{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:RZYXLT7VARZ2AGS55TVGUHERJN","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":"901705bf961323b1d43d614cbe7e0e845071742c09ce7dc1a088abef3140ec8e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-08-18T00:39:50Z","title_canon_sha256":"4306ce3bf34b53609d74e0e64a84f06a660a8277f813c26adfda2da5f797d8c0"},"schema_version":"1.0","source":{"id":"0808.2324","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.2324","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"0808.2324v1","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2324","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"RZYXLT7VARZ2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"RZYXLT7VARZ2AGS5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"RZYXLT7V","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:f15f01ed0f13004c76446570f7dd20030d1f2f0884866d5e94e8c4d5b468364b","target":"graph","created_at":"2026-05-18T04:07:29Z","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"},"paper":{"abstract_excerpt":"We consider $L^2$-critical focusing nonlinear Schroedinger equations with Hartree type nonlinearity $$i \\pr_t u = -\\DD u - \\big (\\Phi \\ast |u|^2 \\big) u \\quad {in $\\RR^4$},$$ where $\\Phi(x)$ is a perturbation of the convolution kernel $|x|^{-2}$. Despite the lack of pseudo conformal invariance for this equation, we prove the existence of critical mass finite-time blowup solutions $u(t,x)$ that exhibit the pseudo-conformal blowup rate $$ \\| \\nabla u(t) \\|_{L^2_x} \\sim \\frac{1}{|t|} \\quad {as} \\quad t \\nearrow 0 . $$ Furthermore, we prove the finite-codimensional stability of this conformal blow","authors_text":"Enno Lenzmann, Joachim Krieger, Pierre Raphael","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-08-18T00:39:50Z","title":"On Stability of Pseudo-Conformal Blowup for L^2-critical Hartree NLS"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2324","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":"sha256:515955e52cb8077a069be48ea16e8aed262d01e42f1835399e8da900e0ad33e2","target":"record","created_at":"2026-05-18T04:07:29Z","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":"901705bf961323b1d43d614cbe7e0e845071742c09ce7dc1a088abef3140ec8e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-08-18T00:39:50Z","title_canon_sha256":"4306ce3bf34b53609d74e0e64a84f06a660a8277f813c26adfda2da5f797d8c0"},"schema_version":"1.0","source":{"id":"0808.2324","kind":"arxiv","version":1}},"canonical_sha256":"8e7175cff50473a01a5decea6a1c914b5a74e4df453cbcc0374cd95a3bd94c9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e7175cff50473a01a5decea6a1c914b5a74e4df453cbcc0374cd95a3bd94c9e","first_computed_at":"2026-05-18T04:07:29.489624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:29.489624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+sNhSRDbiqkvr9m7mJLN9XDbdsinuDZdWpwK+yqlQwW7QBar+vPdRT6zSBNv0u5Gj+wh+PqS41AcOYXsbmN8Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:29.490160Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.2324","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:515955e52cb8077a069be48ea16e8aed262d01e42f1835399e8da900e0ad33e2","sha256:f15f01ed0f13004c76446570f7dd20030d1f2f0884866d5e94e8c4d5b468364b"],"state_sha256":"34616049818c5b602919d62f5c9e7670a28a8a473bb48f8f3dc590c6eceb3d0d"}