{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:D3EGNXCCKRBG7UO5XLPKTPTR67","short_pith_number":"pith:D3EGNXCC","canonical_record":{"source":{"id":"1103.2672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-03-14T14:09:34Z","cross_cats_sorted":[],"title_canon_sha256":"6f608b8538192b393d942146f9cc39dcf0b849bcf2d6968f6e8f58f384f247df","abstract_canon_sha256":"49af77091abb353a14a16ad1df86b674bd34f6a7a4a8322617b8a342e4c3a271"},"schema_version":"1.0"},"canonical_sha256":"1ec866dc4254426fd1ddbadea9be71f7de933d7315bd0c837385b6f5a9a48f9e","source":{"kind":"arxiv","id":"1103.2672","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2672","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2672v1","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2672","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"pith_short_12","alias_value":"D3EGNXCCKRBG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"D3EGNXCCKRBG7UO5","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"D3EGNXCC","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:D3EGNXCCKRBG7UO5XLPKTPTR67","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-03-14T14:09:34Z","cross_cats_sorted":[],"title_canon_sha256":"6f608b8538192b393d942146f9cc39dcf0b849bcf2d6968f6e8f58f384f247df","abstract_canon_sha256":"49af77091abb353a14a16ad1df86b674bd34f6a7a4a8322617b8a342e4c3a271"},"schema_version":"1.0"},"canonical_sha256":"1ec866dc4254426fd1ddbadea9be71f7de933d7315bd0c837385b6f5a9a48f9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:54.391524Z","signature_b64":"zM+T+eYipy3jUdtX2FMh5NwPrHHUjNx3TXfMHHakdFPq7zbMP+vvG5mZsW6H2DOJ/CvIqEF0rYh6K0qWe86BDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ec866dc4254426fd1ddbadea9be71f7de933d7315bd0c837385b6f5a9a48f9e","last_reissued_at":"2026-05-18T04:26:54.390844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:54.390844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2672","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":"2026-05-18T04:26:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6PyHzQgyO7q5Gzl3JMM8kQ6jzH4mXF89wKH7wyte1ogz0WfjrvKgSzuiXCqvMgSXrQ7e8hD3k0Ga9B8gpL89Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:52:12.339107Z"},"content_sha256":"9207c64e88c264bfd5a2a5746a936e56f5a38f4ab19d6bedd81ff89d2d9b9747","schema_version":"1.0","event_id":"sha256:9207c64e88c264bfd5a2a5746a936e56f5a38f4ab19d6bedd81ff89d2d9b9747"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:D3EGNXCCKRBG7UO5XLPKTPTR67","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gaussian pulse dynamics in gain media with Kerr nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Christian Jirauschek, Franz X. K\\\"artner","submitted_at":"2011-03-14T14:09:34Z","abstract_excerpt":"Using the Kantorovitch method in combination with a Gaussian ansatz, we derive the equations of motion for spatial, temporal and spatiotemporal optical propagation in a dispersive Kerr medium with a general transverse and spectral gain profile. By rewriting the variational equations as differential equations for the temporal and spatial Gaussian q parameters, optical ABCD matrices for the Kerr effect, a general transverse gain profile and nonparabolic spectral gain filtering are obtained. Further effects can easily be taken into account by adding the corresponding ABCD matrices. Applications i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2672","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":"2026-05-18T04:26:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"onlFXxqoSBy9ZYsKUE2Cm7aox6Gb3uU0nPWp+UiLAk2AGffTSCdmokWeifssGKBMeU9S3+5AoTqI9lrAvd2dDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:52:12.339571Z"},"content_sha256":"c89c00cfd3d8fee1b7e519b9b0fbb7bfedcb67c1525701d2ba5466b55582d865","schema_version":"1.0","event_id":"sha256:c89c00cfd3d8fee1b7e519b9b0fbb7bfedcb67c1525701d2ba5466b55582d865"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67/bundle.json","state_url":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D3EGNXCCKRBG7UO5XLPKTPTR67/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":"2026-05-29T17:52:12Z","links":{"resolver":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67","bundle":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67/bundle.json","state":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D3EGNXCCKRBG7UO5XLPKTPTR67/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:D3EGNXCCKRBG7UO5XLPKTPTR67","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":"49af77091abb353a14a16ad1df86b674bd34f6a7a4a8322617b8a342e4c3a271","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-03-14T14:09:34Z","title_canon_sha256":"6f608b8538192b393d942146f9cc39dcf0b849bcf2d6968f6e8f58f384f247df"},"schema_version":"1.0","source":{"id":"1103.2672","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2672","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2672v1","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2672","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"pith_short_12","alias_value":"D3EGNXCCKRBG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"D3EGNXCCKRBG7UO5","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"D3EGNXCC","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:c89c00cfd3d8fee1b7e519b9b0fbb7bfedcb67c1525701d2ba5466b55582d865","target":"graph","created_at":"2026-05-18T04:26:54Z","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":"Using the Kantorovitch method in combination with a Gaussian ansatz, we derive the equations of motion for spatial, temporal and spatiotemporal optical propagation in a dispersive Kerr medium with a general transverse and spectral gain profile. By rewriting the variational equations as differential equations for the temporal and spatial Gaussian q parameters, optical ABCD matrices for the Kerr effect, a general transverse gain profile and nonparabolic spectral gain filtering are obtained. Further effects can easily be taken into account by adding the corresponding ABCD matrices. Applications i","authors_text":"Christian Jirauschek, Franz X. K\\\"artner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-03-14T14:09:34Z","title":"Gaussian pulse dynamics in gain media with Kerr nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2672","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":"sha256:9207c64e88c264bfd5a2a5746a936e56f5a38f4ab19d6bedd81ff89d2d9b9747","target":"record","created_at":"2026-05-18T04:26:54Z","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":"49af77091abb353a14a16ad1df86b674bd34f6a7a4a8322617b8a342e4c3a271","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-03-14T14:09:34Z","title_canon_sha256":"6f608b8538192b393d942146f9cc39dcf0b849bcf2d6968f6e8f58f384f247df"},"schema_version":"1.0","source":{"id":"1103.2672","kind":"arxiv","version":1}},"canonical_sha256":"1ec866dc4254426fd1ddbadea9be71f7de933d7315bd0c837385b6f5a9a48f9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ec866dc4254426fd1ddbadea9be71f7de933d7315bd0c837385b6f5a9a48f9e","first_computed_at":"2026-05-18T04:26:54.390844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:54.390844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zM+T+eYipy3jUdtX2FMh5NwPrHHUjNx3TXfMHHakdFPq7zbMP+vvG5mZsW6H2DOJ/CvIqEF0rYh6K0qWe86BDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:54.391524Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2672","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9207c64e88c264bfd5a2a5746a936e56f5a38f4ab19d6bedd81ff89d2d9b9747","sha256:c89c00cfd3d8fee1b7e519b9b0fbb7bfedcb67c1525701d2ba5466b55582d865"],"state_sha256":"388097450577d18474c6ed0f7b2ce74e15fcf220f4139d59c590e50988f337e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dBsove7hThVhJLc7YGcrRDm5uxUgKiAp2lli3M8V9GhIDvMWTvt+qcq6qYaKWnn8Z5k4blHiohInA9AkCWGzAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:52:12.343215Z","bundle_sha256":"0b03b8182c5c9319d43bc0d0cdc22d40a24fdf9b3d57619941109a5a1a9a7de4"}}