{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:N4HYIL2GI7OMXMQMV5CT5X3TLM","short_pith_number":"pith:N4HYIL2G","canonical_record":{"source":{"id":"1212.3974","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2012-12-17T12:48:19Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"a4416da6a0cc9e5850d9ac939e635fd624e9fe2be76daf43474afd234334daeb","abstract_canon_sha256":"94ba8909e8e38ae3e7cb9cef29dad715afc62552fd6338c445087dcbdb6066a3"},"schema_version":"1.0"},"canonical_sha256":"6f0f842f4647dccbb20caf453edf735b152250197e84194fc54a1fd29ab3017c","source":{"kind":"arxiv","id":"1212.3974","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3974","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3974v1","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3974","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"pith_short_12","alias_value":"N4HYIL2GI7OM","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N4HYIL2GI7OMXMQM","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N4HYIL2G","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:N4HYIL2GI7OMXMQMV5CT5X3TLM","target":"record","payload":{"canonical_record":{"source":{"id":"1212.3974","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2012-12-17T12:48:19Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"a4416da6a0cc9e5850d9ac939e635fd624e9fe2be76daf43474afd234334daeb","abstract_canon_sha256":"94ba8909e8e38ae3e7cb9cef29dad715afc62552fd6338c445087dcbdb6066a3"},"schema_version":"1.0"},"canonical_sha256":"6f0f842f4647dccbb20caf453edf735b152250197e84194fc54a1fd29ab3017c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:21.848259Z","signature_b64":"5OD3ZEi5+9seav3WPY2igkRJGC/iBlUI1io682tF7NpmrxCNZa4XLoMdvzSzQODLYT4r4q/FdoXKvNcPb2sbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f0f842f4647dccbb20caf453edf735b152250197e84194fc54a1fd29ab3017c","last_reissued_at":"2026-05-18T03:38:21.847557Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:21.847557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.3974","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":"2026-05-18T03:38:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bWY/cZFMxQMIG6EUwFgRuzYNIDVJNpj/Hbj/IeJg4qa6ZQ+RgficzMUzUidyfB838v3qNi6bm5msKkxtNxwHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:09:44.725057Z"},"content_sha256":"d55eeea15d76d91689b4340f3e9a092e29ac769c4f83febfd2315774248a86ef","schema_version":"1.0","event_id":"sha256:d55eeea15d76d91689b4340f3e9a092e29ac769c4f83febfd2315774248a86ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:N4HYIL2GI7OMXMQMV5CT5X3TLM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cavity equations for a positive or negative refraction index material with electric and magnetic non-linearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"physics.optics","authors_text":"Daniel A. M\\'artin, Miguel Hoyuelos","submitted_at":"2012-12-17T12:48:19Z","abstract_excerpt":"We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative refraction index material with third order effective electric and magnetic non-linearities. Two coupled non-linear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3974","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":"2026-05-18T03:38:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0KjvPZweMVWKX2SwK6oE6LZDMLghA/BdoYJ88wFjkND21eOifhgLHKhtLFjAqtVR4HTgSVAorG67tNjwB/SbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:09:44.725430Z"},"content_sha256":"a0c25bbc4d8f61aa970741d09933b5d76d1f6f689c4a0979c04cd82c34926e43","schema_version":"1.0","event_id":"sha256:a0c25bbc4d8f61aa970741d09933b5d76d1f6f689c4a0979c04cd82c34926e43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N4HYIL2GI7OMXMQMV5CT5X3TLM/bundle.json","state_url":"https://pith.science/pith/N4HYIL2GI7OMXMQMV5CT5X3TLM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N4HYIL2GI7OMXMQMV5CT5X3TLM/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":"2026-06-03T16:09:44Z","links":{"resolver":"https://pith.science/pith/N4HYIL2GI7OMXMQMV5CT5X3TLM","bundle":"https://pith.science/pith/N4HYIL2GI7OMXMQMV5CT5X3TLM/bundle.json","state":"https://pith.science/pith/N4HYIL2GI7OMXMQMV5CT5X3TLM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N4HYIL2GI7OMXMQMV5CT5X3TLM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:N4HYIL2GI7OMXMQMV5CT5X3TLM","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":"94ba8909e8e38ae3e7cb9cef29dad715afc62552fd6338c445087dcbdb6066a3","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2012-12-17T12:48:19Z","title_canon_sha256":"a4416da6a0cc9e5850d9ac939e635fd624e9fe2be76daf43474afd234334daeb"},"schema_version":"1.0","source":{"id":"1212.3974","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3974","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3974v1","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3974","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"pith_short_12","alias_value":"N4HYIL2GI7OM","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N4HYIL2GI7OMXMQM","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N4HYIL2G","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:a0c25bbc4d8f61aa970741d09933b5d76d1f6f689c4a0979c04cd82c34926e43","target":"graph","created_at":"2026-05-18T03:38:21Z","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"},"paper":{"abstract_excerpt":"We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative refraction index material with third order effective electric and magnetic non-linearities. Two coupled non-linear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond ","authors_text":"Daniel A. M\\'artin, Miguel Hoyuelos","cross_cats":["nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2012-12-17T12:48:19Z","title":"Cavity equations for a positive or negative refraction index material with electric and magnetic non-linearities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3974","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:d55eeea15d76d91689b4340f3e9a092e29ac769c4f83febfd2315774248a86ef","target":"record","created_at":"2026-05-18T03:38:21Z","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":"94ba8909e8e38ae3e7cb9cef29dad715afc62552fd6338c445087dcbdb6066a3","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2012-12-17T12:48:19Z","title_canon_sha256":"a4416da6a0cc9e5850d9ac939e635fd624e9fe2be76daf43474afd234334daeb"},"schema_version":"1.0","source":{"id":"1212.3974","kind":"arxiv","version":1}},"canonical_sha256":"6f0f842f4647dccbb20caf453edf735b152250197e84194fc54a1fd29ab3017c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f0f842f4647dccbb20caf453edf735b152250197e84194fc54a1fd29ab3017c","first_computed_at":"2026-05-18T03:38:21.847557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:21.847557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5OD3ZEi5+9seav3WPY2igkRJGC/iBlUI1io682tF7NpmrxCNZa4XLoMdvzSzQODLYT4r4q/FdoXKvNcPb2sbBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:21.848259Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3974","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d55eeea15d76d91689b4340f3e9a092e29ac769c4f83febfd2315774248a86ef","sha256:a0c25bbc4d8f61aa970741d09933b5d76d1f6f689c4a0979c04cd82c34926e43"],"state_sha256":"b828649b37be3e8fadf39ec82d2b587091b0c05b9957781fbe94386ae7406423"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jH/pbI+DQ/FVuqDwiWQEUO9l0AYl1H6ZN4drGlnC8SeD3A+9ps9hocIE+K/6wvPmHJODr/nYVewmB/HcApegDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:09:44.727412Z","bundle_sha256":"85dc2b753cc9778f292ac69ffff843958345346933694dd5511bde7df059d5bc"}}