{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:6QSYXGRYYRELC2RTM22SCMXM3K","short_pith_number":"pith:6QSYXGRY","schema_version":"1.0","canonical_sha256":"f4258b9a38c448b16a3366b52132ecda8bcd49f48c070a0908fa1dbd62f4a45e","source":{"kind":"arxiv","id":"1204.6714","version":1},"attestation_state":"computed","paper":{"title":"Nested recursions with ceiling function solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abraham Isgur, Stephen M. Tanny, Vitaly Kuznetsov","submitted_at":"2012-04-30T17:48:53Z","abstract_excerpt":"Consider a nested, non-homogeneous recursion R(n) defined by R(n) = \\sum_{i=1}^k R(n-s_i-\\sum_{j=1}^{p_i} R(n-a_ij)) + nu, with c initial conditions R(1) = xi_1 > 0,R(2)=xi_2 > 0, ..., R(c)=xi_c > 0, where the parameters are integers satisfying k > 0, p_i > 0 and a_ij > 0. We develop an algorithm to answer the following question: for an arbitrary rational number r/q, is there any set of values for k, p_i, s_i, a_ij and nu such that the ceiling function ceiling{rn/q} is the unique solution generated by R(n) with appropriate initial conditions? We apply this algorithm to explore those ceiling fu"},"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":"1204.6714","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-30T17:48:53Z","cross_cats_sorted":[],"title_canon_sha256":"d42ed26688870e14b159d9ecff7b6509c078832169562024206e2c2f77a9a3e2","abstract_canon_sha256":"a35474b91e9abab21fee2ddeac6216bef41ad8845b0bd8cd4bd3049576a9fc4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:44.040467Z","signature_b64":"R1p3oE9lGuxQVnzA3a7WdEq5ymYaYajRlj5F/JCoF9/sdaexgQQFANS9zx5H++rBz8yMCnbwFswXkJ58BNcTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4258b9a38c448b16a3366b52132ecda8bcd49f48c070a0908fa1dbd62f4a45e","last_reissued_at":"2026-05-18T03:56:44.039923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:44.039923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nested recursions with ceiling function solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abraham Isgur, Stephen M. Tanny, Vitaly Kuznetsov","submitted_at":"2012-04-30T17:48:53Z","abstract_excerpt":"Consider a nested, non-homogeneous recursion R(n) defined by R(n) = \\sum_{i=1}^k R(n-s_i-\\sum_{j=1}^{p_i} R(n-a_ij)) + nu, with c initial conditions R(1) = xi_1 > 0,R(2)=xi_2 > 0, ..., R(c)=xi_c > 0, where the parameters are integers satisfying k > 0, p_i > 0 and a_ij > 0. We develop an algorithm to answer the following question: for an arbitrary rational number r/q, is there any set of values for k, p_i, s_i, a_ij and nu such that the ceiling function ceiling{rn/q} is the unique solution generated by R(n) with appropriate initial conditions? We apply this algorithm to explore those ceiling fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6714","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":"1204.6714","created_at":"2026-05-18T03:56:44.040003+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.6714v1","created_at":"2026-05-18T03:56:44.040003+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6714","created_at":"2026-05-18T03:56:44.040003+00:00"},{"alias_kind":"pith_short_12","alias_value":"6QSYXGRYYREL","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6QSYXGRYYRELC2RT","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6QSYXGRY","created_at":"2026-05-18T12:26:56.085431+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/6QSYXGRYYRELC2RTM22SCMXM3K","json":"https://pith.science/pith/6QSYXGRYYRELC2RTM22SCMXM3K.json","graph_json":"https://pith.science/api/pith-number/6QSYXGRYYRELC2RTM22SCMXM3K/graph.json","events_json":"https://pith.science/api/pith-number/6QSYXGRYYRELC2RTM22SCMXM3K/events.json","paper":"https://pith.science/paper/6QSYXGRY"},"agent_actions":{"view_html":"https://pith.science/pith/6QSYXGRYYRELC2RTM22SCMXM3K","download_json":"https://pith.science/pith/6QSYXGRYYRELC2RTM22SCMXM3K.json","view_paper":"https://pith.science/paper/6QSYXGRY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.6714&json=true","fetch_graph":"https://pith.science/api/pith-number/6QSYXGRYYRELC2RTM22SCMXM3K/graph.json","fetch_events":"https://pith.science/api/pith-number/6QSYXGRYYRELC2RTM22SCMXM3K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6QSYXGRYYRELC2RTM22SCMXM3K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6QSYXGRYYRELC2RTM22SCMXM3K/action/storage_attestation","attest_author":"https://pith.science/pith/6QSYXGRYYRELC2RTM22SCMXM3K/action/author_attestation","sign_citation":"https://pith.science/pith/6QSYXGRYYRELC2RTM22SCMXM3K/action/citation_signature","submit_replication":"https://pith.science/pith/6QSYXGRYYRELC2RTM22SCMXM3K/action/replication_record"}},"created_at":"2026-05-18T03:56:44.040003+00:00","updated_at":"2026-05-18T03:56:44.040003+00:00"}