{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:LTGGTHL2BNEKKEZICVRPXA2UTM","short_pith_number":"pith:LTGGTHL2","canonical_record":{"source":{"id":"nlin/0207026","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.PS","submitted_at":"2002-07-12T21:07:56Z","cross_cats_sorted":[],"title_canon_sha256":"e669093fb39ae78ae228329ea5b6a396b6db926310fa9eb12f774966f91f9b95","abstract_canon_sha256":"8531cb008ab9d3cae3b1a3b08a1193a38a406b0454b2169457a74b8196c4d92d"},"schema_version":"1.0"},"canonical_sha256":"5ccc699d7a0b48a513281562fb83549b065f35a98fadec76c628595a6f09bd53","source":{"kind":"arxiv","id":"nlin/0207026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0207026","created_at":"2026-05-18T01:38:19Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0207026v1","created_at":"2026-05-18T01:38:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0207026","created_at":"2026-05-18T01:38:19Z"},{"alias_kind":"pith_short_12","alias_value":"LTGGTHL2BNEK","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"LTGGTHL2BNEKKEZI","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"LTGGTHL2","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:LTGGTHL2BNEKKEZICVRPXA2UTM","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0207026","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.PS","submitted_at":"2002-07-12T21:07:56Z","cross_cats_sorted":[],"title_canon_sha256":"e669093fb39ae78ae228329ea5b6a396b6db926310fa9eb12f774966f91f9b95","abstract_canon_sha256":"8531cb008ab9d3cae3b1a3b08a1193a38a406b0454b2169457a74b8196c4d92d"},"schema_version":"1.0"},"canonical_sha256":"5ccc699d7a0b48a513281562fb83549b065f35a98fadec76c628595a6f09bd53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:19.769214Z","signature_b64":"64EtDKz4yTe+3jrmgmdk63wf0NEFcDgTYI5Ixy+w8uYVg/fSGAXmUudoP3VPUtlW1Jlwd4ENZ7jwGpgVgQl5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ccc699d7a0b48a513281562fb83549b065f35a98fadec76c628595a6f09bd53","last_reissued_at":"2026-05-18T01:38:19.768630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:19.768630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0207026","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":"2026-05-18T01:38:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MIVknmsphMm49uuBtS+rwDT3gnLWkddt5aKohDJyM86g5fxTFgZJcRj/G8b3YmyTvP3hCRhgeh7JbWCjl8JoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:11:28.860992Z"},"content_sha256":"75b898fa84dbf890ae3c016e2a9b90d45ade033d67896a6614000104d171fb6f","schema_version":"1.0","event_id":"sha256:75b898fa84dbf890ae3c016e2a9b90d45ade033d67896a6614000104d171fb6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:LTGGTHL2BNEKKEZICVRPXA2UTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equilibrium and nonequilibrium solitons in a lossy split-step system with lumped amplification","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Boris Malomed (Dept. of Interdisciplinary Studies, Faculty of Engineering, Israel), Rodislav Driben, Tel Aviv, Tel Aviv University","submitted_at":"2002-07-12T21:07:56Z","abstract_excerpt":"We propose a more realistic version of the recently introduced split-step model (SSM), which consists of periodically alternating dispersive and nonlinear segments, by adding uniformly distributed loss and lumped gain to it. In the case when the loss is exactly balanced by gain, a family of stable equilibrium solitons (ESs) is found. Unless the system's period L is very small, saturation is observed in the dependence of the amplitude of the established ES vs. that of the initial pulse. Stable nonequilibrium solitons (NESs) are found in the case when the gain slightly exceeds (by up to 3%) the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0207026","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":"2026-05-18T01:38:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wu6woCyzN7u1AYXKABLQB8ykz02wlsLSy1xMG8M5F2/oAxNHZaDatYN4ECrmq24/CjIzTRcHXAgDS8WIFgT3CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:11:28.861353Z"},"content_sha256":"0547a7ccff12de0322ca24621d094b2cf535ee5bde1aeb01bf64cc91c795d0a0","schema_version":"1.0","event_id":"sha256:0547a7ccff12de0322ca24621d094b2cf535ee5bde1aeb01bf64cc91c795d0a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LTGGTHL2BNEKKEZICVRPXA2UTM/bundle.json","state_url":"https://pith.science/pith/LTGGTHL2BNEKKEZICVRPXA2UTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LTGGTHL2BNEKKEZICVRPXA2UTM/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":"2026-06-03T08:11:28Z","links":{"resolver":"https://pith.science/pith/LTGGTHL2BNEKKEZICVRPXA2UTM","bundle":"https://pith.science/pith/LTGGTHL2BNEKKEZICVRPXA2UTM/bundle.json","state":"https://pith.science/pith/LTGGTHL2BNEKKEZICVRPXA2UTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LTGGTHL2BNEKKEZICVRPXA2UTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:LTGGTHL2BNEKKEZICVRPXA2UTM","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":"8531cb008ab9d3cae3b1a3b08a1193a38a406b0454b2169457a74b8196c4d92d","cross_cats_sorted":[],"license":"","primary_cat":"nlin.PS","submitted_at":"2002-07-12T21:07:56Z","title_canon_sha256":"e669093fb39ae78ae228329ea5b6a396b6db926310fa9eb12f774966f91f9b95"},"schema_version":"1.0","source":{"id":"nlin/0207026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0207026","created_at":"2026-05-18T01:38:19Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0207026v1","created_at":"2026-05-18T01:38:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0207026","created_at":"2026-05-18T01:38:19Z"},{"alias_kind":"pith_short_12","alias_value":"LTGGTHL2BNEK","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"LTGGTHL2BNEKKEZI","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"LTGGTHL2","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:0547a7ccff12de0322ca24621d094b2cf535ee5bde1aeb01bf64cc91c795d0a0","target":"graph","created_at":"2026-05-18T01:38:19Z","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 propose a more realistic version of the recently introduced split-step model (SSM), which consists of periodically alternating dispersive and nonlinear segments, by adding uniformly distributed loss and lumped gain to it. In the case when the loss is exactly balanced by gain, a family of stable equilibrium solitons (ESs) is found. Unless the system's period L is very small, saturation is observed in the dependence of the amplitude of the established ES vs. that of the initial pulse. Stable nonequilibrium solitons (NESs) are found in the case when the gain slightly exceeds (by up to 3%) the ","authors_text":"Boris Malomed (Dept. of Interdisciplinary Studies, Faculty of Engineering, Israel), Rodislav Driben, Tel Aviv, Tel Aviv University","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.PS","submitted_at":"2002-07-12T21:07:56Z","title":"Equilibrium and nonequilibrium solitons in a lossy split-step system with lumped amplification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0207026","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":"sha256:75b898fa84dbf890ae3c016e2a9b90d45ade033d67896a6614000104d171fb6f","target":"record","created_at":"2026-05-18T01:38:19Z","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":"8531cb008ab9d3cae3b1a3b08a1193a38a406b0454b2169457a74b8196c4d92d","cross_cats_sorted":[],"license":"","primary_cat":"nlin.PS","submitted_at":"2002-07-12T21:07:56Z","title_canon_sha256":"e669093fb39ae78ae228329ea5b6a396b6db926310fa9eb12f774966f91f9b95"},"schema_version":"1.0","source":{"id":"nlin/0207026","kind":"arxiv","version":1}},"canonical_sha256":"5ccc699d7a0b48a513281562fb83549b065f35a98fadec76c628595a6f09bd53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ccc699d7a0b48a513281562fb83549b065f35a98fadec76c628595a6f09bd53","first_computed_at":"2026-05-18T01:38:19.768630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:19.768630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"64EtDKz4yTe+3jrmgmdk63wf0NEFcDgTYI5Ixy+w8uYVg/fSGAXmUudoP3VPUtlW1Jlwd4ENZ7jwGpgVgQl5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:19.769214Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0207026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75b898fa84dbf890ae3c016e2a9b90d45ade033d67896a6614000104d171fb6f","sha256:0547a7ccff12de0322ca24621d094b2cf535ee5bde1aeb01bf64cc91c795d0a0"],"state_sha256":"9b832c64cfd27742bff53f7966e9a0f61ea7c3225a7fa93051d44e9f1b11b473"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pdqbmM56G9L8Aev6SlEtMOQWCitTSKCxajQDSt4XsIcrGyZVSMP1WMBY4qep/Rds8QTGurXwK0T0f/v3VMv5CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:11:28.863293Z","bundle_sha256":"b107a3f68944c8e249d380c68ad01323f788939d4f35568a1e1aa5bf7f7101bb"}}