{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6PJFVEATOQVV4C2SOS5HS5RZ2R","short_pith_number":"pith:6PJFVEAT","schema_version":"1.0","canonical_sha256":"f3d25a9013742b5e0b5274ba797639d4734f4332f5387ec515b54a88b6411e5a","source":{"kind":"arxiv","id":"1511.03237","version":1},"attestation_state":"computed","paper":{"title":"On unavoidable obstructions in Gaussian walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ram Krishna Pandey, Sai Teja Somu","submitted_at":"2015-11-10T19:52:18Z","abstract_excerpt":"In this paper we investigate a problem about certain walks in the ring of Gaussian integers. Let $n,d$ be two natural numbers. Does there exist a sequence of Gaussian integers $z_j$ such that $|z_{j+1}-z_j|=1$ and a pair of indices $r$ and $s$, such that $z_{r}-z_{s}=n$ and for all indices $t$ and $u$, $z_{t}-z_{u}\\neq d$? If there exists such a sequence we call $n$ to be $d$ avoidable. Let $A_n$ be the set of all $d\\in \\mathbb{N}$ such that $n$ is not $d$ avoidable. Recently, Ledoan and Zaharescu proved that $\\{d \\in \\mathbb{N} : d|n\\}\\subset A_n$. We extend this result by giving a necessary "},"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":"1511.03237","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-10T19:52:18Z","cross_cats_sorted":[],"title_canon_sha256":"c7b0b91b170064adcfa16e7ca249f9f289aba0a662984757146dc544a3b326c1","abstract_canon_sha256":"88baac5f351ff0439b8bc9925e803da25f9e938a8df81539916ce20fb4252ff5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:16.709787Z","signature_b64":"rxIY7uyNvI/De8LRM6kX9Ap86tCjO7PpAMkFq5ZEQUqCP4faimqnyezIFaYxAmbAn8Pe/sA2wgWC70rCeTQ5Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3d25a9013742b5e0b5274ba797639d4734f4332f5387ec515b54a88b6411e5a","last_reissued_at":"2026-05-18T01:27:16.709334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:16.709334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On unavoidable obstructions in Gaussian walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ram Krishna Pandey, Sai Teja Somu","submitted_at":"2015-11-10T19:52:18Z","abstract_excerpt":"In this paper we investigate a problem about certain walks in the ring of Gaussian integers. Let $n,d$ be two natural numbers. Does there exist a sequence of Gaussian integers $z_j$ such that $|z_{j+1}-z_j|=1$ and a pair of indices $r$ and $s$, such that $z_{r}-z_{s}=n$ and for all indices $t$ and $u$, $z_{t}-z_{u}\\neq d$? If there exists such a sequence we call $n$ to be $d$ avoidable. Let $A_n$ be the set of all $d\\in \\mathbb{N}$ such that $n$ is not $d$ avoidable. Recently, Ledoan and Zaharescu proved that $\\{d \\in \\mathbb{N} : d|n\\}\\subset A_n$. We extend this result by giving a necessary "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03237","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":"1511.03237","created_at":"2026-05-18T01:27:16.709408+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.03237v1","created_at":"2026-05-18T01:27:16.709408+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03237","created_at":"2026-05-18T01:27:16.709408+00:00"},{"alias_kind":"pith_short_12","alias_value":"6PJFVEATOQVV","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6PJFVEATOQVV4C2S","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6PJFVEAT","created_at":"2026-05-18T12:29:07.941421+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/6PJFVEATOQVV4C2SOS5HS5RZ2R","json":"https://pith.science/pith/6PJFVEATOQVV4C2SOS5HS5RZ2R.json","graph_json":"https://pith.science/api/pith-number/6PJFVEATOQVV4C2SOS5HS5RZ2R/graph.json","events_json":"https://pith.science/api/pith-number/6PJFVEATOQVV4C2SOS5HS5RZ2R/events.json","paper":"https://pith.science/paper/6PJFVEAT"},"agent_actions":{"view_html":"https://pith.science/pith/6PJFVEATOQVV4C2SOS5HS5RZ2R","download_json":"https://pith.science/pith/6PJFVEATOQVV4C2SOS5HS5RZ2R.json","view_paper":"https://pith.science/paper/6PJFVEAT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.03237&json=true","fetch_graph":"https://pith.science/api/pith-number/6PJFVEATOQVV4C2SOS5HS5RZ2R/graph.json","fetch_events":"https://pith.science/api/pith-number/6PJFVEATOQVV4C2SOS5HS5RZ2R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6PJFVEATOQVV4C2SOS5HS5RZ2R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6PJFVEATOQVV4C2SOS5HS5RZ2R/action/storage_attestation","attest_author":"https://pith.science/pith/6PJFVEATOQVV4C2SOS5HS5RZ2R/action/author_attestation","sign_citation":"https://pith.science/pith/6PJFVEATOQVV4C2SOS5HS5RZ2R/action/citation_signature","submit_replication":"https://pith.science/pith/6PJFVEATOQVV4C2SOS5HS5RZ2R/action/replication_record"}},"created_at":"2026-05-18T01:27:16.709408+00:00","updated_at":"2026-05-18T01:27:16.709408+00:00"}