{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:S2KRENRTBXO57JNIMZ66WIOFTN","short_pith_number":"pith:S2KRENRT","schema_version":"1.0","canonical_sha256":"96951236330ddddfa5a8667deb21c59b7176b6578da8baa2d65a5988ac6c1422","source":{"kind":"arxiv","id":"1611.02354","version":3},"attestation_state":"computed","paper":{"title":"On a condition equivalent to the Maximum Distance Separable conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Daniel Kaiser, Jeffery Sun, Steven Damelin","submitted_at":"2016-11-08T01:10:35Z","abstract_excerpt":"We denote by $\\mathcal{P}_q$ the vector space of functions from a finite field $\\mathbb{F}_q$ to itself, which can be represented as the space $\\mathcal{P}_q := \\mathbb{F}_q[x]/(x^q-x)$ of polynomial functions. We denote by $\\mathcal{O}_n \\subset \\mathcal{P}_q$ the set of polynomials that are either the zero polynomial, or have at most $n$ distinct roots in $\\mathbb{F}_q$. Given two subspaces $Y,Z$ of $\\mathcal{P}_q$, we denote by $\\langle Y,Z \\rangle$ their span. We prove that the following are equivalent.\n  A) Let $k, q$ integers, with $q$ a prime power and $2 \\leq k \\leq q$. Suppose that ei"},"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":"1611.02354","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-08T01:10:35Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"75d5d55ea37314d82f83e25617b67dacdd7aea8c32bc14e45f38ba17aef7d64f","abstract_canon_sha256":"2c004158ed514c660669c9de9e4a0a9cac05034a534c2baa3e47abfff6b673ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:05.853686Z","signature_b64":"XtSfZ/TU4f3pa6f4JOqCgApI4xWsgLIcuSzHeS6RGJr437Gp3tNK6qjzO4hIw2yskO2TkyOG85j+uPl6oF8/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96951236330ddddfa5a8667deb21c59b7176b6578da8baa2d65a5988ac6c1422","last_reissued_at":"2026-05-18T00:05:05.852923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:05.852923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a condition equivalent to the Maximum Distance Separable conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Daniel Kaiser, Jeffery Sun, Steven Damelin","submitted_at":"2016-11-08T01:10:35Z","abstract_excerpt":"We denote by $\\mathcal{P}_q$ the vector space of functions from a finite field $\\mathbb{F}_q$ to itself, which can be represented as the space $\\mathcal{P}_q := \\mathbb{F}_q[x]/(x^q-x)$ of polynomial functions. We denote by $\\mathcal{O}_n \\subset \\mathcal{P}_q$ the set of polynomials that are either the zero polynomial, or have at most $n$ distinct roots in $\\mathbb{F}_q$. Given two subspaces $Y,Z$ of $\\mathcal{P}_q$, we denote by $\\langle Y,Z \\rangle$ their span. We prove that the following are equivalent.\n  A) Let $k, q$ integers, with $q$ a prime power and $2 \\leq k \\leq q$. Suppose that ei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02354","kind":"arxiv","version":3},"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":"1611.02354","created_at":"2026-05-18T00:05:05.853035+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.02354v3","created_at":"2026-05-18T00:05:05.853035+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02354","created_at":"2026-05-18T00:05:05.853035+00:00"},{"alias_kind":"pith_short_12","alias_value":"S2KRENRTBXO5","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"S2KRENRTBXO57JNI","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"S2KRENRT","created_at":"2026-05-18T12:30:41.710351+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/S2KRENRTBXO57JNIMZ66WIOFTN","json":"https://pith.science/pith/S2KRENRTBXO57JNIMZ66WIOFTN.json","graph_json":"https://pith.science/api/pith-number/S2KRENRTBXO57JNIMZ66WIOFTN/graph.json","events_json":"https://pith.science/api/pith-number/S2KRENRTBXO57JNIMZ66WIOFTN/events.json","paper":"https://pith.science/paper/S2KRENRT"},"agent_actions":{"view_html":"https://pith.science/pith/S2KRENRTBXO57JNIMZ66WIOFTN","download_json":"https://pith.science/pith/S2KRENRTBXO57JNIMZ66WIOFTN.json","view_paper":"https://pith.science/paper/S2KRENRT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.02354&json=true","fetch_graph":"https://pith.science/api/pith-number/S2KRENRTBXO57JNIMZ66WIOFTN/graph.json","fetch_events":"https://pith.science/api/pith-number/S2KRENRTBXO57JNIMZ66WIOFTN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S2KRENRTBXO57JNIMZ66WIOFTN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S2KRENRTBXO57JNIMZ66WIOFTN/action/storage_attestation","attest_author":"https://pith.science/pith/S2KRENRTBXO57JNIMZ66WIOFTN/action/author_attestation","sign_citation":"https://pith.science/pith/S2KRENRTBXO57JNIMZ66WIOFTN/action/citation_signature","submit_replication":"https://pith.science/pith/S2KRENRTBXO57JNIMZ66WIOFTN/action/replication_record"}},"created_at":"2026-05-18T00:05:05.853035+00:00","updated_at":"2026-05-18T00:05:05.853035+00:00"}