{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JI4F72H6PX4JX7II5RJFDSSFBC","short_pith_number":"pith:JI4F72H6","canonical_record":{"source":{"id":"2605.19934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2026-05-19T14:53:36Z","cross_cats_sorted":[],"title_canon_sha256":"083f3e8ed4591b8cee5009e6d5536e2d6fc515bdbfe2bb6fd00b60c07ee56f85","abstract_canon_sha256":"8146327ea2f6ff7d5a068892b6d83dd7a18ce7b3b54564c533013c7b77e5110b"},"schema_version":"1.0"},"canonical_sha256":"4a385fe8fe7df89bfd08ec5251ca4508ab6aaba7cb0ff116c261e8074f4cf375","source":{"kind":"arxiv","id":"2605.19934","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19934","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19934v1","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19934","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"pith_short_12","alias_value":"JI4F72H6PX4J","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"pith_short_16","alias_value":"JI4F72H6PX4JX7II","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"pith_short_8","alias_value":"JI4F72H6","created_at":"2026-05-20T02:05:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JI4F72H6PX4JX7II5RJFDSSFBC","target":"record","payload":{"canonical_record":{"source":{"id":"2605.19934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2026-05-19T14:53:36Z","cross_cats_sorted":[],"title_canon_sha256":"083f3e8ed4591b8cee5009e6d5536e2d6fc515bdbfe2bb6fd00b60c07ee56f85","abstract_canon_sha256":"8146327ea2f6ff7d5a068892b6d83dd7a18ce7b3b54564c533013c7b77e5110b"},"schema_version":"1.0"},"canonical_sha256":"4a385fe8fe7df89bfd08ec5251ca4508ab6aaba7cb0ff116c261e8074f4cf375","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T02:05:56.002362Z","signature_b64":"sAcDmIxrIQ0A3sX+3Li7ZdZJrTL/ZodhcB2KSTjfpuf8Tf21oIEabYmuWNBn1iwvDIi4XNYitwGwXTNV/SDMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a385fe8fe7df89bfd08ec5251ca4508ab6aaba7cb0ff116c261e8074f4cf375","last_reissued_at":"2026-05-20T02:05:56.001670Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T02:05:56.001670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.19934","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":"2026-05-20T02:05:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FMdyJDBfjFhCHZXLN2uczBCVmrlZTHkwjYep5y0Hao8c/WJdVet9/3S/9ZUUuKu7fq990oARxjEKWZsdjZE0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T17:25:25.685988Z"},"content_sha256":"b6a7fdbaed5f312020bbb357a81bd691bfb66971f927946958b25936351a4a2b","schema_version":"1.0","event_id":"sha256:b6a7fdbaed5f312020bbb357a81bd691bfb66971f927946958b25936351a4a2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JI4F72H6PX4JX7II5RJFDSSFBC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large-space and large-time asymptotics for the mKdV soliton gas with any odd genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Dedi Yan, Kedong Wang, Xianguo Geng","submitted_at":"2026-05-19T14:53:36Z","abstract_excerpt":"We study the large-space and large-time asymptotic behavior of the soliton gas of genus $2n-1$ for the mKdV equation with $n\\in \\mathbb{N}_+$. As $x \\to +\\infty$, we show that the large-space asymptotics of the mKdV soliton gas can be expressed with the Riemann-theta function of genus $2n-1$. For large $t$, based on the nonlinear steepest descent method and $g$-function approach, we establish a global large-time asymptotic description of the mKdV soliton gas. The half-plane $\\{(x,t):-\\infty<x<+\\infty, t>0\\}$ is divided into $2n+1$ separated regions. In each region, the large-time asymptotics o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19934","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/2605.19934/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":"2026-05-20T02:05:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gwaKGaOORoJPGx1AGi+LD7mYUtkwAWlhpryA7gMB+OnkHmziCbLr2jTbn3DGc1BMSSLv8LLo2MPG/3xV4mvkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T17:25:25.686637Z"},"content_sha256":"5469e2a991ca30525175c3f9d84796663585b8dd717e1b62b338f8aa16715da2","schema_version":"1.0","event_id":"sha256:5469e2a991ca30525175c3f9d84796663585b8dd717e1b62b338f8aa16715da2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JI4F72H6PX4JX7II5RJFDSSFBC/bundle.json","state_url":"https://pith.science