{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:32L7NDHRX2IMBFLTN76LY5ZP3H","short_pith_number":"pith:32L7NDHR","canonical_record":{"source":{"id":"2605.21091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2026-05-20T12:22:55Z","cross_cats_sorted":[],"title_canon_sha256":"b3889d472ef08a11abb5d7c87f5ca32d316e1fc241b33844a936c382dda323bb","abstract_canon_sha256":"362ad9fcb336304e45d593bec7b2319330edfc808c793ec514a4392ff38d5ce9"},"schema_version":"1.0"},"canonical_sha256":"de97f68cf1be90c095736ffcbc772fd9c4e7c724a9921c5962140ed153b2f03e","source":{"kind":"arxiv","id":"2605.21091","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.21091","created_at":"2026-05-21T01:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"2605.21091v1","created_at":"2026-05-21T01:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21091","created_at":"2026-05-21T01:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"32L7NDHRX2IM","created_at":"2026-05-21T01:05:36Z"},{"alias_kind":"pith_short_16","alias_value":"32L7NDHRX2IMBFLT","created_at":"2026-05-21T01:05:36Z"},{"alias_kind":"pith_short_8","alias_value":"32L7NDHR","created_at":"2026-05-21T01:05:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:32L7NDHRX2IMBFLTN76LY5ZP3H","target":"record","payload":{"canonical_record":{"source":{"id":"2605.21091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2026-05-20T12:22:55Z","cross_cats_sorted":[],"title_canon_sha256":"b3889d472ef08a11abb5d7c87f5ca32d316e1fc241b33844a936c382dda323bb","abstract_canon_sha256":"362ad9fcb336304e45d593bec7b2319330edfc808c793ec514a4392ff38d5ce9"},"schema_version":"1.0"},"canonical_sha256":"de97f68cf1be90c095736ffcbc772fd9c4e7c724a9921c5962140ed153b2f03e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:36.681520Z","signature_b64":"ha6U5w1RVixJChJ5j3qkrCjx7HaRjLaCHzc44qiq8uhFdLDRXQywydZN3WoXLek7NpXeNcxCjzrCFxqJ7KcADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de97f68cf1be90c095736ffcbc772fd9c4e7c724a9921c5962140ed153b2f03e","last_reissued_at":"2026-05-21T01:05:36.680907Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:36.680907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.21091","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":"2026-05-21T01:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5x7PVu/AmVxRmiePrY/mGpIiC+d2q0VDFkC/8jw/ygeFo6rH963HBPefPwCajcGws4FVpOx5oSs84bqE5pkZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:39:04.404682Z"},"content_sha256":"8ed09b88958ce4c93b284e09af75031fd144288103ea52e3f35e1ea728107546","schema_version":"1.0","event_id":"sha256:8ed09b88958ce4c93b284e09af75031fd144288103ea52e3f35e1ea728107546"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:32L7NDHRX2IMBFLTN76LY5ZP3H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large-space and Large-time Asymptotics for the Focusing Nonlinear Schr\\\"{o}dinger Soliton Gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Dedi Yan, Wei Jiao, Xianguo Geng","submitted_at":"2026-05-20T12:22:55Z","abstract_excerpt":"We investigate the large-space and large-time asymptotic behavior of a soliton gas for the focusing nonlinear Schr\\\"odinger equation. The soliton gas is constructed as the continuum limit of pure $N$-soliton solutions as $N\\to\\infty$, with the discrete spectrum confined to two segments $\\Sigma_1$ and $\\Sigma_2$. In particular, our framework does not require the discrete spectrum to be confined to the imaginary axis. By combining the nonlinear steepest descent method with an appropriate $g$-function mechanism, we show that, as $x\\to-\\infty$, the soliton gas is asymptotically described by a fini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21091","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/2605.21091/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":"2026-05-21T01:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e8w/+M2e0PFCPE6XCUwWJZwq1O+7VhVAbD1N5yWd+0nyLGsAOj2HKmLKZ72CytXrN9GZAjHs7sEdjCRhppjKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:39:04.405228Z"},"content_sha256":"9dfeb19de9fd6861c12fec3c1e7f7467afb0aa284ec2df231572e26f18255757","schema_version":"1.0","event_id":"sha256:9dfeb19de9fd6861c12fec3c1e7f7467afb0aa284ec2df231572e26f18255757"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/32L7NDHRX2IMBFLTN76LY5ZP3H/bundle.json","state_url":"https://pith.science