{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZXKQLMJIHELZPLOAADGU5ALFE4","short_pith_number":"pith:ZXKQLMJI","canonical_record":{"source":{"id":"2607.07624","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T16:39:58Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"50848b59101a4fe599a3a6a36477fa52c18201a4a92f16070a31db3554a37acd","abstract_canon_sha256":"3670d4f50f9fc45543c77b9b11a5a5174373036dc1668bf9988df6f16614d4bc"},"schema_version":"1.0"},"canonical_sha256":"cdd505b128391797adc000cd4e81652706b3bbdb033f01f39fdbdfd0454064f2","source":{"kind":"arxiv","id":"2607.07624","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07624","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07624v1","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07624","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZXKQLMJIHELZ","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"pith_short_16","alias_value":"ZXKQLMJIHELZPLOA","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"pith_short_8","alias_value":"ZXKQLMJI","created_at":"2026-07-09T01:20:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZXKQLMJIHELZPLOAADGU5ALFE4","target":"record","payload":{"canonical_record":{"source":{"id":"2607.07624","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T16:39:58Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"50848b59101a4fe599a3a6a36477fa52c18201a4a92f16070a31db3554a37acd","abstract_canon_sha256":"3670d4f50f9fc45543c77b9b11a5a5174373036dc1668bf9988df6f16614d4bc"},"schema_version":"1.0"},"canonical_sha256":"cdd505b128391797adc000cd4e81652706b3bbdb033f01f39fdbdfd0454064f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:37.117255Z","signature_b64":"tZ6zhWcHw2cL/TdFd4JVUL1+6EtMcjhPFBCrwj0tM/40R65O3wQVOTo2npmlDbtuMz15YhQl09ycgypHWjTOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdd505b128391797adc000cd4e81652706b3bbdb033f01f39fdbdfd0454064f2","last_reissued_at":"2026-07-09T01:20:37.116714Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:37.116714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.07624","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":"2026-07-09T01:20:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6vg1Bs5x+nikAi1rU2jLsCNoW/9BL8dZPBilKai8TaOFlbrzdvs20MMX3EijvAjjFdM9Wzv4F1k/N14lYAyoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T10:43:01.182519Z"},"content_sha256":"039898b75ad578ccc9ef1c5fb46fc04becbc5516e7698ee0aa39be9a67c47ef5","schema_version":"1.0","event_id":"sha256:039898b75ad578ccc9ef1c5fb46fc04becbc5516e7698ee0aa39be9a67c47ef5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZXKQLMJIHELZPLOAADGU5ALFE4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unconditional well-posedness of the stochastic Korteweg-de Vries equation on the real line","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Damiano Greco, Kotaro Tsugawa, Tadahiro Oh","submitted_at":"2026-07-08T16:39:58Z","abstract_excerpt":"We study well-posedness issues of the stochastic Korteweg-de Vries equation (SKdV) with an additive noise, posed on the real line. By using the Fourier restriction norm method adapted to the Fourier-Lebesgue space in time, we first prove global well-posedness of SKdV in $L^2(\\mathbb R)$ without assuming the homogenous Sobolev regularity, which was imposed in a work by de Bouard, Debussche, and Tsutsumi (1999). Then, by adapting the argument by Zhou (1997) to the stochastic setting, we prove optimal pathwise unconditional uniqueness for SKdV in $L^2(\\mathbb R)$. In the appendix, we present a sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07624","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/2607.07624/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":"2026-07-09T01:20:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i3db9E/Gw0D8HLx/MgdW5zEi75u2eBewGTqEqEeBp8iuJFygo4xKSXPyYhdHxQp9GbNmw1uh3PZbN751aE30DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T10:43:01.183744Z"},"content_sha256":"b54c68f692a3da1cea9dc92d8876b6c6cee474e846ddc228e114ed841fa0cea9","schema_version":"1.0","event_id":"sha256:b54c68f692a3da1cea9dc92d8876b6c6cee474e846ddc228e114ed841fa0cea9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZXKQLMJIHELZPLOAADGU5ALFE4/bundle.json","state_url":"https://pith.science