{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:FF4MQN5GCMC4FQCY4NVPT3GL3A","short_pith_number":"pith:FF4MQN5G","schema_version":"1.0","canonical_sha256":"2978c837a61305c2c058e36af9eccbd82296478e00d5ce5e414fea0d255beff9","source":{"kind":"arxiv","id":"1311.4133","version":1},"attestation_state":"computed","paper":{"title":"A lower bound on the orbit growth of a regular self-map of affine space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Vesselin Dimitrov","submitted_at":"2013-11-17T09:16:18Z","abstract_excerpt":"We show that if $f : \\mathbb{A}_{\\bar{\\mathbb{Q}}}^r \\to \\mathbb{A}_{\\bar{\\mathbb{Q}}}^r$ is a regular self-map and $P \\in \\mathbb{A}^r(\\bar{\\mathbb{Q}})$ has $\\limsup_{n \\in \\mathbb{N}} \\frac{\\log{h_{\\mathrm{aff}}(f^nP)}}{\\log{n}} < 1/r$, where $h_{\\textrm{aff}}$ is the affine Weil height, then $\\mathbb{N}$ partitions into a finite set and finitely many full arithmetic progressions, on each of which the coordinates of $f^nP$ are polynomials in $n$.\n  In particular, if $(f^nP)_{n \\in \\mathbb{N}}$ is a Zariski-dense orbit, then either $n = 1$ and $f$ is of the shape $t \\mapsto \\zeta t + c$, $\\z"},"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":"1311.4133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-17T09:16:18Z","cross_cats_sorted":[],"title_canon_sha256":"f7ea7a8375f0c5f78a43ba2bfdf0cc356cff585228645090ff6c9d7a7f4e21ec","abstract_canon_sha256":"0ac7060857c46dd797311b8fb1418a0158785f11168bc5876d33b2b21781012c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:53.506854Z","signature_b64":"5wvJGqeQD+uXvyxWZh8fRixL2oKSsDE+7ji7uNNZZidwgxM6hcLNvG4FZUc7GRHWAF/4pKZ2DH+6DVcFfdeaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2978c837a61305c2c058e36af9eccbd82296478e00d5ce5e414fea0d255beff9","last_reissued_at":"2026-05-18T03:06:53.506089Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:53.506089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A lower bound on the orbit growth of a regular self-map of affine space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Vesselin Dimitrov","submitted_at":"2013-11-17T09:16:18Z","abstract_excerpt":"We show that if $f : \\mathbb{A}_{\\bar{\\mathbb{Q}}}^r \\to \\mathbb{A}_{\\bar{\\mathbb{Q}}}^r$ is a regular self-map and $P \\in \\mathbb{A}^r(\\bar{\\mathbb{Q}})$ has $\\limsup_{n \\in \\mathbb{N}} \\frac{\\log{h_{\\mathrm{aff}}(f^nP)}}{\\log{n}} < 1/r$, where $h_{\\textrm{aff}}$ is the affine Weil height, then $\\mathbb{N}$ partitions into a finite set and finitely many full arithmetic progressions, on each of which the coordinates of $f^nP$ are polynomials in $n$.\n  In particular, if $(f^nP)_{n \\in \\mathbb{N}}$ is a Zariski-dense orbit, then either $n = 1$ and $f$ is of the shape $t \\mapsto \\zeta t + c$, $\\z"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4133","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1311.4133","created_at":"2026-05-18T03:06:53.506232+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.4133v1","created_at":"2026-05-18T03:06:53.506232+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4133","created_at":"2026-05-18T03:06:53.506232+00:00"},{"alias_kind":"pith_short_12","alias_value":"FF4MQN5GCMC4","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"FF4MQN5GCMC4FQCY","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"FF4MQN5G","created_at":"2026-05-18T12:27:45.050594+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/FF4MQN5GCMC4FQCY4NVPT3GL3A","json":"https://pith.science/pith/FF4MQN5GCMC4FQCY4NVPT3GL3A.json","graph_json":"https://pith.science/api/pith-number/FF4MQN5GCMC4FQCY4NVPT3GL3A/graph.json","events_json":"https://pith.science/api/pith-number/FF4MQN5GCMC4FQCY4NVPT3GL3A/events.json","paper":"https://pith.science/paper/FF4MQN5G"},"agent_actions":{"view_html":"https://pith.science/pith/FF4MQN5GCMC4FQCY4NVPT3GL3A","download_json":"https://pith.science/pith/FF4MQN5GCMC4FQCY4NVPT3GL3A.json","view_paper":"https://pith.science/paper/FF4MQN5G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.4133&json=true","fetch_graph":"https://pith.science/api/pith-number/FF4MQN5GCMC4FQCY4NVPT3GL3A/graph.json","fetch_events":"https://pith.science/api/pith-number/FF4MQN5GCMC4FQCY4NVPT3GL3A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FF4MQN5GCMC4FQCY4NVPT3GL3A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FF4MQN5GCMC4FQCY4NVPT3GL3A/action/storage_attestation","attest_author":"https://pith.science/pith/FF4MQN5GCMC4FQCY4NVPT3GL3A/action/author_attestation","sign_citation":"https://pith.science/pith/FF4MQN5GCMC4FQCY4NVPT3GL3A/action/citation_signature","submit_replication":"https://pith.science/pith/FF4MQN5GCMC4FQCY4NVPT3GL3A/action/replication_record"}},"created_at":"2026-05-18T03:06:53.506232+00:00","updated_at":"2026-05-18T03:06:53.506232+00:00"}