/pith/32L7NDHRX2IMBFLTN76LY5ZP3H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/32L7NDHRX2IMBFLTN76LY5ZP3H/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":"2026-05-26T05:39:04Z","links":{"resolver":"https://pith.science/pith/32L7NDHRX2IMBFLTN76LY5ZP3H","bundle":"https://pith.science/pith/32L7NDHRX2IMBFLTN76LY5ZP3H/bundle.json","state":"https://pith.science/pith/32L7NDHRX2IMBFLTN76LY5ZP3H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/32L7NDHRX2IMBFLTN76LY5ZP3H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:32L7NDHRX2IMBFLTN76LY5ZP3H","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":"362ad9fcb336304e45d593bec7b2319330edfc808c793ec514a4392ff38d5ce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2026-05-20T12:22:55Z","title_canon_sha256":"b3889d472ef08a11abb5d7c87f5ca32d316e1fc241b33844a936c382dda323bb"},"schema_version":"1.0","source":{"id":"2605.21091","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.21091","created_at":"2026-05-21T01:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"2605.21091v1","created_at":"2026-05-21T01:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21091","created_at":"2026-05-21T01:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"32L7NDHRX2IM","created_at":"2026-05-21T01:05:36Z"},{"alias_kind":"pith_short_16","alias_value":"32L7NDHRX2IMBFLT","created_at":"2026-05-21T01:05:36Z"},{"alias_kind":"pith_short_8","alias_value":"32L7NDHR","created_at":"2026-05-21T01:05:36Z"}],"graph_snapshots":[{"event_id":"sha256:9dfeb19de9fd6861c12fec3c1e7f7467afb0aa284ec2df231572e26f18255757","target":"graph","created_at":"2026-05-21T01:05:36Z","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/2605.21091/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the large-space and large-time asymptotic behavior of a soliton gas for the focusing nonlinear Schr\\\"odinger equation. The soliton gas is constructed as the continuum limit of pure $N$-soliton solutions as $N\\to\\infty$, with the discrete spectrum confined to two segments $\\Sigma_1$ and $\\Sigma_2$. In particular, our framework does not require the discrete spectrum to be confined to the imaginary axis. By combining the nonlinear steepest descent method with an appropriate $g$-function mechanism, we show that, as $x\\to-\\infty$, the soliton gas is asymptotically described by a fini","authors_text":"Dedi Yan, Wei Jiao, Xianguo Geng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2026-05-20T12:22:55Z","title":"Large-space and Large-time Asymptotics for the Focusing Nonlinear Schr\\\"{o}dinger Soliton Gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21091","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":"sha256:8ed09b88958ce4c93b284e09af75031fd144288103ea52e3f35e1ea728107546","target":"record","created_at":"2026-05-21T01:05:36Z","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":"362ad9fcb336304e45d593bec7b2319330edfc808c793ec514a4392ff38d5ce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2026-05-20T12:22:55Z","title_canon_sha256":"b3889d472ef08a11abb5d7c87f5ca32d316e1fc241b33844a936c382dda323bb"},"schema_version":"1.0","source":{"id":"2605.21091","kind":"arxiv","version":1}},"canonical_sha256":"de97f68cf1be90c095736ffcbc772fd9c4e7c724a9921c5962140ed153b2f03e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de97f68cf1be90c095736ffcbc772fd9c4e7c724a9921c5962140ed153b2f03e","first_computed_at":"2026-05-21T01:05:36.680907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:36.680907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ha6U5w1RVixJChJ5j3qkrCjx7HaRjLaCHzc44qiq8uhFdLDRXQywydZN3WoXLek7NpXeNcxCjzrCFxqJ7KcADg==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:36.681520Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.21091","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ed09b88958ce4c93b284e09af75031fd144288103ea52e3f35e1ea728107546","sha256:9dfeb19de9fd6861c12fec3c1e7f7467afb0aa284ec2df231572e26f18255757"],"state_sha256":"edf04c900343df254223b29f1614ac8ba98500810a98ffa0705e14865608ed08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bEQ/nNCriwJTiFmUPbPwAzAieDRFngk8BIq6FpID/zWOXPQjldebLfxhZzq7p7V0ha8ploeCBNNpEKC0v7QhDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T05:39:04.408595Z","bundle_sha256":"ed70526c81cd270cb947103923ea242682d0abbd3f417964b43f36b4a777c85b"}}