/pith/ZXKQLMJIHELZPLOAADGU5ALFE4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZXKQLMJIHELZPLOAADGU5ALFE4/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":"2026-08-06T10:43:01Z","links":{"resolver":"https://pith.science/pith/ZXKQLMJIHELZPLOAADGU5ALFE4","bundle":"https://pith.science/pith/ZXKQLMJIHELZPLOAADGU5ALFE4/bundle.json","state":"https://pith.science/pith/ZXKQLMJIHELZPLOAADGU5ALFE4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZXKQLMJIHELZPLOAADGU5ALFE4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZXKQLMJIHELZPLOAADGU5ALFE4","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":"3670d4f50f9fc45543c77b9b11a5a5174373036dc1668bf9988df6f16614d4bc","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T16:39:58Z","title_canon_sha256":"50848b59101a4fe599a3a6a36477fa52c18201a4a92f16070a31db3554a37acd"},"schema_version":"1.0","source":{"id":"2607.07624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07624","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07624v1","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07624","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZXKQLMJIHELZ","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"pith_short_16","alias_value":"ZXKQLMJIHELZPLOA","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"pith_short_8","alias_value":"ZXKQLMJI","created_at":"2026-07-09T01:20:37Z"}],"graph_snapshots":[{"event_id":"sha256:b54c68f692a3da1cea9dc92d8876b6c6cee474e846ddc228e114ed841fa0cea9","target":"graph","created_at":"2026-07-09T01:20:37Z","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/2607.07624/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study well-posedness issues of the stochastic Korteweg-de Vries equation (SKdV) with an additive noise, posed on the real line. By using the Fourier restriction norm method adapted to the Fourier-Lebesgue space in time, we first prove global well-posedness of SKdV in $L^2(\\mathbb R)$ without assuming the homogenous Sobolev regularity, which was imposed in a work by de Bouard, Debussche, and Tsutsumi (1999). Then, by adapting the argument by Zhou (1997) to the stochastic setting, we prove optimal pathwise unconditional uniqueness for SKdV in $L^2(\\mathbb R)$. In the appendix, we present a sh","authors_text":"Damiano Greco, Kotaro Tsugawa, Tadahiro Oh","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T16:39:58Z","title":"Unconditional well-posedness of the stochastic Korteweg-de Vries equation on the real line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07624","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":"sha256:039898b75ad578ccc9ef1c5fb46fc04becbc5516e7698ee0aa39be9a67c47ef5","target":"record","created_at":"2026-07-09T01:20:37Z","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":"3670d4f50f9fc45543c77b9b11a5a5174373036dc1668bf9988df6f16614d4bc","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-08T16:39:58Z","title_canon_sha256":"50848b59101a4fe599a3a6a36477fa52c18201a4a92f16070a31db3554a37acd"},"schema_version":"1.0","source":{"id":"2607.07624","kind":"arxiv","version":1}},"canonical_sha256":"cdd505b128391797adc000cd4e81652706b3bbdb033f01f39fdbdfd0454064f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdd505b128391797adc000cd4e81652706b3bbdb033f01f39fdbdfd0454064f2","first_computed_at":"2026-07-09T01:20:37.116714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T01:20:37.116714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tZ6zhWcHw2cL/TdFd4JVUL1+6EtMcjhPFBCrwj0tM/40R65O3wQVOTo2npmlDbtuMz15YhQl09ycgypHWjTOAw==","signature_status":"signed_v1","signed_at":"2026-07-09T01:20:37.117255Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.07624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:039898b75ad578ccc9ef1c5fb46fc04becbc5516e7698ee0aa39be9a67c47ef5","sha256:b54c68f692a3da1cea9dc92d8876b6c6cee474e846ddc228e114ed841fa0cea9"],"state_sha256":"ac7ad567214c3bb6795419e1b8bb88ee3eb991d9ca83fc489efd1d14203ae4e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6LHqbyTzLB8i7mogrxusevDSmm0F5qztbJRCsJc7ZzRa3wDfPlRnpBy7gF/XXNVXLyn3CwiATEmYSp48CPzWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T10:43:01.190812Z","bundle_sha256":"2e66d77fda4a89f89ccd5f77d0ee8e9597315583d5a1c06133a173d7eb51e44b"}}