{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:SCU6GEAUXOW7XR3SGLIVZF6F4K","short_pith_number":"pith:SCU6GEAU","schema_version":"1.0","canonical_sha256":"90a9e31014bbadfbc77232d15c97c5e2ad594fc5fd3be8f7002dda467a738fc4","source":{"kind":"arxiv","id":"1901.01225","version":1},"attestation_state":"computed","paper":{"title":"Invisible knots and rainbow rings: knots not determined by their determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Dan Sours, James Godzik, Jennifer Jones, Nancy Ho, Thomas W. Mattman","submitted_at":"2019-01-04T17:42:45Z","abstract_excerpt":"We determine p-colorability of the paradromic rings. These rings arise by generalizing the well-known experiment of bisecting a Mobius strip. Instead of joining the ends with a single half twist, use $m$ twists, and, rather than bisecting ($n = 2$), cut the strip into $n$ sections. We call the resulting collection of thin strips $P(m,n)$. By replacing each thin strip with its midline, we think of $P(m,n)$ as a link, that is, a collection of circles in space. Using the notion of $p$-colorability from knot theory, we determine, for each $m$ and $n$, which primes $p$ can be used to color $P(m,n)$"},"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":"1901.01225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-01-04T17:42:45Z","cross_cats_sorted":[],"title_canon_sha256":"2a1bf075f68d0920f5079d509b37d326cb3b5230e2b4271d081ce33ef8d7da59","abstract_canon_sha256":"7e058da6f660283edee347a13c5d71c8f0fb8ba1eb51f2b5ae118f20578aba67"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:56.674026Z","signature_b64":"/Mv46iUN9CFWwq+5ppOTyXKzQ12z92b+vVPkFk6q2Td2oh9Np9IrSMRsKHPmkC4Um1UKdgaL8tKH7FiJXNK9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90a9e31014bbadfbc77232d15c97c5e2ad594fc5fd3be8f7002dda467a738fc4","last_reissued_at":"2026-05-17T23:56:56.673341Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:56.673341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invisible knots and rainbow rings: knots not determined by their determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Dan Sours, James Godzik, Jennifer Jones, Nancy Ho, Thomas W. Mattman","submitted_at":"2019-01-04T17:42:45Z","abstract_excerpt":"We determine p-colorability of the paradromic rings. These rings arise by generalizing the well-known experiment of bisecting a Mobius strip. Instead of joining the ends with a single half twist, use $m$ twists, and, rather than bisecting ($n = 2$), cut the strip into $n$ sections. We call the resulting collection of thin strips $P(m,n)$. By replacing each thin strip with its midline, we think of $P(m,n)$ as a link, that is, a collection of circles in space. Using the notion of $p$-colorability from knot theory, we determine, for each $m$ and $n$, which primes $p$ can be used to color $P(m,n)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01225","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":"1901.01225","created_at":"2026-05-17T23:56:56.673450+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.01225v1","created_at":"2026-05-17T23:56:56.673450+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01225","created_at":"2026-05-17T23:56:56.673450+00:00"},{"alias_kind":"pith_short_12","alias_value":"SCU6GEAUXOW7","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"SCU6GEAUXOW7XR3S","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"SCU6GEAU","created_at":"2026-05-18T12:33:27.125529+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/SCU6GEAUXOW7XR3SGLIVZF6F4K","json":"https://pith.science/pith/SCU6GEAUXOW7XR3SGLIVZF6F4K.json","graph_json":"https://pith.science/api/pith-number/SCU6GEAUXOW7XR3SGLIVZF6F4K/graph.json","events_json":"https://pith.science/api/pith-number/SCU6GEAUXOW7XR3SGLIVZF6F4K/events.json","paper":"https://pith.science/paper/SCU6GEAU"},"agent_actions":{"view_html":"https://pith.science/pith/SCU6GEAUXOW7XR3SGLIVZF6F4K","download_json":"https://pith.science/pith/SCU6GEAUXOW7XR3SGLIVZF6F4K.json","view_paper":"https://pith.science/paper/SCU6GEAU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.01225&json=true","fetch_graph":"https://pith.science/api/pith-number/SCU6GEAUXOW7XR3SGLIVZF6F4K/graph.json","fetch_events":"https://pith.science/api/pith-number/SCU6GEAUXOW7XR3SGLIVZF6F4K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SCU6GEAUXOW7XR3SGLIVZF6F4K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SCU6GEAUXOW7XR3SGLIVZF6F4K/action/storage_attestation","attest_author":"https://pith.science/pith/SCU6GEAUXOW7XR3SGLIVZF6F4K/action/author_attestation","sign_citation":"https://pith.science/pith/SCU6GEAUXOW7XR3SGLIVZF6F4K/action/citation_signature","submit_replication":"https://pith.science/pith/SCU6GEAUXOW7XR3SGLIVZF6F4K/action/replication_record"}},"created_at":"2026-05-17T23:56:56.673450+00:00","updated_at":"2026-05-17T23:56:56.673450+00:00"}