{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PQHQI22HQP3RWRKJ4DJJG7JYZX","short_pith_number":"pith:PQHQI22H","canonical_record":{"source":{"id":"1504.06171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-04-23T13:19:41Z","cross_cats_sorted":[],"title_canon_sha256":"a057089c13583dcf1ad0eba62f8c9854323d874497857d57f961eaa9146cafd8","abstract_canon_sha256":"e43ac5e25dc7059fbc41619ae62ec18e73ac1a41f40b641a127703af1b097801"},"schema_version":"1.0"},"canonical_sha256":"7c0f046b4783f71b4549e0d2937d38cdead89ac0397962543a4f665893b90466","source":{"kind":"arxiv","id":"1504.06171","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06171","created_at":"2026-05-18T01:32:37Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06171v1","created_at":"2026-05-18T01:32:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06171","created_at":"2026-05-18T01:32:37Z"},{"alias_kind":"pith_short_12","alias_value":"PQHQI22HQP3R","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PQHQI22HQP3RWRKJ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PQHQI22H","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PQHQI22HQP3RWRKJ4DJJG7JYZX","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-04-23T13:19:41Z","cross_cats_sorted":[],"title_canon_sha256":"a057089c13583dcf1ad0eba62f8c9854323d874497857d57f961eaa9146cafd8","abstract_canon_sha256":"e43ac5e25dc7059fbc41619ae62ec18e73ac1a41f40b641a127703af1b097801"},"schema_version":"1.0"},"canonical_sha256":"7c0f046b4783f71b4549e0d2937d38cdead89ac0397962543a4f665893b90466","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:37.176305Z","signature_b64":"Jm2ij4yd9GoLS7Z8IjtRT1ArGPnJR8hn8hDTUfSiZc1i84Ef1CvFJi72tp5jERNJLehTTftgRN3SbTbJ48ovDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c0f046b4783f71b4549e0d2937d38cdead89ac0397962543a4f665893b90466","last_reissued_at":"2026-05-18T01:32:37.175707Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:37.175707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06171","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":"2026-05-18T01:32:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eRcrFOtuRJfsScLkTyMRq4DdjavjzgpOqYGO9gWMIIdZd35ImPrwB61aP9U3+VUu+Qdtxlj4/gceb134IITcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:53:36.966890Z"},"content_sha256":"d68c0274b578881fded846cda0ff4abfb03f4685a390004cb5c200b2a6a834fb","schema_version":"1.0","event_id":"sha256:d68c0274b578881fded846cda0ff4abfb03f4685a390004cb5c200b2a6a834fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PQHQI22HQP3RWRKJ4DJJG7JYZX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Laplace-Fourier analysis and instabilities of a gainy slab","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Hans Olaf H{\\aa}genvik, Johannes Skaar","submitted_at":"2015-04-23T13:19:41Z","abstract_excerpt":"The idealization of monochromatic plane waves leads to considerable simplifications in the analysis of electromagnetic systems. However, for active systems this idealization may be dangerous due to the presence of growing waves. Here we consider a gainy slab, and use a realistic incident beam, which is both causal and has finite width. This clarifies some apparent paradoxes arising from earlier analyses of this setup. In general it turns out to be necessary to involve complex frequencies $\\omega$ and/or complex transversal wavenumbers $k_x$. Simultaneously real $\\omega$ and $k_x$ cannot descri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06171","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":"2026-05-18T01:32:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ihLMDOdKBrC8EiXMbUqEgMFgqvQ5I5belewHdTuqypwNOjygeUgSGZGi3WHMd7WXcDGfOt2uCkKR0dlgUUcjDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:53:36.967609Z"},"content_sha256":"48525abee2df26294a0e3e3e0e32a86fdb979701d3ee8ad7226c8ad7a6fdc1aa","schema_version":"1.0","event_id":"sha256:48525abee2df26294a0e3e3e0e32a86fdb979701d3ee8ad7226c8ad7a6fdc1aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PQHQI22HQP3RWRKJ4DJJG7JYZX/bundle.json","state_url":"https://pith.science/pith/PQHQI22HQP3RWRKJ4DJJG7JYZX