{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:E46DJNTCEU6Q66EHCRYCG6L7RV","short_pith_number":"pith:E46DJNTC","canonical_record":{"source":{"id":"2607.01119","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-01T16:05:52Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4bf12e4c6e3038bdc55d66cb0e15a8b18e0b16915ebcfa239474a20663220ce8","abstract_canon_sha256":"b4684f0e844a8e70254662696fde01f6cf18a1497058e6cc56294b17c6b196b8"},"schema_version":"1.0"},"canonical_sha256":"273c34b662253d0f7887147023797f8d408e1d13adee6b993547c33302ddc157","source":{"kind":"arxiv","id":"2607.01119","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01119","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01119v1","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01119","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"pith_short_12","alias_value":"E46DJNTCEU6Q","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"pith_short_16","alias_value":"E46DJNTCEU6Q66EH","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"pith_short_8","alias_value":"E46DJNTC","created_at":"2026-07-02T01:18:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:E46DJNTCEU6Q66EHCRYCG6L7RV","target":"record","payload":{"canonical_record":{"source":{"id":"2607.01119","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-01T16:05:52Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4bf12e4c6e3038bdc55d66cb0e15a8b18e0b16915ebcfa239474a20663220ce8","abstract_canon_sha256":"b4684f0e844a8e70254662696fde01f6cf18a1497058e6cc56294b17c6b196b8"},"schema_version":"1.0"},"canonical_sha256":"273c34b662253d0f7887147023797f8d408e1d13adee6b993547c33302ddc157","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:18:29.554806Z","signature_b64":"EZYwg9YCVU608awjiQhPIGrnQTr17b8CVC4nLUXXDfgtc3h8/Pc6M2lEtkfFW4wnHz0YGdFz78qF6I5H8bFsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"273c34b662253d0f7887147023797f8d408e1d13adee6b993547c33302ddc157","last_reissued_at":"2026-07-02T01:18:29.554410Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:18:29.554410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.01119","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":"2026-07-02T01:18:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qWA1/g7k7vz5FsmNTmTMAA0Elx0HypuS8Zi8yAQIMe/i4LYMSxIGA0Jgb6kYkX0yiDOcqd2csLwDeZimvxplBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T15:33:20.098017Z"},"content_sha256":"5b5eab33ef7b121c57104044ac39409609d794edee1e6888f21f84d0a801abc3","schema_version":"1.0","event_id":"sha256:5b5eab33ef7b121c57104044ac39409609d794edee1e6888f21f84d0a801abc3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:E46DJNTCEU6Q66EHCRYCG6L7RV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak and dissipative solutions for the Hasegawa-Mima equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Michele Gorini","submitted_at":"2026-07-01T16:05:52Z","abstract_excerpt":"We consider the Hasegawa-Mima equation in its ``Euler-like'' velocity form: \\[\\partial_t(u-\\Delta^{-1}u)+(u\\cdot\\nabla)u-u^\\perp\\log n_0=0,\\] $n_0$ being the time-independent function appearing in the particle count $n=n_0e^{\\frac{e\\varphi}{T}}$, and $u$ being the drift velocity $\\nabla^\\perp\\varphi=-\\nabla\\varphi\\times\\hat z$. Adapting the notion from Lions' book on the Euler equations, we prove the existence of dissipative solutions for this equation for any $L^2$ divergence free initial condition $w\\in L^2(D)$, for $D=\\mathbb T^2$ and $D\\subset\\mathbb R^2$ a bounded $\\mathcal{C}^1$ domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01119","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/2607.01119/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":"2026-07-02T01:18:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZMA7OfAQQH6O8KYodZzqaewuqvWgi3wf2hl0ye5cmwTOfFGFtSrA9cRjyz2e3pBtDTVEqgy8fJZu5ZvrSvn1Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T15:33:20.098365Z"},"content_sha256":"94c214c2a5f7caf1ee9dc31c0b383c8ec6d9e35dd1f16bf5fc1dfb49f0456b61","schema_version":"1.0","event_id":"sha256:94c214c2a5f7caf1ee9dc31c0b383c8ec6d9e35dd1f16bf5fc1dfb49f0456b61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E46DJNTCEU6Q66EHCRYCG6L7RV/bundle.json","state_url":"https://