{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GPCJHSE7X7X5E7U4VUT35XWYI5","short_pith_number":"pith:GPCJHSE7","canonical_record":{"source":{"id":"2605.30657","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T23:34:28Z","cross_cats_sorted":[],"title_canon_sha256":"1975254ce3612b2a0ce36600f0ef4055d18e916190edfabc2b8107ba01ff1afe","abstract_canon_sha256":"ba5c4689026d990beca755452df21497b4fd536989ec25d04a7ca6682d1446a5"},"schema_version":"1.0"},"canonical_sha256":"33c493c89fbfefd27e9cad27beded8475a24b6b8e62dfdce70c95363f9f69409","source":{"kind":"arxiv","id":"2605.30657","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30657","created_at":"2026-06-01T01:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30657v1","created_at":"2026-06-01T01:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30657","created_at":"2026-06-01T01:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"GPCJHSE7X7X5","created_at":"2026-06-01T01:03:06Z"},{"alias_kind":"pith_short_16","alias_value":"GPCJHSE7X7X5E7U4","created_at":"2026-06-01T01:03:06Z"},{"alias_kind":"pith_short_8","alias_value":"GPCJHSE7","created_at":"2026-06-01T01:03:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GPCJHSE7X7X5E7U4VUT35XWYI5","target":"record","payload":{"canonical_record":{"source":{"id":"2605.30657","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T23:34:28Z","cross_cats_sorted":[],"title_canon_sha256":"1975254ce3612b2a0ce36600f0ef4055d18e916190edfabc2b8107ba01ff1afe","abstract_canon_sha256":"ba5c4689026d990beca755452df21497b4fd536989ec25d04a7ca6682d1446a5"},"schema_version":"1.0"},"canonical_sha256":"33c493c89fbfefd27e9cad27beded8475a24b6b8e62dfdce70c95363f9f69409","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:03:06.715394Z","signature_b64":"ZXLCpvZBiCGvf1kVx6sTqFrrs6zYrXMEB3pbx2N8hpKYCTWpdGH+sL3NORNRHA6Hvr0NTYxFFHWOoZw3V7eZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33c493c89fbfefd27e9cad27beded8475a24b6b8e62dfdce70c95363f9f69409","last_reissued_at":"2026-06-01T01:03:06.714594Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:03:06.714594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.30657","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":"2026-06-01T01:03:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AYPEIuw6uHlDsN69rPvRNHu8mIllIaxNsrbsVMnkd09T0x+sJDBfONsy1WRU5tCJhgeDMwSZEvrAf+J72Kg4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T11:06:16.420674Z"},"content_sha256":"b9bfda34c2e046aba2a244187f3a6908863be8368449d2d288f80a8ea07b42ff","schema_version":"1.0","event_id":"sha256:b9bfda34c2e046aba2a244187f3a6908863be8368449d2d288f80a8ea07b42ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GPCJHSE7X7X5E7U4VUT35XWYI5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-posedness for the periodic Intermediate nonlinear Schr\\\"{o}dinger equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andreia Chapouto, Justin Forlano, Thierry Laurens","submitted_at":"2026-05-28T23:34:28Z","abstract_excerpt":"We study the well-posedness for the intermediate nonlinear Schr\\\"{o}dinger equation (INLS) with periodic boundary conditions. Using a gauge transform, we obtain large data local well-posedness in $H^{s}(\\mathbb{T})$ for any $s\\geq \\frac 12$. We extend this result to global well-posedness under a small $L^2$-norm constraint by exploiting the complete integrability of the continuum Calogero-Moser equation (CCM). We also establish additional results such as the unconditional well-posedness in the energy space and the convergence of solutions to INLS to those of CCM in the infinite-depth limit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30657","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/2605.30657/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":"2026-06-01T01:03:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nolAE8LbEw3Ce8aFinmHEfs485SZFqOtfKIuz3QJECGn0u52/NqQAs6sqkxOuBsyKxL0n8SLFOgTt05nhTLdCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T11:06:16.421045Z"},"content_sha256":"fb3e3f7904b4214a6f289252510dd6848d3740d3bafc07a529aff1dc397199a8","schema_version":"1.0","event_id":"sha256:fb3e3f7904b4214a6f289252510dd6848d3740d3bafc07a529aff1dc397199a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GPCJHSE7X7X5E7U4VUT35XWYI5/bundle.json","state_url":"https://pith