{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:C6TEW4JBT7IL46JR2657WGRUZ3","short_pith_number":"pith:C6TEW4JB","canonical_record":{"source":{"id":"2607.05054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-06T13:28:38Z","cross_cats_sorted":["math.AP","math.DS"],"title_canon_sha256":"c5c8b615ca55f0e08f9acec84c954fd708e36920cd936a09f53e6fbc39cb0b9e","abstract_canon_sha256":"c5fe75e6eb83b21c8bc39789705cbb1a8b2082c640aa9b755bb4cae6ae38926d"},"schema_version":"1.0"},"canonical_sha256":"17a64b71219fd0be7931d7bbfb1a34ced6059ee3bd8468ac100421f72f1bfe0c","source":{"kind":"arxiv","id":"2607.05054","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:C6TEW4JBT7IL46JR2657WGRUZ3","target":"record","payload":{"canonical_record":{"source":{"id":"2607.05054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-06T13:28:38Z","cross_cats_sorted":["math.AP","math.DS"],"title_canon_sha256":"c5c8b615ca55f0e08f9acec84c954fd708e36920cd936a09f53e6fbc39cb0b9e","abstract_canon_sha256":"c5fe75e6eb83b21c8bc39789705cbb1a8b2082c640aa9b755bb4cae6ae38926d"},"schema_version":"1.0"},"canonical_sha256":"17a64b71219fd0be7931d7bbfb1a34ced6059ee3bd8468ac100421f72f1bfe0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:20:20.930718Z","signature_b64":"dXQlHXgBRIu6B6UOvkEGfweQoLP5jVS9kB3e/jH2bBsYl/TORC9Tl9v4XxFBqsmh4vWvnAX7bU/hdLIJdEw6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17a64b71219fd0be7931d7bbfb1a34ced6059ee3bd8468ac100421f72f1bfe0c","last_reissued_at":"2026-07-07T02:20:20.929848Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:20:20.929848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.05054","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":"2026-07-07T02:20:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vn/t1sQqooheuog3kT2JQzNqdpq0rZYnv+MxHhhJVVvT/oO0xo9ERijAFplrAtUAGaiSPUUZy9/ZC+vXSh/KBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T05:53:13.084067Z"},"content_sha256":"9c7f1ba1b2ccd42bbc622a8aa9d25e3c795599df1bee05728be64ccca486e201","schema_version":"1.0","event_id":"sha256:9c7f1ba1b2ccd42bbc622a8aa9d25e3c795599df1bee05728be64ccca486e201"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:C6TEW4JBT7IL46JR2657WGRUZ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Root Dynamics of Differentiated Polynomials with Rotationally Invariant Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS"],"primary_cat":"math.PR","authors_text":"Joseph Najnudel, Truong Vu","submitted_at":"2026-07-06T13:28:38Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05054","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/2607.05054/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":"2026-07-07T02:20:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p1N5dzPw8hP4wk60eWbhGxysMTURbwX5AtvCvD5zhQqyto5eauVrU2eGJWVf36wakRKftY9vf7Ue/vfmGR10AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T05:53:13.084575Z"},"content_sha256":"4d41310a8777c815c6ec74be82f1078e2b38847dec498be0790abf0407428515","schema_version":"1.0","event_id":"sha256:4d41310a8777c815c6ec74be82f1078e2b38847dec498be0790abf0407428515"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C6TEW4JBT7IL46JR2657WGRUZ3/bundle.json","state_url":"https://pith.science/pith/C6TEW4JBT7IL46JR2657WGRUZ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C6TEW4JBT7IL46JR2657WGRUZ3/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":"2026-08-09T05:53:13Z","links":{"resolver":"https://pith.science/pith/C6TEW4JBT7IL46JR2657WGRUZ3","bundle":"https://pith.science/pith/C6TEW4JBT7IL46JR2657WGRUZ3/bundle.json","state":"https://pith.science/pith/C6TEW4JBT7IL46JR2657WGRUZ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C6TEW4JBT7IL46JR2657WGRUZ3/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I06/OxqnbTQSr5itwLK4LiOteM9WMnvl0sU0wI0NYmk6wW9zQc5uaKB/YLpKMx7aH8In9ROJivnatvedrwqxBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T05:53:13.088159Z","bundle_sha256":"7e7ebbcfa3d9f2b05f2f5ae982f7b3925023310afd43c0bea14ccfe2d4d8e09f"}}