/pith/JI4F72H6PX4JX7II5RJFDSSFBC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JI4F72H6PX4JX7II5RJFDSSFBC/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":"2026-05-21T17:25:25Z","links":{"resolver":"https://pith.science/pith/JI4F72H6PX4JX7II5RJFDSSFBC","bundle":"https://pith.science/pith/JI4F72H6PX4JX7II5RJFDSSFBC/bundle.json","state":"https://pith.science/pith/JI4F72H6PX4JX7II5RJFDSSFBC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JI4F72H6PX4JX7II5RJFDSSFBC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JI4F72H6PX4JX7II5RJFDSSFBC","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":"8146327ea2f6ff7d5a068892b6d83dd7a18ce7b3b54564c533013c7b77e5110b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2026-05-19T14:53:36Z","title_canon_sha256":"083f3e8ed4591b8cee5009e6d5536e2d6fc515bdbfe2bb6fd00b60c07ee56f85"},"schema_version":"1.0","source":{"id":"2605.19934","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19934","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19934v1","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19934","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"pith_short_12","alias_value":"JI4F72H6PX4J","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"pith_short_16","alias_value":"JI4F72H6PX4JX7II","created_at":"2026-05-20T02:05:56Z"},{"alias_kind":"pith_short_8","alias_value":"JI4F72H6","created_at":"2026-05-20T02:05:56Z"}],"graph_snapshots":[{"event_id":"sha256:5469e2a991ca30525175c3f9d84796663585b8dd717e1b62b338f8aa16715da2","target":"graph","created_at":"2026-05-20T02:05:56Z","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/2605.19934/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the large-space and large-time asymptotic behavior of the soliton gas of genus $2n-1$ for the mKdV equation with $n\\in \\mathbb{N}_+$. As $x \\to +\\infty$, we show that the large-space asymptotics of the mKdV soliton gas can be expressed with the Riemann-theta function of genus $2n-1$. For large $t$, based on the nonlinear steepest descent method and $g$-function approach, we establish a global large-time asymptotic description of the mKdV soliton gas. The half-plane $\\{(x,t):-\\infty<x<+\\infty, t>0\\}$ is divided into $2n+1$ separated regions. In each region, the large-time asymptotics o","authors_text":"Dedi Yan, Kedong Wang, Xianguo Geng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2026-05-19T14:53:36Z","title":"Large-space and large-time asymptotics for the mKdV soliton gas with any odd genus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19934","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:b6a7fdbaed5f312020bbb357a81bd691bfb66971f927946958b25936351a4a2b","target":"record","created_at":"2026-05-20T02:05:56Z","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":"8146327ea2f6ff7d5a068892b6d83dd7a18ce7b3b54564c533013c7b77e5110b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2026-05-19T14:53:36Z","title_canon_sha256":"083f3e8ed4591b8cee5009e6d5536e2d6fc515bdbfe2bb6fd00b60c07ee56f85"},"schema_version":"1.0","source":{"id":"2605.19934","kind":"arxiv","version":1}},"canonical_sha256":"4a385fe8fe7df89bfd08ec5251ca4508ab6aaba7cb0ff116c261e8074f4cf375","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a385fe8fe7df89bfd08ec5251ca4508ab6aaba7cb0ff116c261e8074f4cf375","first_computed_at":"2026-05-20T02:05:56.001670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T02:05:56.001670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sAcDmIxrIQ0A3sX+3Li7ZdZJrTL/ZodhcB2KSTjfpuf8Tf21oIEabYmuWNBn1iwvDIi4XNYitwGwXTNV/SDMCQ==","signature_status":"signed_v1","signed_at":"2026-05-20T02:05:56.002362Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.19934","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6a7fdbaed5f312020bbb357a81bd691bfb66971f927946958b25936351a4a2b","sha256:5469e2a991ca30525175c3f9d84796663585b8dd717e1b62b338f8aa16715da2"],"state_sha256":"62ceae2f56a71a8192bc6a529e8de61b0b74bf885ddd7a6259af5f137e555897"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BeGkmtmbcwGCB7hhO4ARVetlH3/TJ/q2E8gP2V0rg0szJRl/Wq6uDZWdm23ftiWzODbvavTsNQmVX8PQ8LXNAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T17:25:25.691145Z","bundle_sha256":"3d6ff457fba6bdb8dfe9a73d8f845c1eabde3e177579aac52d49f72e0e72e622"}}