{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:FDOND5TI53JBPNRIIUZANX426P","short_pith_number":"pith:FDOND5TI","schema_version":"1.0","canonical_sha256":"28dcd1f668eed217b628453206df9af3d1cb933212001e2f23f2b90cd9096d91","source":{"kind":"arxiv","id":"1101.0526","version":2},"attestation_state":"computed","paper":{"title":"Hadamard grade of power series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"J.-P. Allouche, M. Mend\\`es France","submitted_at":"2011-01-03T14:06:58Z","abstract_excerpt":"The Hadamard product of two power series $\\sum a_n z^n$ and $\\sum b_n z^n$ is the power series $\\sum a_n b_n z^n$. We define the (Hadamard) grade of a power series $A$ to be the least number (finite or infinite) of algebraic power series, the Hadamard product of which equals $A$. We study and discuss this notion."},"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":"1101.0526","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-01-03T14:06:58Z","cross_cats_sorted":[],"title_canon_sha256":"511427362782b9382534569794c102627aeca2e120b69e5cfdc6ccde24a47233","abstract_canon_sha256":"86c4ac75d00864d1abf2ee548673c888c1daab5cea6615f24e94e7c89e2167ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:33.332009Z","signature_b64":"UVXU11wVwZOSZ7Y/fSwiYz5t9JQ0a3elqHwEqxCci3aXlhqBliIk0WerhYHQx2cbWoYqbAgdJ8fzh9o4sNoxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28dcd1f668eed217b628453206df9af3d1cb933212001e2f23f2b90cd9096d91","last_reissued_at":"2026-05-18T04:06:33.331444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:33.331444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hadamard grade of power series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"J.-P. Allouche, M. Mend\\`es France","submitted_at":"2011-01-03T14:06:58Z","abstract_excerpt":"The Hadamard product of two power series $\\sum a_n z^n$ and $\\sum b_n z^n$ is the power series $\\sum a_n b_n z^n$. We define the (Hadamard) grade of a power series $A$ to be the least number (finite or infinite) of algebraic power series, the Hadamard product of which equals $A$. We study and discuss this notion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0526","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":"1101.0526","created_at":"2026-05-18T04:06:33.331540+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.0526v2","created_at":"2026-05-18T04:06:33.331540+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0526","created_at":"2026-05-18T04:06:33.331540+00:00"},{"alias_kind":"pith_short_12","alias_value":"FDOND5TI53JB","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FDOND5TI53JBPNRI","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FDOND5TI","created_at":"2026-05-18T12:26:28.662955+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/FDOND5TI53JBPNRIIUZANX426P","json":"https://pith.science/pith/FDOND5TI53JBPNRIIUZANX426P.json","graph_json":"https://pith.science/api/pith-number/FDOND5TI53JBPNRIIUZANX426P/graph.json","events_json":"https://pith.science/api/pith-number/FDOND5TI53JBPNRIIUZANX426P/events.json","paper":"https://pith.science/paper/FDOND5TI"},"agent_actions":{"view_html":"https://pith.science/pith/FDOND5TI53JBPNRIIUZANX426P","download_json":"https://pith.science/pith/FDOND5TI53JBPNRIIUZANX426P.json","view_paper":"https://pith.science/paper/FDOND5TI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.0526&json=true","fetch_graph":"https://pith.science/api/pith-number/FDOND5TI53JBPNRIIUZANX426P/graph.json","fetch_events":"https://pith.science/api/pith-number/FDOND5TI53JBPNRIIUZANX426P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FDOND5TI53JBPNRIIUZANX426P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FDOND5TI53JBPNRIIUZANX426P/action/storage_attestation","attest_author":"https://pith.science/pith/FDOND5TI53JBPNRIIUZANX426P/action/author_attestation","sign_citation":"https://pith.science/pith/FDOND5TI53JBPNRIIUZANX426P/action/citation_signature","submit_replication":"https://pith.science/pith/FDOND5TI53JBPNRIIUZANX426P/action/replication_record"}},"created_at":"2026-05-18T04:06:33.331540+00:00","updated_at":"2026-05-18T04:06:33.331540+00:00"}