pith.science/pith/E46DJNTCEU6Q66EHCRYCG6L7RV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E46DJNTCEU6Q66EHCRYCG6L7RV/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":"2026-08-21T15:33:20Z","links":{"resolver":"https://pith.science/pith/E46DJNTCEU6Q66EHCRYCG6L7RV","bundle":"https://pith.science/pith/E46DJNTCEU6Q66EHCRYCG6L7RV/bundle.json","state":"https://pith.science/pith/E46DJNTCEU6Q66EHCRYCG6L7RV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E46DJNTCEU6Q66EHCRYCG6L7RV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:E46DJNTCEU6Q66EHCRYCG6L7RV","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":"b4684f0e844a8e70254662696fde01f6cf18a1497058e6cc56294b17c6b196b8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-01T16:05:52Z","title_canon_sha256":"4bf12e4c6e3038bdc55d66cb0e15a8b18e0b16915ebcfa239474a20663220ce8"},"schema_version":"1.0","source":{"id":"2607.01119","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01119","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01119v1","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01119","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"pith_short_12","alias_value":"E46DJNTCEU6Q","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"pith_short_16","alias_value":"E46DJNTCEU6Q66EH","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"pith_short_8","alias_value":"E46DJNTC","created_at":"2026-07-02T01:18:29Z"}],"graph_snapshots":[{"event_id":"sha256:94c214c2a5f7caf1ee9dc31c0b383c8ec6d9e35dd1f16bf5fc1dfb49f0456b61","target":"graph","created_at":"2026-07-02T01:18:29Z","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/2607.01119/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the Hasegawa-Mima equation in its ``Euler-like'' velocity form: \\[\\partial_t(u-\\Delta^{-1}u)+(u\\cdot\\nabla)u-u^\\perp\\log n_0=0,\\] $n_0$ being the time-independent function appearing in the particle count $n=n_0e^{\\frac{e\\varphi}{T}}$, and $u$ being the drift velocity $\\nabla^\\perp\\varphi=-\\nabla\\varphi\\times\\hat z$. Adapting the notion from Lions' book on the Euler equations, we prove the existence of dissipative solutions for this equation for any $L^2$ divergence free initial condition $w\\in L^2(D)$, for $D=\\mathbb T^2$ and $D\\subset\\mathbb R^2$ a bounded $\\mathcal{C}^1$ domain.","authors_text":"Michele Gorini","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-01T16:05:52Z","title":"Weak and dissipative solutions for the Hasegawa-Mima equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01119","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":"sha256:5b5eab33ef7b121c57104044ac39409609d794edee1e6888f21f84d0a801abc3","target":"record","created_at":"2026-07-02T01:18:29Z","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":"b4684f0e844a8e70254662696fde01f6cf18a1497058e6cc56294b17c6b196b8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-01T16:05:52Z","title_canon_sha256":"4bf12e4c6e3038bdc55d66cb0e15a8b18e0b16915ebcfa239474a20663220ce8"},"schema_version":"1.0","source":{"id":"2607.01119","kind":"arxiv","version":1}},"canonical_sha256":"273c34b662253d0f7887147023797f8d408e1d13adee6b993547c33302ddc157","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"273c34b662253d0f7887147023797f8d408e1d13adee6b993547c33302ddc157","first_computed_at":"2026-07-02T01:18:29.554410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:18:29.554410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EZYwg9YCVU608awjiQhPIGrnQTr17b8CVC4nLUXXDfgtc3h8/Pc6M2lEtkfFW4wnHz0YGdFz78qF6I5H8bFsAA==","signature_status":"signed_v1","signed_at":"2026-07-02T01:18:29.554806Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01119","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b5eab33ef7b121c57104044ac39409609d794edee1e6888f21f84d0a801abc3","sha256:94c214c2a5f7caf1ee9dc31c0b383c8ec6d9e35dd1f16bf5fc1dfb49f0456b61"],"state_sha256":"4eb0608dfdbd6dc5405804244235750c45d9a7bb4aeef95314cc3ba0b5f49b99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mqKOnMcxqbosxIEDAqiJi5EMm5tUgOkR1v8y+CJgHXZLt8BFdJ4JDZj2t9buShc822Ywf3jEiOKaC8rStqFqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T15:33:20.102338Z","bundle_sha256":"22f6c50710fbb5086ba01bd26805c3881cb176d9929c44a0e1dd58f63ceccc7c"}}