{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:W3A57MGTYX5UFZJU4UUFX3SL7N","short_pith_number":"pith:W3A57MGT","canonical_record":{"source":{"id":"1501.01566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2015-01-07T17:22:42Z","cross_cats_sorted":["physics.optics"],"title_canon_sha256":"aa9c5cc656c0db23420f8105bea00c4a1187c017c5d4dd2a61e91d58ec391cf0","abstract_canon_sha256":"5e5200a5a63247f0f2d12a628ac27f99a34054f449f45ea2aa05afef441633e7"},"schema_version":"1.0"},"canonical_sha256":"b6c1dfb0d3c5fb42e534e5285bee4bfb735fd495c863f927ede27fec83d7dd55","source":{"kind":"arxiv","id":"1501.01566","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01566","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01566v1","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01566","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"W3A57MGTYX5U","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W3A57MGTYX5UFZJU","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W3A57MGT","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:W3A57MGTYX5UFZJU4UUFX3SL7N","target":"record","payload":{"canonical_record":{"source":{"id":"1501.01566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2015-01-07T17:22:42Z","cross_cats_sorted":["physics.optics"],"title_canon_sha256":"aa9c5cc656c0db23420f8105bea00c4a1187c017c5d4dd2a61e91d58ec391cf0","abstract_canon_sha256":"5e5200a5a63247f0f2d12a628ac27f99a34054f449f45ea2aa05afef441633e7"},"schema_version":"1.0"},"canonical_sha256":"b6c1dfb0d3c5fb42e534e5285bee4bfb735fd495c863f927ede27fec83d7dd55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:53.764313Z","signature_b64":"9UWzR9R0dELOmcLTKhGDTKBsQVlq8dTzi9CmiVXtEDN+iTPvr/DFJsn9ZPQAarESc0rjkZ3GU1YCK3Ja+NUoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6c1dfb0d3c5fb42e534e5285bee4bfb735fd495c863f927ede27fec83d7dd55","last_reissued_at":"2026-05-18T02:29:53.763650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:53.763650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.01566","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":"2026-05-18T02:29:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N/o3THsjw+Buly92Ed/n/X+fGBmW5n3L0H9IVpUefSFCDhVZ4wyY7+o/2/p33BZ+PY8yQQ2MHhYuoq6rxNz5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:20:11.533040Z"},"content_sha256":"7869952a03c9858bc931a19016d83b3f65c12eb35e9f83b387a9c54daef12479","schema_version":"1.0","event_id":"sha256:7869952a03c9858bc931a19016d83b3f65c12eb35e9f83b387a9c54daef12479"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:W3A57MGTYX5UFZJU4UUFX3SL7N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modulational instability windows in the nonlinear Schr\\\"odinger equation involving higher-order Kerr responses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.optics"],"primary_cat":"nlin.PS","authors_text":"Daniele Tommasini, David Novoa, Jos\\'e A. N\\'ovoa-L\\'opez","submitted_at":"2015-01-07T17:22:42Z","abstract_excerpt":"We introduce a complete analytical and numerical study of the modulational instability process in a system governed by a canonical nonlinear Schr\\\"odinger equation involving local, arbitrary nonlinear responses to the applied field. In particular, our theory accounts for the recently proposed higher-order Kerr nonlinearities, providing very simple analytical criteria for the identification of multiple regimes of stability and instability of plane-wave solutions in such systems. Moreover, we discuss a new parametric regime in the higher-order Kerr response which allows for the observation of se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01566","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":"2026-05-18T02:29:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQOurtBYkekLx0JNHOs05GI6b/fMY8d3jELewzivQ5gBFW6KVAVmbQ9C7zRL+AtPHyHoYcSrgoDhPDosTDx/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:20:11.533638Z"},"content_sha256":"625199eff8342f6296a8c8d07ad5437e3e3a8ade4c205c97cfa363b0f8cce523","schema_version":"1.0","event_id":"sha256:625199eff8342f6296a8c8d07ad5437e3e3a8ade4c205c97cfa363b0f8cce523"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W3A57MGTYX5UFZJU4UUFX3SL7N/bundle.json","state_url":"https://pith.science/pith/W3A57MGTYX5UFZJU4UUFX3SL7N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W3A57MGTYX5UFZJU4UUFX3SL7N/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":"2026-06-06T22:20:11Z","links":{"resolver":"https://pith.science/pith/W3A57MGTYX5UFZJU4UUFX3SL7N","bundle":"https://pith.science/pith/W3A57MGTYX5UFZJU4UUFX3SL7N/bundle.json","state":"https://pith.science/pith/W3A57MGTYX5UFZJU4UUFX3SL7N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W3A57MGTYX5UFZJU4UUFX3SL7N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:W3A57MGTYX5UFZJU4UUFX3SL7N","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":"5e5200a5a63247f0f2d12a628ac27f99a34054f449f45ea2aa05afef441633e7","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2015-01-07T17:22:42Z","title_canon_sha256":"aa9c5cc656c0db23420f8105bea00c4a1187c017c5d4dd2a61e91d58ec391cf0"},"schema_version":"1.0","source":{"id":"1501.01566","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01566","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01566v1","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01566","created_at":"2026-05-18T02:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"W3A57MGTYX5U","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W3A57MGTYX5UFZJU","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W3A57MGT","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:625199eff8342f6296a8c8d07ad5437e3e3a8ade4c205c97cfa363b0f8cce523","target":"graph","created_at":"2026-05-18T02:29:53Z","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 introduce a complete analytical and numerical study of the modulational instability process in a system governed by a canonical nonlinear Schr\\\"odinger equation involving local, arbitrary nonlinear responses to the applied field. In particular, our theory accounts for the recently proposed higher-order Kerr nonlinearities, providing very simple analytical criteria for the identification of multiple regimes of stability and instability of plane-wave solutions in such systems. Moreover, we discuss a new parametric regime in the higher-order Kerr response which allows for the observation of se","authors_text":"Daniele Tommasini, David Novoa, Jos\\'e A. N\\'ovoa-L\\'opez","cross_cats":["physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2015-01-07T17:22:42Z","title":"Modulational instability windows in the nonlinear Schr\\\"odinger equation involving higher-order Kerr responses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01566","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":"sha256:7869952a03c9858bc931a19016d83b3f65c12eb35e9f83b387a9c54daef12479","target":"record","created_at":"2026-05-18T02:29:53Z","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":"5e5200a5a63247f0f2d12a628ac27f99a34054f449f45ea2aa05afef441633e7","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2015-01-07T17:22:42Z","title_canon_sha256":"aa9c5cc656c0db23420f8105bea00c4a1187c017c5d4dd2a61e91d58ec391cf0"},"schema_version":"1.0","source":{"id":"1501.01566","kind":"arxiv","version":1}},"canonical_sha256":"b6c1dfb0d3c5fb42e534e5285bee4bfb735fd495c863f927ede27fec83d7dd55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6c1dfb0d3c5fb42e534e5285bee4bfb735fd495c863f927ede27fec83d7dd55","first_computed_at":"2026-05-18T02:29:53.763650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:53.763650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9UWzR9R0dELOmcLTKhGDTKBsQVlq8dTzi9CmiVXtEDN+iTPvr/DFJsn9ZPQAarESc0rjkZ3GU1YCK3Ja+NUoBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:53.764313Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01566","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7869952a03c9858bc931a19016d83b3f65c12eb35e9f83b387a9c54daef12479","sha256:625199eff8342f6296a8c8d07ad5437e3e3a8ade4c205c97cfa363b0f8cce523"],"state_sha256":"9ea2a55203e0279c289dc2f35b5514e67328e40b12e5eac8c2c08a7ad70706fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Urvl0OFfaDGm5xriDkJYXE1rWGL/QUJ8EuPNaPrsb8Z7XzsEtrgjjBlH4Btt4Z1Y5IMpcKk7ZG8d37BxfQDCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T22:20:11.537464Z","bundle_sha256":"c9eb84b40caca3136a9aa0a2b9fd9763bd77ecad9762d7eb0952576e2253cf28"}}