{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PUYMG3BOTT6TZK6JLS4L4TZQHY","short_pith_number":"pith:PUYMG3BO","schema_version":"1.0","canonical_sha256":"7d30c36c2e9cfd3cabc95cb8be4f303e1a7ac8dc408a90b98e88f0151692e03c","source":{"kind":"arxiv","id":"1506.03726","version":2},"attestation_state":"computed","paper":{"title":"Lacunaryx: Computing bounded-degree factors of lacunary polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"cs.MS","authors_text":"Bruno Grenet","submitted_at":"2015-06-11T16:08:54Z","abstract_excerpt":"In this paper, we report on an implementation in the free software Mathemagix of lacunary factorization algorithms, distributed as a library called Lacunaryx. These algorithms take as input a polynomial in sparse representation, that is as a list of nonzero monomials, and an integer $d$, and compute its irreducible degree-$\\le d$ factors. The complexity of these algorithms is polynomial in the sparse size of the input polynomial and $d$."},"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":"1506.03726","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2015-06-11T16:08:54Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"3e068ccc57b017aa24a866c125a40fd44780bb969c6941b4db5a1ad2aeb2c536","abstract_canon_sha256":"0d60a3da24c917e3d6f23489f5b0b112fe1265b8c38c2a51244f15bdb7e8dacc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:26.155355Z","signature_b64":"XA6ev/9SnPuJmZ+qB3vwj0py4TWNplcfdhjMhOZhcJ9ApEgKSh6NxgQFQF51X5efMYNWgE+IvXwHLbIIoRBrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d30c36c2e9cfd3cabc95cb8be4f303e1a7ac8dc408a90b98e88f0151692e03c","last_reissued_at":"2026-05-18T01:20:26.154690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:26.154690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lacunaryx: Computing bounded-degree factors of lacunary polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"cs.MS","authors_text":"Bruno Grenet","submitted_at":"2015-06-11T16:08:54Z","abstract_excerpt":"In this paper, we report on an implementation in the free software Mathemagix of lacunary factorization algorithms, distributed as a library called Lacunaryx. These algorithms take as input a polynomial in sparse representation, that is as a list of nonzero monomials, and an integer $d$, and compute its irreducible degree-$\\le d$ factors. The complexity of these algorithms is polynomial in the sparse size of the input polynomial and $d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03726","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":"1506.03726","created_at":"2026-05-18T01:20:26.154787+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.03726v2","created_at":"2026-05-18T01:20:26.154787+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03726","created_at":"2026-05-18T01:20:26.154787+00:00"},{"alias_kind":"pith_short_12","alias_value":"PUYMG3BOTT6T","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PUYMG3BOTT6TZK6J","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PUYMG3BO","created_at":"2026-05-18T12:29:37.295048+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/PUYMG3BOTT6TZK6JLS4L4TZQHY","json":"https://pith.science/pith/PUYMG3BOTT6TZK6JLS4L4TZQHY.json","graph_json":"https://pith.science/api/pith-number/PUYMG3BOTT6TZK6JLS4L4TZQHY/graph.json","events_json":"https://pith.science/api/pith-number/PUYMG3BOTT6TZK6JLS4L4TZQHY/events.json","paper":"https://pith.science/paper/PUYMG3BO"},"agent_actions":{"view_html":"https://pith.science/pith/PUYMG3BOTT6TZK6JLS4L4TZQHY","download_json":"https://pith.science/pith/PUYMG3BOTT6TZK6JLS4L4TZQHY.json","view_paper":"https://pith.science/paper/PUYMG3BO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.03726&json=true","fetch_graph":"https://pith.science/api/pith-number/PUYMG3BOTT6TZK6JLS4L4TZQHY/graph.json","fetch_events":"https://pith.science/api/pith-number/PUYMG3BOTT6TZK6JLS4L4TZQHY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PUYMG3BOTT6TZK6JLS4L4TZQHY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PUYMG3BOTT6TZK6JLS4L4TZQHY/action/storage_attestation","attest_author":"https://pith.science/pith/PUYMG3BOTT6TZK6JLS4L4TZQHY/action/author_attestation","sign_citation":"https://pith.science/pith/PUYMG3BOTT6TZK6JLS4L4TZQHY/action/citation_signature","submit_replication":"https://pith.science/pith/PUYMG3BOTT6TZK6JLS4L4TZQHY/action/replication_record"}},"created_at":"2026-05-18T01:20:26.154787+00:00","updated_at":"2026-05-18T01:20:26.154787+00:00"}