{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DOUT2Z5A7C6RB3UDLOJT6QEWR5","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":"55fa5b76275984350b2ed42a344dfc7a0c6b3caac678c2e59e5d061da8bd9ad8","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-07-17T14:56:46Z","title_canon_sha256":"c037389c99cbe946e57a1a1e240022ed5f484f0eaf0e7f01aefef3546fd638a6"},"schema_version":"1.0","source":{"id":"1807.06483","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06483","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06483v1","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06483","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"pith_short_12","alias_value":"DOUT2Z5A7C6R","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DOUT2Z5A7C6RB3UD","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DOUT2Z5A","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:c93da921a4c0cf3df24d330085f5528191536c3b5f2c98d063606c6b4152bca4","target":"graph","created_at":"2026-05-18T00:10:32Z","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":"Let $f : X\\to X$ be a dominating meromorphic map on a compact K\\\"ahler manifold $X$ of dimension $k$. We extend the notion of topological entropy $h^l_{\\mathrm{top}}(f)$ for the action of $f$ on (local) analytic sets of dimension $0\\leq l \\leq k$. For an ergodic probability measure $\\nu$, we extend similarly the notion of measure-theoretic entropy $h_{\\nu}^l(f)$.\n  Under mild hypothesis, we compute $h^l_{\\mathrm{top}}(f)$ in term of the dynamical degrees of $f$. In the particular case of endomorphisms of $\\mathbb{P}^2$ of degree $d$, we show that $h^1_{\\mathrm{top}}(f)= \\log d$ for a large cla","authors_text":"Gabriel Vigny, Henry De Th\\'elin","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-07-17T14:56:46Z","title":"Entropy of meromorphic maps acting on analytic sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06483","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":"sha256:6cfde28856bc823472977aca9f2f394fe4c23b7c93e10955871b35f7889d1943","target":"record","created_at":"2026-05-18T00:10:32Z","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":"55fa5b76275984350b2ed42a344dfc7a0c6b3caac678c2e59e5d061da8bd9ad8","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-07-17T14:56:46Z","title_canon_sha256":"c037389c99cbe946e57a1a1e240022ed5f484f0eaf0e7f01aefef3546fd638a6"},"schema_version":"1.0","source":{"id":"1807.06483","kind":"arxiv","version":1}},"canonical_sha256":"1ba93d67a0f8bd10ee835b933f40968f751ce400aa80dbdacdc5e9f11d168e7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ba93d67a0f8bd10ee835b933f40968f751ce400aa80dbdacdc5e9f11d168e7d","first_computed_at":"2026-05-18T00:10:32.886997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:32.886997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/bwLpNvLuUr5Rf7K+h0a4rAQ4uubwm2NhQ36+d1NSaNjo3qZmECK44T8VycJqORv9bAi3Ayry0UnvwvBd5N1Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:32.887733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06483","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cfde28856bc823472977aca9f2f394fe4c23b7c93e10955871b35f7889d1943","sha256:c93da921a4c0cf3df24d330085f5528191536c3b5f2c98d063606c6b4152bca4"],"state_sha256":"c18f18125ee7f3c57e79f6230ae820b541dc2ca7edbe2623d39702657231f43c"}