{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:S2B43Q4NWJYNPW5ZQUEMYOOFEJ","short_pith_number":"pith:S2B43Q4N","canonical_record":{"source":{"id":"2607.01939","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-02T09:32:55Z","cross_cats_sorted":[],"title_canon_sha256":"93f0585c6fab6109b28beef8d04f2c05b9b6d14a7b398125e4d5acbbca87049b","abstract_canon_sha256":"e067deb80d60833f3cb1ad38d35f633baab718a9c4a2ece4a5a717bd95065438"},"schema_version":"1.0"},"canonical_sha256":"9683cdc38db270d7dbb98508cc39c5227e869d7293d61357e0dc20e3d2cae361","source":{"kind":"arxiv","id":"2607.01939","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01939","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01939v1","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01939","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"pith_short_12","alias_value":"S2B43Q4NWJYN","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"pith_short_16","alias_value":"S2B43Q4NWJYNPW5Z","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"pith_short_8","alias_value":"S2B43Q4N","created_at":"2026-07-03T01:17:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:S2B43Q4NWJYNPW5ZQUEMYOOFEJ","target":"record","payload":{"canonical_record":{"source":{"id":"2607.01939","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-02T09:32:55Z","cross_cats_sorted":[],"title_canon_sha256":"93f0585c6fab6109b28beef8d04f2c05b9b6d14a7b398125e4d5acbbca87049b","abstract_canon_sha256":"e067deb80d60833f3cb1ad38d35f633baab718a9c4a2ece4a5a717bd95065438"},"schema_version":"1.0"},"canonical_sha256":"9683cdc38db270d7dbb98508cc39c5227e869d7293d61357e0dc20e3d2cae361","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:33.942125Z","signature_b64":"OQYlonmY8X2T4xJFxqGtTTZMLYX8CPJ8bi7lkFqgtGIJSfhssuPmjWyaCepR+OxFLfpEB9+f2e20Cmdo9lXhAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9683cdc38db270d7dbb98508cc39c5227e869d7293d61357e0dc20e3d2cae361","last_reissued_at":"2026-07-03T01:17:33.941519Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:33.941519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.01939","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":"2026-07-03T01:17:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hrdCNbQxprulkhGI1Bcp18kw20nN7ZThNWSoFxXcx8smNJASU7+Gba2YQp5JehI7VumkgsZ2eOkkUDqEUmOmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T23:58:33.067789Z"},"content_sha256":"c8beecf9ef3daf6f83dc7df6869cdc8c73e3edbe32ecb399534e6ff0755d9c41","schema_version":"1.0","event_id":"sha256:c8beecf9ef3daf6f83dc7df6869cdc8c73e3edbe32ecb399534e6ff0755d9c41"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:S2B43Q4NWJYNPW5ZQUEMYOOFEJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"McLean resonances and $3d$ spectral instability of Stokes waves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Maspero, Antonio Milosh Radakovic, Massimiliano Berti","submitted_at":"2026-07-02T09:32:55Z","abstract_excerpt":"The spectral instability of traveling periodic water waves has been investigated for more than sixty years, since the seminal discovery of Benjamin and Feir. Despite an extensive literature, no rigorous theory has been available for arbitrary three-dimensional -- longitudinal and transverse -- perturbations. We establish the first rigorous description of the $3d $ unstable spectrum of small-amplitude gravity Stokes waves in deep water in a full neighborhood of the McLean resonant curves. Our results reveal that the Benjamin-Feir instability and the first longitudinal high-frequency isola origi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01939","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/2607.01939/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":"2026-07-03T01:17:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PVB0QkhYmWfvRDCNfnvli117IYFFZ7OFgjREUyKGzAJ47+tFH4WOxqdpirDGGxmF4eAqzNh+cLvxl8sm78T5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T23:58:33.068283Z"},"content_sha256":"7ca660b174f6b84545776f0ddddefee97d2297a96fbf7c117c85c7990cf5c424","schema_version":"1.0","event_id":"sha256:7ca660b174f6b84545776f0ddddefee97d2297a96fbf7c117c85c7990cf5c424"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S2B43Q4NWJYNPW5ZQUEMYOOFEJ/bundle.json","state_url":"https://pith