{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:QTRFV7SX72DUU3LHYC7VBNO4NE","short_pith_number":"pith:QTRFV7SX","canonical_record":{"source":{"id":"2207.07548","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-07-15T15:42:46Z","cross_cats_sorted":["nlin.PS","nlin.SI"],"title_canon_sha256":"5b381a8acf73b895adb42337525b742953c0734589cc6157fb47894dca2a534d","abstract_canon_sha256":"47bdb173c20b8f7f5f29ccc1619312577ddeba518bf0d560f9b85efcf0ae6378"},"schema_version":"1.0"},"canonical_sha256":"84e25afe57fe874a6d67c0bf50b5dc6905c9916083a53fc1f5a19713ad3f4cfb","source":{"kind":"arxiv","id":"2207.07548","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.07548","created_at":"2026-07-05T04:40:33Z"},{"alias_kind":"arxiv_version","alias_value":"2207.07548v1","created_at":"2026-07-05T04:40:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.07548","created_at":"2026-07-05T04:40:33Z"},{"alias_kind":"pith_short_12","alias_value":"QTRFV7SX72DU","created_at":"2026-07-05T04:40:33Z"},{"alias_kind":"pith_short_16","alias_value":"QTRFV7SX72DUU3LH","created_at":"2026-07-05T04:40:33Z"},{"alias_kind":"pith_short_8","alias_value":"QTRFV7SX","created_at":"2026-07-05T04:40:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:QTRFV7SX72DUU3LHYC7VBNO4NE","target":"record","payload":{"canonical_record":{"source":{"id":"2207.07548","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-07-15T15:42:46Z","cross_cats_sorted":["nlin.PS","nlin.SI"],"title_canon_sha256":"5b381a8acf73b895adb42337525b742953c0734589cc6157fb47894dca2a534d","abstract_canon_sha256":"47bdb173c20b8f7f5f29ccc1619312577ddeba518bf0d560f9b85efcf0ae6378"},"schema_version":"1.0"},"canonical_sha256":"84e25afe57fe874a6d67c0bf50b5dc6905c9916083a53fc1f5a19713ad3f4cfb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:40:33.662273Z","signature_b64":"wbGprkqAEQDLp2JbHOCe0KAqwnUA241eR/NvjkzNTwJAa40zjQT+u7oNWn4TB/wicFUqofPtym28hvUeEeiuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84e25afe57fe874a6d67c0bf50b5dc6905c9916083a53fc1f5a19713ad3f4cfb","last_reissued_at":"2026-07-05T04:40:33.661928Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:40:33.661928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.07548","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":"2026-07-05T04:40:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yOFxa3UfqC7lryFsntTsoUDg6VD68QFdHMcLL8jkjCGSaa6l/QK20F3iWhy198kGiVHwgOvhD5kENQ2NocLjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:04:53.857049Z"},"content_sha256":"32affd2956b2cf29531de5733ce3dc1896fa49ddae490229fc5ada2715932858","schema_version":"1.0","event_id":"sha256:32affd2956b2cf29531de5733ce3dc1896fa49ddae490229fc5ada2715932858"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:QTRFV7SX72DUU3LHYC7VBNO4NE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global existence and singularity formation for the generalized Constantin-Lax-Majda equation with dissipation: The real line vs. periodic domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["nlin.PS","nlin.SI"],"primary_cat":"math.AP","authors_text":"David M. Ambrose, Denis A. Silantyev, Michael Siegel, Pavel M. Lushnikov","submitted_at":"2022-07-15T15:42:46Z","abstract_excerpt":"The question of global existence versus finite-time singularity formation is considered for the generalized Constantin-Lax-Majda equation with dissipation $-\\Lambda^\\sigma$, where $\\widehat {{\\Lambda}^\\sigma}=|k|^\\sigma$, both for the problem on the circle $x \\in [-\\pi,\\pi]$ and the real line. In the periodic geometry, two complementary approaches are used to prove global-in-time existence of solutions for $\\sigma \\geq 1$ and all real values of an advection parameter $a$ when the data is small. We also derive new analytical solutions in both geometries when $a=0$, and on the real line when $a="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.07548","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/2207.07548/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":"2026-07-05T04:40:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BsYmMAwtNT7ve1TspHXcAIgNjz1oil+jP1pnOcBNFHjwypq0SNielOVlJFOCrvbs7iFKkpoOrx/7EN4JWx+EDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:04:53.858004Z"},"content_sha256":"d736631a6cc680ee8070ec4f82e90f54164bf88dfc5ab3d47b9ba912cc2fb343","schema_version":"1.0","event_id":"sha256:d736631a6cc680ee8070ec4f82e90f54164bf88dfc5ab3d47b9ba912cc2fb343"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QTRFV7SX72DUU3LHYC7VBNO4NE/bundle.json","state_url":"https://pith.science/pith/QTRFV7SX72DUU3LHYC7VBNO4NE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QTRFV7SX72DUU3LHYC7VBNO4NE/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":"2026-08-08T22:04:53Z","links":{"resolver":"https://pith.science/pith/QTRFV7SX72DUU3LHYC7VBNO4NE","bundle":"https://pith.science/pith/QTRFV7SX72DUU3LHYC7VBNO4NE/bundle.json","state":"https://pith.science/pith/QTRFV7SX72DUU3LHYC7VBNO4NE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QTRFV7SX72DUU3LHYC7VBNO4NE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:QTRFV7SX72DUU3LHYC7VBNO4NE","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":"47bdb173c20b8f7f5f29ccc1619312577ddeba518bf0d560f9b85efcf0ae6378","cross_cats_sorted":["nlin.PS","nlin.SI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-07-15T15:42:46Z","title_canon_sha256":"5b381a8acf73b895adb42337525b742953c0734589cc6157fb47894dca2a534d"},"schema_version":"1.0","source":{"id":"2207.07548","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.07548","created_at":"2026-07-05T04:40:33Z"},{"alias_kind":"arxiv_version","alias_value":"2207.07548v1","created_at":"2026-07-05T04:40:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.07548","created_at":"2026-07-05T04:40:33Z"},{"alias_kind":"pith_short_12","alias_value":"QTRFV7SX72DU","created_at":"2026-07-05T04:40:33Z"},{"alias_kind":"pith_short_16","alias_value":"QTRFV7SX72DUU3LH","created_at":"2026-07-05T04:40:33Z"},{"alias_kind":"pith_short_8","alias_value":"QTRFV7SX","created_at":"2026-07-05T04:40:33Z"}],"graph_snapshots":[{"event_id":"sha256:d736631a6cc680ee8070ec4f82e90f54164bf88dfc5ab3d47b9ba912cc2fb343","target":"graph","created_at":"2026-07-05T04:40:33Z","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/2207.07548/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The question of global existence versus finite-time singularity formation is considered for the generalized Constantin-Lax-Majda equation with dissipation $-\\Lambda^\\sigma$, where $\\widehat {{\\Lambda}^\\sigma}=|k|^\\sigma$, both for the problem on the circle $x \\in [-\\pi,\\pi]$ and the real line. In the periodic geometry, two complementary approaches are used to prove global-in-time existence of solutions for $\\sigma \\geq 1$ and all real values of an advection parameter $a$ when the data is small. We also derive new analytical solutions in both geometries when $a=0$, and on the real line when $a=","authors_text":"David M. Ambrose, Denis A. Silantyev, Michael Siegel, Pavel M. Lushnikov","cross_cats":["nlin.PS","nlin.SI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-07-15T15:42:46Z","title":"Global existence and singularity formation for the generalized Constantin-Lax-Majda equation with dissipation: The real line vs. periodic domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.07548","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":"sha256:32affd2956b2cf29531de5733ce3dc1896fa49ddae490229fc5ada2715932858","target":"record","created_at":"2026-07-05T04:40:33Z","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":"47bdb173c20b8f7f5f29ccc1619312577ddeba518bf0d560f9b85efcf0ae6378","cross_cats_sorted":["nlin.PS","nlin.SI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-07-15T15:42:46Z","title_canon_sha256":"5b381a8acf73b895adb42337525b742953c0734589cc6157fb47894dca2a534d"},"schema_version":"1.0","source":{"id":"2207.07548","kind":"arxiv","version":1}},"canonical_sha256":"84e25afe57fe874a6d67c0bf50b5dc6905c9916083a53fc1f5a19713ad3f4cfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84e25afe57fe874a6d67c0bf50b5dc6905c9916083a53fc1f5a19713ad3f4cfb","first_computed_at":"2026-07-05T04:40:33.661928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:40:33.661928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wbGprkqAEQDLp2JbHOCe0KAqwnUA241eR/NvjkzNTwJAa40zjQT+u7oNWn4TB/wicFUqofPtym28hvUeEeiuAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:40:33.662273Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.07548","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32affd2956b2cf29531de5733ce3dc1896fa49ddae490229fc5ada2715932858","sha256:d736631a6cc680ee8070ec4f82e90f54164bf88dfc5ab3d47b9ba912cc2fb343"],"state_sha256":"f18fec32efe24093d4d6655cc4523fb9d3f665b4d2edc2277713fd191f397e7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GO5BScoWNTrGZclTsuwjMSB7JVF5Ea+HW7C4kBQm2AoAT8kBd/E0Ly+GLMJ4L5U6QsNBlwYvE0KF1BSNS1RmAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T22:04:53.868600Z","bundle_sha256":"eb16feab6e645eb068504973d1a233c002c93018aa8aa591e5ae8fd8556fc09b"}}