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PQHQI22HQP3RWRKJ4DJJG7JYZX/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":"2026-06-06T22:53:36Z","links":{"resolver":"https://pith.science/pith/PQHQI22HQP3RWRKJ4DJJG7JYZX","bundle":"https://pith.science/pith/PQHQI22HQP3RWRKJ4DJJG7JYZX/bundle.json","state":"https://pith.science/pith/PQHQI22HQP3RWRKJ4DJJG7JYZX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PQHQI22HQP3RWRKJ4DJJG7JYZX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PQHQI22HQP3RWRKJ4DJJG7JYZX","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":"e43ac5e25dc7059fbc41619ae62ec18e73ac1a41f40b641a127703af1b097801","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-04-23T13:19:41Z","title_canon_sha256":"a057089c13583dcf1ad0eba62f8c9854323d874497857d57f961eaa9146cafd8"},"schema_version":"1.0","source":{"id":"1504.06171","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06171","created_at":"2026-05-18T01:32:37Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06171v1","created_at":"2026-05-18T01:32:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06171","created_at":"2026-05-18T01:32:37Z"},{"alias_kind":"pith_short_12","alias_value":"PQHQI22HQP3R","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PQHQI22HQP3RWRKJ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PQHQI22H","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:48525abee2df26294a0e3e3e0e32a86fdb979701d3ee8ad7226c8ad7a6fdc1aa","target":"graph","created_at":"2026-05-18T01:32:37Z","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 idealization of monochromatic plane waves leads to considerable simplifications in the analysis of electromagnetic systems. However, for active systems this idealization may be dangerous due to the presence of growing waves. Here we consider a gainy slab, and use a realistic incident beam, which is both causal and has finite width. This clarifies some apparent paradoxes arising from earlier analyses of this setup. In general it turns out to be necessary to involve complex frequencies $\\omega$ and/or complex transversal wavenumbers $k_x$. Simultaneously real $\\omega$ and $k_x$ cannot descri","authors_text":"Hans Olaf H{\\aa}genvik, Johannes Skaar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-04-23T13:19:41Z","title":"Laplace-Fourier analysis and instabilities of a gainy slab"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06171","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:d68c0274b578881fded846cda0ff4abfb03f4685a390004cb5c200b2a6a834fb","target":"record","created_at":"2026-05-18T01:32:37Z","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":"e43ac5e25dc7059fbc41619ae62ec18e73ac1a41f40b641a127703af1b097801","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-04-23T13:19:41Z","title_canon_sha256":"a057089c13583dcf1ad0eba62f8c9854323d874497857d57f961eaa9146cafd8"},"schema_version":"1.0","source":{"id":"1504.06171","kind":"arxiv","version":1}},"canonical_sha256":"7c0f046b4783f71b4549e0d2937d38cdead89ac0397962543a4f665893b90466","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c0f046b4783f71b4549e0d2937d38cdead89ac0397962543a4f665893b90466","first_computed_at":"2026-05-18T01:32:37.175707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:37.175707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jm2ij4yd9GoLS7Z8IjtRT1ArGPnJR8hn8hDTUfSiZc1i84Ef1CvFJi72tp5jERNJLehTTftgRN3SbTbJ48ovDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:37.176305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06171","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d68c0274b578881fded846cda0ff4abfb03f4685a390004cb5c200b2a6a834fb","sha256:48525abee2df26294a0e3e3e0e32a86fdb979701d3ee8ad7226c8ad7a6fdc1aa"],"state_sha256":"eb8ba54aa2a0cb204ee42997cce903b005b3f880ef8e9b7e580301e4ab7e8577"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UEwQpxacdzxNvJh7YAQpSAnBe3d7cKL3tQ1O4UPj0nVgN8yDaFVYehzgecF4oKEfTkSCBpz+pIOzdys3pQJLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T22:53:36.971349Z","bundle_sha256":"e828e2c5c76c65f9774cd2cc0088c84e9d2262c5432724ebe4bc4cbbd4ae2be8"}}