{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:JUHAJK3CJQEMAHC2MHXAJR5FNY","short_pith_number":"pith:JUHAJK3C","canonical_record":{"source":{"id":"2209.14641","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2022-09-29T09:04:04Z","cross_cats_sorted":["physics.optics"],"title_canon_sha256":"9bfa0f06ce79482008e889a9ed851cbf063e896a697e5b4bf920b1e16b55eb4c","abstract_canon_sha256":"052a88c35bad102b1a153483b46c1d6316f907ff91e4e7f0caba584e11519c76"},"schema_version":"1.0"},"canonical_sha256":"4d0e04ab624c08c01c5a61ee04c7a56e169abc45081f52e995002f7825dff560","source":{"kind":"arxiv","id":"2209.14641","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.14641","created_at":"2026-07-05T05:02:04Z"},{"alias_kind":"arxiv_version","alias_value":"2209.14641v1","created_at":"2026-07-05T05:02:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.14641","created_at":"2026-07-05T05:02:04Z"},{"alias_kind":"pith_short_12","alias_value":"JUHAJK3CJQEM","created_at":"2026-07-05T05:02:04Z"},{"alias_kind":"pith_short_16","alias_value":"JUHAJK3CJQEMAHC2","created_at":"2026-07-05T05:02:04Z"},{"alias_kind":"pith_short_8","alias_value":"JUHAJK3C","created_at":"2026-07-05T05:02:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:JUHAJK3CJQEMAHC2MHXAJR5FNY","target":"record","payload":{"canonical_record":{"source":{"id":"2209.14641","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2022-09-29T09:04:04Z","cross_cats_sorted":["physics.optics"],"title_canon_sha256":"9bfa0f06ce79482008e889a9ed851cbf063e896a697e5b4bf920b1e16b55eb4c","abstract_canon_sha256":"052a88c35bad102b1a153483b46c1d6316f907ff91e4e7f0caba584e11519c76"},"schema_version":"1.0"},"canonical_sha256":"4d0e04ab624c08c01c5a61ee04c7a56e169abc45081f52e995002f7825dff560","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:02:04.172440Z","signature_b64":"zwIKKcR2f5GQSqUM48/pH26sym5Pfe0zSmsN0hizMnxuGyakMUJHUFpwHNKRAMwJrPGiup89PZnjwx6KhSteDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d0e04ab624c08c01c5a61ee04c7a56e169abc45081f52e995002f7825dff560","last_reissued_at":"2026-07-05T05:02:04.172017Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:02:04.172017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.14641","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":"2026-07-05T05:02:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tVPr0WYmmSdOfHItCkF86gSDf0p85o/rInInCzcfyhH6StkZCRBIfc3uG0ZCiC3MkJctjBdt0Aws9CFCYlbHBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:56:36.333225Z"},"content_sha256":"005bce430529f2698276f9e351f1c073c23566e8b765e879fe38d73520e582db","schema_version":"1.0","event_id":"sha256:005bce430529f2698276f9e351f1c073c23566e8b765e879fe38d73520e582db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:JUHAJK3CJQEMAHC2MHXAJR5FNY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scaling transformation of the multimode nonlinear Schr\\\"odinger equation for physics-informed neural networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.optics"],"primary_cat":"cs.NE","authors_text":"Dmitry Efremenko, Ivan Chuprov, Jiexing Gao, Pavel Anisimov, Viacheslav Zemlyakov","submitted_at":"2022-09-29T09:04:04Z","abstract_excerpt":"Single-mode optical fibers (SMFs) have become the backbone of modern communication systems. However, their throughput is expected to reach its theoretical limit in the nearest future. Utilization of multimode fibers (MMFs) is considered as one of the most promising solutions rectifying this capacity crunch. Nevertheless, differential equations describing light propagation in MMFs are a way more sophisticated than those for SMFs, which makes numerical modelling of MMF-based systems computationally demanding and impractical for the most part of realistic scenarios. Physics-informed neural networ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.14641","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.14641/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:02:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BJJsRRUof/H8oy9k0MrL7qZJdCJxVehz1MRlWSg4hkZzwxqAuZm85DTdK/a0qB2cZ/JZQIsyyJocebvAvAguAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:56:36.334131Z"},"content_sha256":"f59164a8a095c1329379fcab7fdf376319109854272f313efdabcc568723498e","schema_version":"1.0","event_id":"sha256:f59164a8a095c1329379fcab7fdf376319109854272f313efdabcc568723498e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JUHAJK3CJQEMAHC2MHXAJR5FNY/bundle.json","state_url":"https://pith.science/pith/JUHAJK3CJQEMAHC2MHXAJR5FNY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JUHAJK3CJQEMAHC2MHXAJR5FNY/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":"2026-08-04T12:56:36Z","links":{"resolver":"https://pith.science/pith/JUHAJK3CJQEMAHC2MHXAJR5FNY","bundle":"https://pith.science/pith/JUHAJK3CJQEMAHC2MHXAJR5FNY/bundle.json","state":"https://pith.science/pith/JUHAJK3CJQEMAHC2MHXAJR5FNY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JUHAJK3CJQEMAHC2MHXAJR5FNY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:JUHAJK3CJQEMAHC2MHXAJR5FNY","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":"052a88c35bad102b1a153483b46c1d6316f907ff91e4e7f0caba584e11519c76","cross_cats_sorted":["physics.optics"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2022-09-29T09:04:04Z","title_canon_sha256":"9bfa0f06ce79482008e889a9ed851cbf063e896a697e5b4bf920b1e16b55eb4c"},"schema_version":"1.0","source":{"id":"2209.14641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.14641","created_at":"2026-07-05T05:02:04Z"},{"alias_kind":"arxiv_version","alias_value":"2209.14641v1","created_at":"2026-07-05T05:02:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.14641","created_at":"2026-07-05T05:02:04Z"},{"alias_kind":"pith_short_12","alias_value":"JUHAJK3CJQEM","created_at":"2026-07-05T05:02:04Z"},{"alias_kind":"pith_short_16","alias_value":"JUHAJK3CJQEMAHC2","created_at":"2026-07-05T05:02:04Z"},{"alias_kind":"pith_short_8","alias_value":"JUHAJK3C","created_at":"2026-07-05T05:02:04Z"}],"graph_snapshots":[{"event_id":"sha256:f59164a8a095c1329379fcab7fdf376319109854272f313efdabcc568723498e","target":"graph","created_at":"2026-07-05T05:02:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.14641/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Single-mode optical fibers (SMFs) have become the backbone of modern communication systems. However, their throughput is expected to reach its theoretical limit in the nearest future. Utilization of multimode fibers (MMFs) is considered as one of the most promising solutions rectifying this capacity crunch. Nevertheless, differential equations describing light propagation in MMFs are a way more sophisticated than those for SMFs, which makes numerical modelling of MMF-based systems computationally demanding and impractical for the most part of realistic scenarios. Physics-informed neural networ","authors_text":"Dmitry Efremenko, Ivan Chuprov, Jiexing Gao, Pavel Anisimov, Viacheslav Zemlyakov","cross_cats":["physics.optics"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2022-09-29T09:04:04Z","title":"Scaling transformation of the multimode nonlinear Schr\\\"odinger equation for physics-informed neural networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.14641","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":"sha256:005bce430529f2698276f9e351f1c073c23566e8b765e879fe38d73520e582db","target":"record","created_at":"2026-07-05T05:02:04Z","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":"052a88c35bad102b1a153483b46c1d6316f907ff91e4e7f0caba584e11519c76","cross_cats_sorted":["physics.optics"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2022-09-29T09:04:04Z","title_canon_sha256":"9bfa0f06ce79482008e889a9ed851cbf063e896a697e5b4bf920b1e16b55eb4c"},"schema_version":"1.0","source":{"id":"2209.14641","kind":"arxiv","version":1}},"canonical_sha256":"4d0e04ab624c08c01c5a61ee04c7a56e169abc45081f52e995002f7825dff560","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d0e04ab624c08c01c5a61ee04c7a56e169abc45081f52e995002f7825dff560","first_computed_at":"2026-07-05T05:02:04.172017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:02:04.172017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zwIKKcR2f5GQSqUM48/pH26sym5Pfe0zSmsN0hizMnxuGyakMUJHUFpwHNKRAMwJrPGiup89PZnjwx6KhSteDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:02:04.172440Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.14641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:005bce430529f2698276f9e351f1c073c23566e8b765e879fe38d73520e582db","sha256:f59164a8a095c1329379fcab7fdf376319109854272f313efdabcc568723498e"],"state_sha256":"098f3e9f823f7cd174fa2c0fe9f4a74c56ef948c542496e8f84aeeecefcc047c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1usLDbwT9BvtEtJnBtBX8TH5pR55hXgYZvcw14Y45EJTZq5K/kMcYW40ebkOt1mm6MGrmp9zwJf6PshDMESVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T12:56:36.415700Z","bundle_sha256":"b77d506487f7c759fc7008174cce7ff24f21fc0b346e684e005dacf59f306f1d"}}