{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:EFDO6PABWX2FWX426KRQH7CEXS","short_pith_number":"pith:EFDO6PAB","canonical_record":{"source":{"id":"2411.12856","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-11-19T20:56:51Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"e0afb23037db01c25c1e50a510fd4d2142f8f5f9753514cf405231b6e10d8453","abstract_canon_sha256":"3c05bde01eceb32f17b9e8163e0bfd894385c3ce78206e36e0137e91aae7026c"},"schema_version":"1.0"},"canonical_sha256":"2146ef3c01b5f45b5f9af2a303fc44bca9a41f7780c2143f9275352aff386ea7","source":{"kind":"arxiv","id":"2411.12856","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.12856","created_at":"2026-07-05T09:58:43Z"},{"alias_kind":"arxiv_version","alias_value":"2411.12856v2","created_at":"2026-07-05T09:58:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12856","created_at":"2026-07-05T09:58:43Z"},{"alias_kind":"pith_short_12","alias_value":"EFDO6PABWX2F","created_at":"2026-07-05T09:58:43Z"},{"alias_kind":"pith_short_16","alias_value":"EFDO6PABWX2FWX42","created_at":"2026-07-05T09:58:43Z"},{"alias_kind":"pith_short_8","alias_value":"EFDO6PAB","created_at":"2026-07-05T09:58:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:EFDO6PABWX2FWX426KRQH7CEXS","target":"record","payload":{"canonical_record":{"source":{"id":"2411.12856","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-11-19T20:56:51Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"e0afb23037db01c25c1e50a510fd4d2142f8f5f9753514cf405231b6e10d8453","abstract_canon_sha256":"3c05bde01eceb32f17b9e8163e0bfd894385c3ce78206e36e0137e91aae7026c"},"schema_version":"1.0"},"canonical_sha256":"2146ef3c01b5f45b5f9af2a303fc44bca9a41f7780c2143f9275352aff386ea7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:58:43.830033Z","signature_b64":"UQ/+E5dC0yproY0dEL+NRFq3Y2CQ96AeBjd+gruw3FgNzpJDWHbiZtEy+qEl/dXyl66JB8J2MhuwucWPBs4oDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2146ef3c01b5f45b5f9af2a303fc44bca9a41f7780c2143f9275352aff386ea7","last_reissued_at":"2026-07-05T09:58:43.829630Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:58:43.829630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.12856","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:58:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yAzyTna2fGSSWrjd1laMmecmMDiq9YyeoRD78UAxEBhVZ6f2s+Hnqc4/qtKLWY82qLYM4+hPMG9fumwBDfd1Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T17:14:45.251898Z"},"content_sha256":"61a1ab046cd1401fd0b84926be96603c96fcaa7b1f49fea1797e6d5dac3ab0bc","schema_version":"1.0","event_id":"sha256:61a1ab046cd1401fd0b84926be96603c96fcaa7b1f49fea1797e6d5dac3ab0bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:EFDO6PABWX2FWX426KRQH7CEXS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Independence of multipliers in several variables complex dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Igors Gorbovickis, Johan Taflin","submitted_at":"2024-11-19T20:56:51Z","abstract_excerpt":"We establish the independence of multipliers for polynomial endomorphisms of $\\mathbb C^n$ and endomorphisms of $\\mathbb P^n.$ This allows us to extend results about the bifurcation measure and the critical height obtained in \\cite{arXiv:2305.02246} to the case of polynomial endomorphisms of $\\mathbb C^n$ for $n\\geq 3$. An important step in the proof is the irreducibility of the spaces of endomorphisms with $N$ marked periodic points, which is of independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12856","kind":"arxiv","version":2},"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/2411.12856/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":"2026-07-05T09:58:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"43hEVcVBOidwSPtWkCFHTKnK3Nl4S6aK5sJxAaXFqT6C8bj3DWzPV3UzFt8un2c03YwpvSbemUYup8hUaBt9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T17:14:45.252229Z"},"content_sha256":"89648f23c41a8258ce426a64a99fa60e45b4e9570e7ef50c72b6d39a7a71f118","schema_version":"1.0","event_id":"sha256:89648f23c41a8258ce426a64a99fa60e45b4e9570e7ef50c72b6d39a7a71f118"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EFDO6PABWX2FWX426KRQH7CEXS/bundle.json","state_url":"https://pith.science/