{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:C6TEW4JBT7IL46JR2657WGRUZ3","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":"c5fe75e6eb83b21c8bc39789705cbb1a8b2082c640aa9b755bb4cae6ae38926d","cross_cats_sorted":["math.AP","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-06T13:28:38Z","title_canon_sha256":"c5c8b615ca55f0e08f9acec84c954fd708e36920cd936a09f53e6fbc39cb0b9e"},"schema_version":"1.0","source":{"id":"2607.05054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.05054","created_at":"2026-07-07T02:20:20Z"},{"alias_kind":"arxiv_version","alias_value":"2607.05054v1","created_at":"2026-07-07T02:20:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05054","created_at":"2026-07-07T02:20:20Z"},{"alias_kind":"pith_short_12","alias_value":"C6TEW4JBT7IL","created_at":"2026-07-07T02:20:20Z"},{"alias_kind":"pith_short_16","alias_value":"C6TEW4JBT7IL46JR","created_at":"2026-07-07T02:20:20Z"},{"alias_kind":"pith_short_8","alias_value":"C6TEW4JB","created_at":"2026-07-07T02:20:20Z"}],"graph_snapshots":[{"event_id":"sha256:4d41310a8777c815c6ec74be82f1078e2b38847dec498be0790abf0407428515","target":"graph","created_at":"2026-07-07T02:20:20Z","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/2607.05054/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The dynamics of polynomial roots under repeated differentiation has recently been conjectured to converge to a limiting measure governed by specific nonlinear PDEs, the conjectures being shown in some particular settings. For rotationally invariant initial distributions, a deterministic structured sampling model placing roots on concentric circles was recently introduced by Galligo, Najnudel, and Vu. In this paper, the authors proved convergence under the technical growth condition $m_n / (n \\log n) \\to \\infty$, where $n$ is the number of circles and $m_n$ is the number of points per circle. I","authors_text":"Joseph Najnudel, Truong Vu","cross_cats":["math.AP","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-06T13:28:38Z","title":"Root Dynamics of Differentiated Polynomials with Rotationally Invariant Structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05054","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":"sha256:9c7f1ba1b2ccd42bbc622a8aa9d25e3c795599df1bee05728be64ccca486e201","target":"record","created_at":"2026-07-07T02:20:20Z","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":"c5fe75e6eb83b21c8bc39789705cbb1a8b2082c640aa9b755bb4cae6ae38926d","cross_cats_sorted":["math.AP","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-06T13:28:38Z","title_canon_sha256":"c5c8b615ca55f0e08f9acec84c954fd708e36920cd936a09f53e6fbc39cb0b9e"},"schema_version":"1.0","source":{"id":"2607.05054","kind":"arxiv","version":1}},"canonical_sha256":"17a64b71219fd0be7931d7bbfb1a34ced6059ee3bd8468ac100421f72f1bfe0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17a64b71219fd0be7931d7bbfb1a34ced6059ee3bd8468ac100421f72f1bfe0c","first_computed_at":"2026-07-07T02:20:20.929848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:20:20.929848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dXQlHXgBRIu6B6UOvkEGfweQoLP5jVS9kB3e/jH2bBsYl/TORC9Tl9v4XxFBqsmh4vWvnAX7bU/hdLIJdEw6BA==","signature_status":"signed_v1","signed_at":"2026-07-07T02:20:20.930718Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.05054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c7f1ba1b2ccd42bbc622a8aa9d25e3c795599df1bee05728be64ccca486e201","sha256:4d41310a8777c815c6ec74be82f1078e2b38847dec498be0790abf0407428515"],"state_sha256":"b007b7f695d66075fa43374678392d0970c44a8680333a3b25f93c55b3aeb8e1"}