02T17:51:46Z","abstract_excerpt":"An explicit formula is derived for the electromagnetic (EM) field scattered by one small impedance particle $D$ of an arbitrary shape. If $a$ is the characteristic size of the particle, $\\lambda$ is the wavelength, $a<<\\lambda$ and $\\zeta$ is the boundary impedance of $D$, $[N,[E,N]]=\\zeta [N,H]$ on $S$, where $S$ is the surface of the particle, $N$ is the unit outer normal to $S$, and $E$, $H$ is the EM field, then the scattered field is $E_{sc}=[\\nabla g(x,x_1), Q]$. Here $g(x,y)=\\frac{e^{ik|x-y|}}{4\\pi |x-y|}$, $k$ is the wave number, $x_1\\in D$ is an arbitrary point, and $Q=-\\frac{\\zeta |S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00639","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":"2026-05-18T02:25:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/X3cagCxWzONOzdDlP/9EHTxVVxBQwpkSAIiatT6M5cEgGIVGob1GdLd52UTaaQ8remO1d7Rglh09nfpAUhODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:55:48.726533Z"},"content_sha256":"654919a9171d4cd19553c6c06b4b57f05b67ba4f14872f7bf18a951a53d1fe39","schema_version":"1.0","event_id":"sha256:654919a9171d4cd19553c6c06b4b57f05b67ba4f14872f7bf18a951a53d1fe39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SXROOFN4LH5XRRV5YGTMYFC53T/bundle.json","state_url":"https://pith.science/pith/SXROOFN4LH5XRRV5YGTMYFC53T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SXROOFN4LH5XRRV5YGTMYFC53T/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":"2026-06-27T08:55:48Z","links":{"resolver":"https://pith.science/pith/SXROOFN4LH5XRRV5YGTMYFC53T","bundle":"https://pith.science/pith/SXROOFN4LH5XRRV5YGTMYFC53T/bundle.json","state":"https://pith.science/pith/SXROOFN4LH5XRRV5YGTMYFC53T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SXROOFN4LH5XRRV5YGTMYFC53T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SXROOFN4LH5XRRV5YGTMYFC53T","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":"932243390ac61fa8d6f07380531541c02eb29147a76f4f6ae48d88c311540bb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-03-02T17:51:46Z","title_canon_sha256":"8314f2001e2cd807ae2295add917dc5a7854721e8f34f51aac73bbe5c24fe227"},"schema_version":"1.0","source":{"id":"1503.00639","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00639","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00639v1","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00639","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"pith_short_12","alias_value":"SXROOFN4LH5X","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SXROOFN4LH5XRRV5","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SXROOFN4","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:654919a9171d4cd19553c6c06b4b57f05b67ba4f14872f7bf18a951a53d1fe39","target":"graph","created_at":"2026-05-18T02:25:49Z","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":"An explicit formula is derived for the electromagnetic (EM) field scattered by one small impedance particle $D$ of an arbitrary shape. If $a$ is the characteristic size of the particle, $\\lambda$ is the wavelength, $a<<\\lambda$ and $\\zeta$ is the boundary impedance of $D$, $[N,[E,N]]=\\zeta [N,H]$ on $S$, where $S$ is the surface of the particle, $N$ is the unit outer normal to $S$, and $E$, $H$ is the EM field, then the scattered field is $E_{sc}=[\\nabla g(x,x_1), Q]$. Here $g(x,y)=\\frac{e^{ik|x-y|}}{4\\pi |x-y|}$, $k$ is the wave number, $x_1\\in D$ is an arbitrary point, and $Q=-\\frac{\\zeta |S","authors_text":"Alexander G. Ramm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-03-02T17:51:46Z","title":"Scattering of electromagnetic waves by small impedance particles of an arbitrary shape"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00639","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:d4b0614b51f713be905c477de25215d7633da00fcf83721aa9331b653dc1e083","target":"record","created_at":"2026-05-18T02:25:49Z","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":"932243390ac61fa8d6f07380531541c02eb29147a76f4f6ae48d88c311540bb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-03-02T17:51:46Z","title_canon_sha256":"8314f2001e2cd807ae2295add917dc5a7854721e8f34f51aac73bbe5c24fe227"},"schema_version":"1.0","source":{"id":"1503.00639","kind":"arxiv","version":1}},"canonical_sha256":"95e2e715bc59fb78c6bdc1a6cc145ddccd1e9670d628097598fc5a1744edd622","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95e2e715bc59fb78c6bdc1a6cc145ddccd1e9670d628097598fc5a1744edd622","first_computed_at":"2026-05-18T02:25:49.613717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:49.613717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o8WUUNQjFTJk8tEDlWKDDa3K6S+TUw65radOeTBXICLPbnvhS48PsmBR/H6z5U31JCL29Z7+7hIVhuLFGSttBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:49.614263Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00639","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4b0614b51f713be905c477de25215d7633da00fcf83721aa9331b653dc1e083","sha256:654919a9171d4cd19553c6c06b4b57f05b67ba4f14872f7bf18a951a53d1fe39"],"state_sha256":"612e63148f7ff98d78f192511c39a262da75bfbffc374008b6a3b726da5898e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+8SRvu2PnRcJMV8qfIB6e5lBuan9vdCMIl2fubVjisOGsMUphyQ2U53LamQowCcoaTwqq7fkySG+ItCe5zavCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T08:55:48.728436Z","bundle_sha256":"fd711952a096c6c2decf66843167290663dbdaa25ac2d5cbeb3e04d672c851dd"}}