{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5YWNQ3B2DCGEB2QGCVST7PSY5E","short_pith_number":"pith:5YWNQ3B2","schema_version":"1.0","canonical_sha256":"ee2cd86c3a188c40ea0615653fbe58e91b9332af082c1489b0ee3ea2e1de3770","source":{"kind":"arxiv","id":"1611.04664","version":2},"attestation_state":"computed","paper":{"title":"Convergence to the Mahler measure and the distribution of periodic points for algebraic Noetherian $\\mathbb{Z}^d$-actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Vesselin Dimitrov","submitted_at":"2016-11-15T01:13:18Z","abstract_excerpt":"For every $P \\in \\mathbb{Z}[x_1^{\\pm 1}, \\ldots, x_d^{\\pm 1}] \\setminus \\{0\\}$, and every $\\varepsilon > 0$, we prove that there are a computable function $M = M(d,\\varepsilon,\\deg{P},h(P)) < \\infty$ and a finite union $Z = Z(d,\\varepsilon,\\deg{P},h(P))$ of proper torsion cosets $\\boldsymbol{\\mu} T \\subsetneq \\mathbb{G}_m^d$ such that, for every $N \\in \\mathbb{N}$, $Z$ contains all but at most $M$ of the torsion points $\\boldsymbol{\\zeta} \\in \\mu_N^d$ satisfying $|P(\\boldsymbol{\\zeta})| < e^{-\\varepsilon \\phi(N)}$. This extends a well known structural theorem from torsion points lying exactly "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.04664","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-15T01:13:18Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"e4701294915d0a31973ebe6db8a167753bf06b065af6436e8f4901ad5c8d6c32","abstract_canon_sha256":"aefc30d0645e39033684501949464536c0171e388448f342bffc827341848475"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:39.804308Z","signature_b64":"xp6tX+00vQovItsy+35GYe2DbuguBVd5G2PPZUfX/32z/qhfVH/piq6l4Vyj0E518gUajpDIG+ymxtEb2I0LDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee2cd86c3a188c40ea0615653fbe58e91b9332af082c1489b0ee3ea2e1de3770","last_reissued_at":"2026-05-18T00:53:39.803940Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:39.803940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence to the Mahler measure and the distribution of periodic points for algebraic Noetherian $\\mathbb{Z}^d$-actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Vesselin Dimitrov","submitted_at":"2016-11-15T01:13:18Z","abstract_excerpt":"For every $P \\in \\mathbb{Z}[x_1^{\\pm 1}, \\ldots, x_d^{\\pm 1}] \\setminus \\{0\\}$, and every $\\varepsilon > 0$, we prove that there are a computable function $M = M(d,\\varepsilon,\\deg{P},h(P)) < \\infty$ and a finite union $Z = Z(d,\\varepsilon,\\deg{P},h(P))$ of proper torsion cosets $\\boldsymbol{\\mu} T \\subsetneq \\mathbb{G}_m^d$ such that, for every $N \\in \\mathbb{N}$, $Z$ contains all but at most $M$ of the torsion points $\\boldsymbol{\\zeta} \\in \\mu_N^d$ satisfying $|P(\\boldsymbol{\\zeta})| < e^{-\\varepsilon \\phi(N)}$. This extends a well known structural theorem from torsion points lying exactly "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04664","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.04664","created_at":"2026-05-18T00:53:39.804007+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.04664v2","created_at":"2026-05-18T00:53:39.804007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04664","created_at":"2026-05-18T00:53:39.804007+00:00"},{"alias_kind":"pith_short_12","alias_value":"5YWNQ3B2DCGE","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5YWNQ3B2DCGEB2QG","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5YWNQ3B2","created_at":"2026-05-18T12:30:01.593930+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5YWNQ3B2DCGEB2QGCVST7PSY5E","json":"https://pith.science/pith/5YWNQ3B2DCGEB2QGCVST7PSY5E.json","graph_json":"https://pith.science/api/pith-number/5YWNQ3B2DCGEB2QGCVST7PSY5E/graph.json","events_json":"https://pith.science/api/pith-number/5YWNQ3B2DCGEB2QGCVST7PSY5E/events.json","paper":"https://pith.science/paper/5YWNQ3B2"},"agent_actions":{"view_html":"https://pith.science/pith/5YWNQ3B2DCGEB2QGCVST7PSY5E","download_json":"https://pith.science/pith/5YWNQ3B2DCGEB2QGCVST7PSY5E.json","view_paper":"https://pith.science/paper/5YWNQ3B2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.04664&json=true","fetch_graph":"https://pith.science/api/pith-number/5YWNQ3B2DCGEB2QGCVST7PSY5E/graph.json","fetch_events":"https://pith.science/api/pith-number/5YWNQ3B2DCGEB2QGCVST7PSY5E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5YWNQ3B2DCGEB2QGCVST7PSY5E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5YWNQ3B2DCGEB2QGCVST7PSY5E/action/storage_attestation","attest_author":"https://pith.science/pith/5YWNQ3B2DCGEB2QGCVST7PSY5E/action/author_attestation","sign_citation":"https://pith.science/pith/5YWNQ3B2DCGEB2QGCVST7PSY5E/action/citation_signature","submit_replication":"https://pith.science/pith/5YWNQ3B2DCGEB2QGCVST7PSY5E/action/replication_record"}},"created_at":"2026-05-18T00:53:39.804007+00:00","updated_at":"2026-05-18T00:53:39.804007+00:00"}