pith/EFDO6PABWX2FWX426KRQH7CEXS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EFDO6PABWX2FWX426KRQH7CEXS/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":"2026-08-20T17:14:45Z","links":{"resolver":"https://pith.science/pith/EFDO6PABWX2FWX426KRQH7CEXS","bundle":"https://pith.science/pith/EFDO6PABWX2FWX426KRQH7CEXS/bundle.json","state":"https://pith.science/pith/EFDO6PABWX2FWX426KRQH7CEXS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EFDO6PABWX2FWX426KRQH7CEXS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:EFDO6PABWX2FWX426KRQH7CEXS","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":"3c05bde01eceb32f17b9e8163e0bfd894385c3ce78206e36e0137e91aae7026c","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-11-19T20:56:51Z","title_canon_sha256":"e0afb23037db01c25c1e50a510fd4d2142f8f5f9753514cf405231b6e10d8453"},"schema_version":"1.0","source":{"id":"2411.12856","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.12856","created_at":"2026-07-05T09:58:43Z"},{"alias_kind":"arxiv_version","alias_value":"2411.12856v2","created_at":"2026-07-05T09:58:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12856","created_at":"2026-07-05T09:58:43Z"},{"alias_kind":"pith_short_12","alias_value":"EFDO6PABWX2F","created_at":"2026-07-05T09:58:43Z"},{"alias_kind":"pith_short_16","alias_value":"EFDO6PABWX2FWX42","created_at":"2026-07-05T09:58:43Z"},{"alias_kind":"pith_short_8","alias_value":"EFDO6PAB","created_at":"2026-07-05T09:58:43Z"}],"graph_snapshots":[{"event_id":"sha256:89648f23c41a8258ce426a64a99fa60e45b4e9570e7ef50c72b6d39a7a71f118","target":"graph","created_at":"2026-07-05T09:58:43Z","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/2411.12856/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish the independence of multipliers for polynomial endomorphisms of $\\mathbb C^n$ and endomorphisms of $\\mathbb P^n.$ This allows us to extend results about the bifurcation measure and the critical height obtained in \\cite{arXiv:2305.02246} to the case of polynomial endomorphisms of $\\mathbb C^n$ for $n\\geq 3$. An important step in the proof is the irreducibility of the spaces of endomorphisms with $N$ marked periodic points, which is of independent interest.","authors_text":"Igors Gorbovickis, Johan Taflin","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-11-19T20:56:51Z","title":"Independence of multipliers in several variables complex dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12856","kind":"arxiv","version":2},"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":"sha256:61a1ab046cd1401fd0b84926be96603c96fcaa7b1f49fea1797e6d5dac3ab0bc","target":"record","created_at":"2026-07-05T09:58:43Z","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":"3c05bde01eceb32f17b9e8163e0bfd894385c3ce78206e36e0137e91aae7026c","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-11-19T20:56:51Z","title_canon_sha256":"e0afb23037db01c25c1e50a510fd4d2142f8f5f9753514cf405231b6e10d8453"},"schema_version":"1.0","source":{"id":"2411.12856","kind":"arxiv","version":2}},"canonical_sha256":"2146ef3c01b5f45b5f9af2a303fc44bca9a41f7780c2143f9275352aff386ea7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2146ef3c01b5f45b5f9af2a303fc44bca9a41f7780c2143f9275352aff386ea7","first_computed_at":"2026-07-05T09:58:43.829630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:58:43.829630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UQ/+E5dC0yproY0dEL+NRFq3Y2CQ96AeBjd+gruw3FgNzpJDWHbiZtEy+qEl/dXyl66JB8J2MhuwucWPBs4oDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:58:43.830033Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.12856","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61a1ab046cd1401fd0b84926be96603c96fcaa7b1f49fea1797e6d5dac3ab0bc","sha256:89648f23c41a8258ce426a64a99fa60e45b4e9570e7ef50c72b6d39a7a71f118"],"state_sha256":"5fb9f3652f94b327660c7af727fff7aa97aec2c5024b124c5687353b42f2f7a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d1ePCEAKv1Qmbz24au0IAQCBDmIqE5svDPmFJYpprWAjws2h6Ls0CSkiletHjdUZfg4zyacENDCCVGWp6eu7DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T17:14:45.255290Z","bundle_sha256":"e322f425bd38fa373a856ffef1a9f4b51b35b7c072e687e0ee1094462cab53ff"}}