.science/pith/GPCJHSE7X7X5E7U4VUT35XWYI5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GPCJHSE7X7X5E7U4VUT35XWYI5/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":"2026-06-30T11:06:16Z","links":{"resolver":"https://pith.science/pith/GPCJHSE7X7X5E7U4VUT35XWYI5","bundle":"https://pith.science/pith/GPCJHSE7X7X5E7U4VUT35XWYI5/bundle.json","state":"https://pith.science/pith/GPCJHSE7X7X5E7U4VUT35XWYI5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GPCJHSE7X7X5E7U4VUT35XWYI5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GPCJHSE7X7X5E7U4VUT35XWYI5","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":"ba5c4689026d990beca755452df21497b4fd536989ec25d04a7ca6682d1446a5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T23:34:28Z","title_canon_sha256":"1975254ce3612b2a0ce36600f0ef4055d18e916190edfabc2b8107ba01ff1afe"},"schema_version":"1.0","source":{"id":"2605.30657","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30657","created_at":"2026-06-01T01:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30657v1","created_at":"2026-06-01T01:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30657","created_at":"2026-06-01T01:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"GPCJHSE7X7X5","created_at":"2026-06-01T01:03:06Z"},{"alias_kind":"pith_short_16","alias_value":"GPCJHSE7X7X5E7U4","created_at":"2026-06-01T01:03:06Z"},{"alias_kind":"pith_short_8","alias_value":"GPCJHSE7","created_at":"2026-06-01T01:03:06Z"}],"graph_snapshots":[{"event_id":"sha256:fb3e3f7904b4214a6f289252510dd6848d3740d3bafc07a529aff1dc397199a8","target":"graph","created_at":"2026-06-01T01:03:06Z","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/2605.30657/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the well-posedness for the intermediate nonlinear Schr\\\"{o}dinger equation (INLS) with periodic boundary conditions. Using a gauge transform, we obtain large data local well-posedness in $H^{s}(\\mathbb{T})$ for any $s\\geq \\frac 12$. We extend this result to global well-posedness under a small $L^2$-norm constraint by exploiting the complete integrability of the continuum Calogero-Moser equation (CCM). We also establish additional results such as the unconditional well-posedness in the energy space and the convergence of solutions to INLS to those of CCM in the infinite-depth limit.","authors_text":"Andreia Chapouto, Justin Forlano, Thierry Laurens","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T23:34:28Z","title":"Well-posedness for the periodic Intermediate nonlinear Schr\\\"{o}dinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30657","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:b9bfda34c2e046aba2a244187f3a6908863be8368449d2d288f80a8ea07b42ff","target":"record","created_at":"2026-06-01T01:03:06Z","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":"ba5c4689026d990beca755452df21497b4fd536989ec25d04a7ca6682d1446a5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T23:34:28Z","title_canon_sha256":"1975254ce3612b2a0ce36600f0ef4055d18e916190edfabc2b8107ba01ff1afe"},"schema_version":"1.0","source":{"id":"2605.30657","kind":"arxiv","version":1}},"canonical_sha256":"33c493c89fbfefd27e9cad27beded8475a24b6b8e62dfdce70c95363f9f69409","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33c493c89fbfefd27e9cad27beded8475a24b6b8e62dfdce70c95363f9f69409","first_computed_at":"2026-06-01T01:03:06.714594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T01:03:06.714594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZXLCpvZBiCGvf1kVx6sTqFrrs6zYrXMEB3pbx2N8hpKYCTWpdGH+sL3NORNRHA6Hvr0NTYxFFHWOoZw3V7eZCg==","signature_status":"signed_v1","signed_at":"2026-06-01T01:03:06.715394Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.30657","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9bfda34c2e046aba2a244187f3a6908863be8368449d2d288f80a8ea07b42ff","sha256:fb3e3f7904b4214a6f289252510dd6848d3740d3bafc07a529aff1dc397199a8"],"state_sha256":"ab0d3b8eac08b70b9dba351c604a843418faaf8ed382d4d0fac6b632aff7b08f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b8EQARr7oeepNWPeBOMwpUx6I9YD5S2DGULDtNtKSR4KzI5VlIvt0OgodNhyiChvO2QTjvukTxgVdMN/BTbKAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T11:06:16.423064Z","bundle_sha256":"567d00ab18f16822f4bbe3676ce185d80a5f081fdcde23441317bdf5ae0a5301"}}