{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5RFW2Q2QBC5CLML44RRWSKEBRW","short_pith_number":"pith:5RFW2Q2Q","canonical_record":{"source":{"id":"1303.5535","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-22T07:39:52Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"beef741206512c8d986f3eab5f57321297747a58a02c28e23095697572e2261b","abstract_canon_sha256":"b091317c738f2a6ecff8976436d91a177aa9ff827ae4c321dd014515163ba993"},"schema_version":"1.0"},"canonical_sha256":"ec4b6d435008ba25b17ce4636928818d9c09afbda8361482527ace4431d6f7fd","source":{"kind":"arxiv","id":"1303.5535","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5535","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5535v2","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5535","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"pith_short_12","alias_value":"5RFW2Q2QBC5C","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5RFW2Q2QBC5CLML4","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5RFW2Q2Q","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5RFW2Q2QBC5CLML44RRWSKEBRW","target":"record","payload":{"canonical_record":{"source":{"id":"1303.5535","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-22T07:39:52Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"beef741206512c8d986f3eab5f57321297747a58a02c28e23095697572e2261b","abstract_canon_sha256":"b091317c738f2a6ecff8976436d91a177aa9ff827ae4c321dd014515163ba993"},"schema_version":"1.0"},"canonical_sha256":"ec4b6d435008ba25b17ce4636928818d9c09afbda8361482527ace4431d6f7fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:42.444254Z","signature_b64":"DyWMji8gPM5AVkp1UfMqu5VN2o0sPsxM7o9yATxe37rr5enMtp0u9JqwL9mj82izjQImiw8DcwtJLgGYGol7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec4b6d435008ba25b17ce4636928818d9c09afbda8361482527ace4431d6f7fd","last_reissued_at":"2026-05-18T03:26:42.443509Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:42.443509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.5535","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jic+1e5Sf0ohjN3AtTeSYHW03PAJqEbWrZqJGUJsU04UeMhCVa7MMT5Br9UTWkGZSkERCDxuK8yHA/CNXw3HBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:38:40.300689Z"},"content_sha256":"cb42ccde339a9b88610b675767475d17e07190334c4d84b9cd4faec1b9a8ed92","schema_version":"1.0","event_id":"sha256:cb42ccde339a9b88610b675767475d17e07190334c4d84b9cd4faec1b9a8ed92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5RFW2Q2QBC5CLML44RRWSKEBRW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Electromagnetic Media with no Dispersion Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alberto Favaro, Ismo V. Lindell","submitted_at":"2013-03-22T07:39:52Z","abstract_excerpt":"It has been known through some examples that parameters of an electromagnetic medium can be so defined that there is no dispersion equation (Fresnel equation) to restrict the choice of the wave vector of a plane wave in such a medium, i.e., that the dispersion equation is satisfied identically for any wave vector. In the present paper, a more systematic study to define classes of media with no dispersion equation is attempted. The analysis makes use of coordinate-free four-dimensional formalism in terms of multivectors, multiforms and dyadics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5535","kind":"arxiv","version":2},"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":"2026-05-18T03:26:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+BSRmHA/FzAtLokzvkD+202/iv9G+tUnypCQi3qtsjV0XLf6ZeFBad3bkcjgflYsxIe/oPqT0EridWNeyRWFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:38:40.301035Z"},"content_sha256":"0c5677e937a1b442ca79b62954055a190474b85bf413bccd0dc779da985f5ba7","schema_version":"1.0","event_id":"sha256:0c5677e937a1b442ca79b62954055a190474b85bf413bccd0dc779da985f5ba7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RFW2Q2QBC5CLML44RRWSKEBRW/bundle.json","state_url":"https://pith.science/pith/5RFW2Q2QBC5CLML44RRWSKEBRW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RFW2Q2QBC5CLML44RRWSKEBRW/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":"2026-06-24T05:38:40Z","links":{"resolver":"https://pith.science/pith/5RFW2Q2QBC5CLML44RRWSKEBRW","bundle":"https://pith.science/pith/5RFW2Q2QBC5CLML44RRWSKEBRW/bundle.json","state":"https://pith.science/pith/5RFW2Q2QBC5CLML44RRWSKEBRW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RFW2Q2QBC5CLML44RRWSKEBRW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5RFW2Q2QBC5CLML44RRWSKEBRW","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":"b091317c738f2a6ecff8976436d91a177aa9ff827ae4c321dd014515163ba993","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-22T07:39:52Z","title_canon_sha256":"beef741206512c8d986f3eab5f57321297747a58a02c28e23095697572e2261b"},"schema_version":"1.0","source":{"id":"1303.5535","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5535","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5535v2","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5535","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"pith_short_12","alias_value":"5RFW2Q2QBC5C","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5RFW2Q2QBC5CLML4","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5RFW2Q2Q","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:0c5677e937a1b442ca79b62954055a190474b85bf413bccd0dc779da985f5ba7","target":"graph","created_at":"2026-05-18T03:26:42Z","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":"It has been known through some examples that parameters of an electromagnetic medium can be so defined that there is no dispersion equation (Fresnel equation) to restrict the choice of the wave vector of a plane wave in such a medium, i.e., that the dispersion equation is satisfied identically for any wave vector. In the present paper, a more systematic study to define classes of media with no dispersion equation is attempted. The analysis makes use of coordinate-free four-dimensional formalism in terms of multivectors, multiforms and dyadics.","authors_text":"Alberto Favaro, Ismo V. Lindell","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-22T07:39:52Z","title":"Electromagnetic Media with no Dispersion Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5535","kind":"arxiv","version":2},"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:cb42ccde339a9b88610b675767475d17e07190334c4d84b9cd4faec1b9a8ed92","target":"record","created_at":"2026-05-18T03:26:42Z","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":"b091317c738f2a6ecff8976436d91a177aa9ff827ae4c321dd014515163ba993","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-22T07:39:52Z","title_canon_sha256":"beef741206512c8d986f3eab5f57321297747a58a02c28e23095697572e2261b"},"schema_version":"1.0","source":{"id":"1303.5535","kind":"arxiv","version":2}},"canonical_sha256":"ec4b6d435008ba25b17ce4636928818d9c09afbda8361482527ace4431d6f7fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec4b6d435008ba25b17ce4636928818d9c09afbda8361482527ace4431d6f7fd","first_computed_at":"2026-05-18T03:26:42.443509Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:42.443509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DyWMji8gPM5AVkp1UfMqu5VN2o0sPsxM7o9yATxe37rr5enMtp0u9JqwL9mj82izjQImiw8DcwtJLgGYGol7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:42.444254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.5535","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb42ccde339a9b88610b675767475d17e07190334c4d84b9cd4faec1b9a8ed92","sha256:0c5677e937a1b442ca79b62954055a190474b85bf413bccd0dc779da985f5ba7"],"state_sha256":"a09b3681d5eb8a6fd798dece612dd3c7fd68606c68d2c14e944ca77d7fffcfab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"50EOoG5fDv09H3aoaH54BtXdMXamkN9IN1J6ZbaslNw0CeL4wKNE7yCAYGPqn9QZaWBxv1OVVCCsYtdQEW88CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:38:40.303112Z","bundle_sha256":"b73562a4ac2be76558f7d96a8af77568e84cf853bd4ec7384cddb69d0f807ac5"}}