.science/pith/S2B43Q4NWJYNPW5ZQUEMYOOFEJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S2B43Q4NWJYNPW5ZQUEMYOOFEJ/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":"2026-08-09T23:58:33Z","links":{"resolver":"https://pith.science/pith/S2B43Q4NWJYNPW5ZQUEMYOOFEJ","bundle":"https://pith.science/pith/S2B43Q4NWJYNPW5ZQUEMYOOFEJ/bundle.json","state":"https://pith.science/pith/S2B43Q4NWJYNPW5ZQUEMYOOFEJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S2B43Q4NWJYNPW5ZQUEMYOOFEJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:S2B43Q4NWJYNPW5ZQUEMYOOFEJ","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":"e067deb80d60833f3cb1ad38d35f633baab718a9c4a2ece4a5a717bd95065438","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-02T09:32:55Z","title_canon_sha256":"93f0585c6fab6109b28beef8d04f2c05b9b6d14a7b398125e4d5acbbca87049b"},"schema_version":"1.0","source":{"id":"2607.01939","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01939","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01939v1","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01939","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"pith_short_12","alias_value":"S2B43Q4NWJYN","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"pith_short_16","alias_value":"S2B43Q4NWJYNPW5Z","created_at":"2026-07-03T01:17:33Z"},{"alias_kind":"pith_short_8","alias_value":"S2B43Q4N","created_at":"2026-07-03T01:17:33Z"}],"graph_snapshots":[{"event_id":"sha256:7ca660b174f6b84545776f0ddddefee97d2297a96fbf7c117c85c7990cf5c424","target":"graph","created_at":"2026-07-03T01:17:33Z","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/2607.01939/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The spectral instability of traveling periodic water waves has been investigated for more than sixty years, since the seminal discovery of Benjamin and Feir. Despite an extensive literature, no rigorous theory has been available for arbitrary three-dimensional -- longitudinal and transverse -- perturbations. We establish the first rigorous description of the $3d $ unstable spectrum of small-amplitude gravity Stokes waves in deep water in a full neighborhood of the McLean resonant curves. Our results reveal that the Benjamin-Feir instability and the first longitudinal high-frequency isola origi","authors_text":"Alberto Maspero, Antonio Milosh Radakovic, Massimiliano Berti","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-02T09:32:55Z","title":"McLean resonances and $3d$ spectral instability of Stokes waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01939","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:c8beecf9ef3daf6f83dc7df6869cdc8c73e3edbe32ecb399534e6ff0755d9c41","target":"record","created_at":"2026-07-03T01:17:33Z","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":"e067deb80d60833f3cb1ad38d35f633baab718a9c4a2ece4a5a717bd95065438","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-02T09:32:55Z","title_canon_sha256":"93f0585c6fab6109b28beef8d04f2c05b9b6d14a7b398125e4d5acbbca87049b"},"schema_version":"1.0","source":{"id":"2607.01939","kind":"arxiv","version":1}},"canonical_sha256":"9683cdc38db270d7dbb98508cc39c5227e869d7293d61357e0dc20e3d2cae361","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9683cdc38db270d7dbb98508cc39c5227e869d7293d61357e0dc20e3d2cae361","first_computed_at":"2026-07-03T01:17:33.941519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:33.941519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OQYlonmY8X2T4xJFxqGtTTZMLYX8CPJ8bi7lkFqgtGIJSfhssuPmjWyaCepR+OxFLfpEB9+f2e20Cmdo9lXhAw==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:33.942125Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01939","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8beecf9ef3daf6f83dc7df6869cdc8c73e3edbe32ecb399534e6ff0755d9c41","sha256:7ca660b174f6b84545776f0ddddefee97d2297a96fbf7c117c85c7990cf5c424"],"state_sha256":"52142be08d8fdad1baa70cfad328a764a0235d5e8ae7450bd944969408f64a7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oA3E9VE8ql1lnW/6lEpMVJyIkQgYBEnurAkfDY+oRQ4MlXJ/jNIFngTV3NVbtB0fRZdE+sHs4QOXJxURzL/pAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T23:58:33.072415Z","bundle_sha256":"ffedf1dcdf36aed06c9c9b09d0aa3aa956a38e6683160715cc1e7d1cf7526676"}}