{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JZADY7CF4Q54C7AFBPZB6T6ZHK","short_pith_number":"pith:JZADY7CF","schema_version":"1.0","canonical_sha256":"4e403c7c45e43bc17c050bf21f4fd93aaf15867d58b3d00e4f0e868444cf428e","source":{"kind":"arxiv","id":"1907.00763","version":1},"attestation_state":"computed","paper":{"title":"Entire functions polynomially bounded in several variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jorge Mozo Fern\\'andez","submitted_at":"2019-07-01T13:39:38Z","abstract_excerpt":"In this paper we show that if an entire function $f(z_1,z_2)$ of two (or more) complex variables verifies $\\norm{f(z_1,z_2)}\\leq K(\\norm{P(z_1,z_2)})$, where $P(z_1,z_2)$ is a polynomial that is not a power in $\\CC[[z_1,z_2]]$, and $K$ is any positive-valued real function, then $f(z_1,z_2)$ can be written as a holomorphic function of $P$."},"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":"1907.00763","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-07-01T13:39:38Z","cross_cats_sorted":[],"title_canon_sha256":"2b4d8ce6b3c8cb2f07c5de0cbfb2c500be0b2ab7f4c79e0eb10c7ab676d5d7d6","abstract_canon_sha256":"e800b0106af3344b20c48cb054fe7143c6b4da55da222581acd675a8bcb9e8d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:48.202908Z","signature_b64":"BydrqjyTEb2ipV+VKpR8S/8d8/sC17USayGF3SEihp+u4koHtzQ/KRygSQ4fco8lFK+oIh2l7rCpyh79AGY7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e403c7c45e43bc17c050bf21f4fd93aaf15867d58b3d00e4f0e868444cf428e","last_reissued_at":"2026-05-17T23:41:48.202115Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:48.202115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entire functions polynomially bounded in several variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jorge Mozo Fern\\'andez","submitted_at":"2019-07-01T13:39:38Z","abstract_excerpt":"In this paper we show that if an entire function $f(z_1,z_2)$ of two (or more) complex variables verifies $\\norm{f(z_1,z_2)}\\leq K(\\norm{P(z_1,z_2)})$, where $P(z_1,z_2)$ is a polynomial that is not a power in $\\CC[[z_1,z_2]]$, and $K$ is any positive-valued real function, then $f(z_1,z_2)$ can be written as a holomorphic function of $P$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00763","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":"1907.00763","created_at":"2026-05-17T23:41:48.202240+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.00763v1","created_at":"2026-05-17T23:41:48.202240+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00763","created_at":"2026-05-17T23:41:48.202240+00:00"},{"alias_kind":"pith_short_12","alias_value":"JZADY7CF4Q54","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"JZADY7CF4Q54C7AF","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"JZADY7CF","created_at":"2026-05-18T12:33:21.387695+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/JZADY7CF4Q54C7AFBPZB6T6ZHK","json":"https://pith.science/pith/JZADY7CF4Q54C7AFBPZB6T6ZHK.json","graph_json":"https://pith.science/api/pith-number/JZADY7CF4Q54C7AFBPZB6T6ZHK/graph.json","events_json":"https://pith.science/api/pith-number/JZADY7CF4Q54C7AFBPZB6T6ZHK/events.json","paper":"https://pith.science/paper/JZADY7CF"},"agent_actions":{"view_html":"https://pith.science/pith/JZADY7CF4Q54C7AFBPZB6T6ZHK","download_json":"https://pith.science/pith/JZADY7CF4Q54C7AFBPZB6T6ZHK.json","view_paper":"https://pith.science/paper/JZADY7CF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.00763&json=true","fetch_graph":"https://pith.science/api/pith-number/JZADY7CF4Q54C7AFBPZB6T6ZHK/graph.json","fetch_events":"https://pith.science/api/pith-number/JZADY7CF4Q54C7AFBPZB6T6ZHK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JZADY7CF4Q54C7AFBPZB6T6ZHK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JZADY7CF4Q54C7AFBPZB6T6ZHK/action/storage_attestation","attest_author":"https://pith.science/pith/JZADY7CF4Q54C7AFBPZB6T6ZHK/action/author_attestation","sign_citation":"https://pith.science/pith/JZADY7CF4Q54C7AFBPZB6T6ZHK/action/citation_signature","submit_replication":"https://pith.science/pith/JZADY7CF4Q54C7AFBPZB6T6ZHK/action/replication_record"}},"created_at":"2026-05-17T23:41:48.202240+00:00","updated_at":"2026-05-17T23:41:48.202240+00:00"}