{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AQMMQKBVJNUPEK2KTZJXHWKRZP","short_pith_number":"pith:AQMMQKBV","canonical_record":{"source":{"id":"1606.05422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-17T05:40:15Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"ea0cf64a49fe296e59e582afe9ead8708f7e1b44c3d119fa02f0fc940c0282a0","abstract_canon_sha256":"cd82ec1fffa08a41e679d610942d101a5f7f22353da99397a45651b294be4c24"},"schema_version":"1.0"},"canonical_sha256":"0418c828354b68f22b4a9e5373d951cbc3f944e85be113f2d19f20c0bf88a89a","source":{"kind":"arxiv","id":"1606.05422","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05422","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05422v1","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05422","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"AQMMQKBVJNUP","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AQMMQKBVJNUPEK2K","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AQMMQKBV","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AQMMQKBVJNUPEK2KTZJXHWKRZP","target":"record","payload":{"canonical_record":{"source":{"id":"1606.05422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-17T05:40:15Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"ea0cf64a49fe296e59e582afe9ead8708f7e1b44c3d119fa02f0fc940c0282a0","abstract_canon_sha256":"cd82ec1fffa08a41e679d610942d101a5f7f22353da99397a45651b294be4c24"},"schema_version":"1.0"},"canonical_sha256":"0418c828354b68f22b4a9e5373d951cbc3f944e85be113f2d19f20c0bf88a89a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:19.584447Z","signature_b64":"rdCQ/EDL/C05sBx6ZCPJw8Z8/emUF2HgaWSieqQjggv+relKnNAJiKgou7Q/LPANFPl9lAwI4CHuzpzlP+xxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0418c828354b68f22b4a9e5373d951cbc3f944e85be113f2d19f20c0bf88a89a","last_reissued_at":"2026-05-18T01:12:19.584101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:19.584101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.05422","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":"2026-05-18T01:12:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V2Bip5zGdkU+iIPIO1+ANQTa/uchMjMG7JNUMTofKws5RovNYgzEZC5sMMiI+7t29CBKq4WEEz0MQFlEu3BeBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:08:43.481406Z"},"content_sha256":"1f8919a5a560dd65b2f49e09ad5e252330de037d3ccfebf9b0b7e9f4ad982029","schema_version":"1.0","event_id":"sha256:1f8919a5a560dd65b2f49e09ad5e252330de037d3ccfebf9b0b7e9f4ad982029"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AQMMQKBVJNUPEK2KTZJXHWKRZP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution of points with prescribed derivative in polynomial dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Gabriel Vigny, Thomas Gauthier","submitted_at":"2016-06-17T05:40:15Z","abstract_excerpt":"In analogy to the equidistribution of preimages of a prescribed point by the iterates of a polynomial map in the complex plane towards the equilibrium measure, we show here the equidistribution of points for which the derivative of the n-th iterate of the polynomial takes a suitable prescribed value towards the equilibrium measure. We then give a similar statement in the space of degree d polynomials for the equidistribution of parameters for which the n-derivative at a given critical value has a prescribed derivative towards the activity current of the corresponding critical point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05422","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":""},"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":"2026-05-18T01:12:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"isIiV/cXp1A6745BR1pFStZDb5KbisgY7BCOoKdRQcIRsEUIMe+8r4jNB4D75Le8UVLNMLO9jGBemcH7qI22AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:08:43.481764Z"},"content_sha256":"ef87dd74f47545dd87d74e60be1d7336308eca3c397826de599a727eb96dd3c5","schema_version":"1.0","event_id":"sha256:ef87dd74f47545dd87d74e60be1d7336308eca3c397826de599a727eb96dd3c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQMMQKBVJNUPEK2KTZJXHWKRZP/bundle.json","state_url":"https://pith.science/pith/AQMMQKBVJNUPEK2KTZJXHWKRZP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQMMQKBVJNUPEK2KTZJXHWKRZP/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":"2026-06-23T17:08:43Z","links":{"resolver":"https://pith.science/pith/AQMMQKBVJNUPEK2KTZJXHWKRZP","bundle":"https://pith.science/pith/AQMMQKBVJNUPEK2KTZJXHWKRZP/bundle.json","state":"https://pith.science/pith/AQMMQKBVJNUPEK2KTZJXHWKRZP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQMMQKBVJNUPEK2KTZJXHWKRZP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AQMMQKBVJNUPEK2KTZJXHWKRZP","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":"cd82ec1fffa08a41e679d610942d101a5f7f22353da99397a45651b294be4c24","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-17T05:40:15Z","title_canon_sha256":"ea0cf64a49fe296e59e582afe9ead8708f7e1b44c3d119fa02f0fc940c0282a0"},"schema_version":"1.0","source":{"id":"1606.05422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05422","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05422v1","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05422","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"AQMMQKBVJNUP","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AQMMQKBVJNUPEK2K","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AQMMQKBV","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:ef87dd74f47545dd87d74e60be1d7336308eca3c397826de599a727eb96dd3c5","target":"graph","created_at":"2026-05-18T01:12:19Z","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":"In analogy to the equidistribution of preimages of a prescribed point by the iterates of a polynomial map in the complex plane towards the equilibrium measure, we show here the equidistribution of points for which the derivative of the n-th iterate of the polynomial takes a suitable prescribed value towards the equilibrium measure. We then give a similar statement in the space of degree d polynomials for the equidistribution of parameters for which the n-derivative at a given critical value has a prescribed derivative towards the activity current of the corresponding critical point.","authors_text":"Gabriel Vigny, Thomas Gauthier","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-17T05:40:15Z","title":"Distribution of points with prescribed derivative in polynomial dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05422","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":"sha256:1f8919a5a560dd65b2f49e09ad5e252330de037d3ccfebf9b0b7e9f4ad982029","target":"record","created_at":"2026-05-18T01:12:19Z","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":"cd82ec1fffa08a41e679d610942d101a5f7f22353da99397a45651b294be4c24","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-17T05:40:15Z","title_canon_sha256":"ea0cf64a49fe296e59e582afe9ead8708f7e1b44c3d119fa02f0fc940c0282a0"},"schema_version":"1.0","source":{"id":"1606.05422","kind":"arxiv","version":1}},"canonical_sha256":"0418c828354b68f22b4a9e5373d951cbc3f944e85be113f2d19f20c0bf88a89a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0418c828354b68f22b4a9e5373d951cbc3f944e85be113f2d19f20c0bf88a89a","first_computed_at":"2026-05-18T01:12:19.584101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:19.584101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rdCQ/EDL/C05sBx6ZCPJw8Z8/emUF2HgaWSieqQjggv+relKnNAJiKgou7Q/LPANFPl9lAwI4CHuzpzlP+xxAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:19.584447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.05422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f8919a5a560dd65b2f49e09ad5e252330de037d3ccfebf9b0b7e9f4ad982029","sha256:ef87dd74f47545dd87d74e60be1d7336308eca3c397826de599a727eb96dd3c5"],"state_sha256":"780e6ab64d3f608726cc9c65d3be887d1e8de5e1a2c8d1463a87c3397ecb395b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O6Pp2cA3K1S5BG+zeCCtMnTjz2NwIXB9ykbXPieZaP5uEkBjzrENy2jtSGIPzI0vU3XKSFf5qsSw7RsidEUXBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:08:43.483913Z","bundle_sha256":"441b44fd8ffc18a230fd0eda13c212e7dcc156d379530ce00dc92bdab2be0d59"}}