{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:5BLSGANGPHV7II2HIBIEDNMRWO","short_pith_number":"pith:5BLSGANG","schema_version":"1.0","canonical_sha256":"e8572301a679ebf42347405041b591b39583fedd294a46f8943d6ddecdd2c73f","source":{"kind":"arxiv","id":"1502.06009","version":2},"attestation_state":"computed","paper":{"title":"The Parametric Frobenius Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Bjarke Hammersholt Roune, Kevin Woods","submitted_at":"2015-02-20T21:13:42Z","abstract_excerpt":"Given relatively prime positive integers a_1,...,a_n, the Frobenius number is the largest integer that cannot be written as a nonnegative integer combination of the a_i. We examine the parametric version of this problem: given a_i=a_i(t) as functions of t, compute the Frobenius number as a function of t. A function f is a quasi-polynomial if there exists a period m and polynomials f_0,...,f_{m-1} such that f(t)=f_{t mod m}(t) for all positive integers t. We conjecture that, if the a_i(t) are polynomials (or quasi-polynomials) in t, then the Frobenius number agrees with a quasi-polynomial, for "},"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":"1502.06009","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-20T21:13:42Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"8b9b8f46a293ec27d57526362e2e3dea2c1e63b13ccb0470a64f0ae92ec2e57d","abstract_canon_sha256":"1cf902bb3eee05b3287340778ee346a853ef496360b18fdbc19dc3c80233f65f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:50.451373Z","signature_b64":"gakRbcxg4n5EfkbMwqJgo0LdFzlGMYWzMpm1+d2Gsk14jrVGx28c/qOEI2CAS1uRoBsv2zKQgH/+UDfuEX3oCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8572301a679ebf42347405041b591b39583fedd294a46f8943d6ddecdd2c73f","last_reissued_at":"2026-05-18T02:03:50.450527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:50.450527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Parametric Frobenius Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Bjarke Hammersholt Roune, Kevin Woods","submitted_at":"2015-02-20T21:13:42Z","abstract_excerpt":"Given relatively prime positive integers a_1,...,a_n, the Frobenius number is the largest integer that cannot be written as a nonnegative integer combination of the a_i. We examine the parametric version of this problem: given a_i=a_i(t) as functions of t, compute the Frobenius number as a function of t. A function f is a quasi-polynomial if there exists a period m and polynomials f_0,...,f_{m-1} such that f(t)=f_{t mod m}(t) for all positive integers t. We conjecture that, if the a_i(t) are polynomials (or quasi-polynomials) in t, then the Frobenius number agrees with a quasi-polynomial, for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06009","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":"1502.06009","created_at":"2026-05-18T02:03:50.450663+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.06009v2","created_at":"2026-05-18T02:03:50.450663+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06009","created_at":"2026-05-18T02:03:50.450663+00:00"},{"alias_kind":"pith_short_12","alias_value":"5BLSGANGPHV7","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"5BLSGANGPHV7II2H","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"5BLSGANG","created_at":"2026-05-18T12:29:05.191682+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/5BLSGANGPHV7II2HIBIEDNMRWO","json":"https://pith.science/pith/5BLSGANGPHV7II2HIBIEDNMRWO.json","graph_json":"https://pith.science/api/pith-number/5BLSGANGPHV7II2HIBIEDNMRWO/graph.json","events_json":"https://pith.science/api/pith-number/5BLSGANGPHV7II2HIBIEDNMRWO/events.json","paper":"https://pith.science/paper/5BLSGANG"},"agent_actions":{"view_html":"https://pith.science/pith/5BLSGANGPHV7II2HIBIEDNMRWO","download_json":"https://pith.science/pith/5BLSGANGPHV7II2HIBIEDNMRWO.json","view_paper":"https://pith.science/paper/5BLSGANG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.06009&json=true","fetch_graph":"https://pith.science/api/pith-number/5BLSGANGPHV7II2HIBIEDNMRWO/graph.json","fetch_events":"https://pith.science/api/pith-number/5BLSGANGPHV7II2HIBIEDNMRWO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5BLSGANGPHV7II2HIBIEDNMRWO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5BLSGANGPHV7II2HIBIEDNMRWO/action/storage_attestation","attest_author":"https://pith.science/pith/5BLSGANGPHV7II2HIBIEDNMRWO/action/author_attestation","sign_citation":"https://pith.science/pith/5BLSGANGPHV7II2HIBIEDNMRWO/action/citation_signature","submit_replication":"https://pith.science/pith/5BLSGANGPHV7II2HIBIEDNMRWO/action/replication_record"}},"created_at":"2026-05-18T02:03:50.450663+00:00","updated_at":"2026-05-18T02:03:50.450663+00:00"}