{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:EMGFJU6QQV2NNEWJALOJMGMZH6","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":"61df8ae2f9e227401956be189b16de8fa49b990eb3a6d9354850e269ec7ffc96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-02T07:35:48Z","title_canon_sha256":"68cdf61a0e74aefdfbf32dbb4febd377dedc5efc1679d73cb6359546122d8bb5"},"schema_version":"1.0","source":{"id":"2412.01216","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.01216","created_at":"2026-07-05T10:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"2412.01216v2","created_at":"2026-07-05T10:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.01216","created_at":"2026-07-05T10:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"EMGFJU6QQV2N","created_at":"2026-07-05T10:41:18Z"},{"alias_kind":"pith_short_16","alias_value":"EMGFJU6QQV2NNEWJ","created_at":"2026-07-05T10:41:18Z"},{"alias_kind":"pith_short_8","alias_value":"EMGFJU6Q","created_at":"2026-07-05T10:41:18Z"}],"graph_snapshots":[{"event_id":"sha256:46a275b8034a24f1cf730b018783c92fcf433bfd5c077dcbab67e0b25a95f65c","target":"graph","created_at":"2026-07-05T10:41:18Z","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/2412.01216/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X$ be a smooth irreducible projective variety over a field $\\mathbf{k}$ of dimension $d.$ Let $\\tau: \\mathbb{Q}_l\\to \\mathbb{C}$ be any field embedding. Let $f: X\\to X$ be a surjective endomorphism. We show that for every $i=0,\\dots,2d$, the spectral radius of $f^*$ on the numerical group $N^i(X)\\otimes \\mathbb{R}$ and on the $l$-adic cohomology group $H^{2i}(X_{\\overline{\\mathbf{k}}},\\mathbb{Q}_l)\\otimes \\mathbb{C}$ are the same. As a consequence, if $f$ is $q$-polarized for some $q>1$, we show that the norm of every eigenvalue of $f^*$ on the $j$-th cohomology group is $q^{j/2}$ for all","authors_text":"Junyi Xie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-02T07:35:48Z","title":"Numerical spectrums control Cohomological spectrums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.01216","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:fe1fd71d7b4b7edc226d2010f3443c4d23a41263adad6b5ca1bcdac9cc2de1b2","target":"record","created_at":"2026-07-05T10:41:18Z","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":"61df8ae2f9e227401956be189b16de8fa49b990eb3a6d9354850e269ec7ffc96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-02T07:35:48Z","title_canon_sha256":"68cdf61a0e74aefdfbf32dbb4febd377dedc5efc1679d73cb6359546122d8bb5"},"schema_version":"1.0","source":{"id":"2412.01216","kind":"arxiv","version":2}},"canonical_sha256":"230c54d3d08574d692c902dc9619993f896411bd974b1dac251bda91af878e20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"230c54d3d08574d692c902dc9619993f896411bd974b1dac251bda91af878e20","first_computed_at":"2026-07-05T10:41:18.126539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:41:18.126539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ACg5iLRUZXn97DRKzoXVrBnWLG+ScxMyzODjrxif37ivBbQWy+AedEuwjieTLzaTr1ZQVXKm++iMvSc9gp+PBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:41:18.127028Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.01216","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe1fd71d7b4b7edc226d2010f3443c4d23a41263adad6b5ca1bcdac9cc2de1b2","sha256:46a275b8034a24f1cf730b018783c92fcf433bfd5c077dcbab67e0b25a95f65c"],"state_sha256":"f4bea60781a2d0d12d616175316aa5034c021c7f50bf354ba4c8d2b452e5367f"}