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A $2$-block intersection graph ($2$-BIG) of a ${\\rm{TS}}(v,\\lambda)$ is a graph where each vertex is represented by a block from the ${\\rm{TS}}(v,\\lambda)$ and each pair of blocks $B_i,B_j\\in \\mathcal{B}$ are joined by an edge if $|B_i\\cap B_j|=2$. Using constructions for ${\\rm{TS}}(v,\\lambda)$ given by Schreiber, we show that there exists a ${\\rm{TS}}(v,\\lambda)$ for $v\\equiv 0$ or $4\\pmod{12}$ wh"},"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":"1805.00535","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-01T20:05:41Z","cross_cats_sorted":[],"title_canon_sha256":"d29f3eb3b9d73c23e4942e9573016f051b289c64b4d30c6be83bcdfbe552ceca","abstract_canon_sha256":"d20ed6a546983146ac6dd1c945ab8bd70c4d49897dc99b853746a43d34a5fc73"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:41.368598Z","signature_b64":"o+jloSl4k1ZAYt1iIJWaxkmP9jiUL75raWXwu5rtZsBpdc2YnrByEUL9eudjX7lVhOepQihaB2ak5rJuni/gAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76af204d666a0f16fc2525fbc180ebd8709fb94ea4e7f073cb35bbea2aaa659f","last_reissued_at":"2026-05-17T23:56:41.368143Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:41.368143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"${\\rm{TS}}(v,\\lambda)$ with cyclic 2-intersecting Gray codes: $v\\equiv 0$ or $4\\pmod{12}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"John Asplund, Melissa Keranen","submitted_at":"2018-05-01T20:05:41Z","abstract_excerpt":"A ${\\rm{TS}}(v,\\lambda)$ is a pair $(V,\\mathcal{B})$ where $V$ contains $v$ points and $\\mathcal{B}$ contains $3$-element subsets of $V$ so that each pair in $V$ appears in exactly $\\lambda$ blocks. A $2$-block intersection graph ($2$-BIG) of a ${\\rm{TS}}(v,\\lambda)$ is a graph where each vertex is represented by a block from the ${\\rm{TS}}(v,\\lambda)$ and each pair of blocks $B_i,B_j\\in \\mathcal{B}$ are joined by an edge if $|B_i\\cap B_j|=2$. Using constructions for ${\\rm{TS}}(v,\\lambda)$ given by Schreiber, we show that there exists a ${\\rm{TS}}(v,\\lambda)$ for $v\\equiv 0$ or $4\\pmod{12}$ wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00535","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":"1805.00535","created_at":"2026-05-17T23:56:41.368213+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.00535v2","created_at":"2026-05-17T23:56:41.368213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00535","created_at":"2026-05-17T23:56:41.368213+00:00"},{"alias_kind":"pith_short_12","alias_value":"O2XSATLGNIHR","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"O2XSATLGNIHRN7BF","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"O2XSATLG","created_at":"2026-05-18T12:32:40.477152+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/O2XSATLGNIHRN7BFEX54DAHL3B","json":"https://pith.science/pith/O2XSATLGNIHRN7BFEX54DAHL3B.json","graph_json":"https://pith.science/api/pith-number/O2XSATLGNIHRN7BFEX54DAHL3B/graph.json","events_json":"https://pith.science/api/pith-number/O2XSATLGNIHRN7BFEX54DAHL3B/events.json","paper":"https://pith.science/paper/O2XSATLG"},"agent_actions":{"view_html":"https://pith.science/pith/O2XSATLGNIHRN7BFEX54DAHL3B","download_json":"https://pith.science/pith/O2XSATLGNIHRN7BFEX54DAHL3B.json","view_paper":"https://pith.science/paper/O2XSATLG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.00535&json=true","fetch_graph":"https://pith.science/api/pith-number/O2XSATLGNIHRN7BFEX54DAHL3B/graph.json","fetch_events":"https://pith.science/api/pith-number/O2XSATLGNIHRN7BFEX54DAHL3B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O2XSATLGNIHRN7BFEX54DAHL3B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O2XSATLGNIHRN7BFEX54DAHL3B/action/storage_attestation","attest_author":"https://pith.science/pith/O2XSATLGNIHRN7BFEX54DAHL3B/action/author_attestation","sign_citation":"https://pith.science/pith/O2XSATLGNIHRN7BFEX54DAHL3B/action/citation_signature","submit_replication":"https://pith.science/pith/O2XSATLGNIHRN7BFEX54DAHL3B/action/replication_record"}},"created_at":"2026-05-17T23:56:41.368213+00:00","updated_at":"2026-05-17T23:56:41.368213+00:00"}