{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:O2XSATLGNIHRN7BFEX54DAHL3B","short_pith_number":"pith:O2XSATLG","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"},"canonical_sha256":"76af204d666a0f16fc2525fbc180ebd8709fb94ea4e7f073cb35bbea2aaa659f","source":{"kind":"arxiv","id":"1805.00535","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00535","created_at":"2026-05-17T23:56:41Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00535v2","created_at":"2026-05-17T23:56:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00535","created_at":"2026-05-17T23:56:41Z"},{"alias_kind":"pith_short_12","alias_value":"O2XSATLGNIHR","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"O2XSATLGNIHRN7BF","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"O2XSATLG","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:O2XSATLGNIHRN7BFEX54DAHL3B","target":"record","payload":{"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"},"canonical_sha256":"76af204d666a0f16fc2525fbc180ebd8709fb94ea4e7f073cb35bbea2aaa659f","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"},"source_kind":"arxiv","source_id":"1805.00535","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JjlD3fUD6XvGmMqLXkrDNeEg2E7o9fN2hSiWSb1zXsG10gxslm1WuB4nFN9uyeFF6dOj3ioLBHj5uQ7bEzmYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:03:25.313170Z"},"content_sha256":"0fe4f55e6302fa39ff2fef2758c46b4c32c92ea0cc18fa79806981dd03a45543","schema_version":"1.0","event_id":"sha256:0fe4f55e6302fa39ff2fef2758c46b4c32c92ea0cc18fa79806981dd03a45543"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:O2XSATLGNIHRN7BFEX54DAHL3B","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CsvgySBV3HehwJYbPnRRVU3czQRT8+vCG6dtk7C9vZzMuWBtfFBjjOCWU4YAzrIbI9C3La2WSZRMpFXlwatFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:03:25.313529Z"},"content_sha256":"23b0cfe75667538c0fdbd15affa96ea7175b9b812411dabd935f7ce6d07810c8","schema_version":"1.0","event_id":"sha256:23b0cfe75667538c0fdbd15affa96ea7175b9b812411dabd935f7ce6d07810c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O2XSATLGNIHRN7BFEX54DAHL3B/bundle.json","state_url":"https://pith.science/pith/O2XSATLGNIHRN7BFEX54DAHL3B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O2XSATLGNIHRN7BFEX54DAHL3B/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T23:03:25Z","links":{"resolver":"https://pith.science/pith/O2XSATLGNIHRN7BFEX54DAHL3B","bundle":"https://pith.science/pith/O2XSATLGNIHRN7BFEX54DAHL3B/bundle.json","state":"https://pith.science/pith/O2XSATLGNIHRN7BFEX54DAHL3B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O2XSATLGNIHRN7BFEX54DAHL3B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O2XSATLGNIHRN7BFEX54DAHL3B","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d20ed6a546983146ac6dd1c945ab8bd70c4d49897dc99b853746a43d34a5fc73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-01T20:05:41Z","title_canon_sha256":"d29f3eb3b9d73c23e4942e9573016f051b289c64b4d30c6be83bcdfbe552ceca"},"schema_version":"1.0","source":{"id":"1805.00535","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00535","created_at":"2026-05-17T23:56:41Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00535v2","created_at":"2026-05-17T23:56:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00535","created_at":"2026-05-17T23:56:41Z"},{"alias_kind":"pith_short_12","alias_value":"O2XSATLGNIHR","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"O2XSATLGNIHRN7BF","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"O2XSATLG","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:23b0cfe75667538c0fdbd15affa96ea7175b9b812411dabd935f7ce6d07810c8","target":"graph","created_at":"2026-05-17T23:56:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"John Asplund, Melissa Keranen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-01T20:05:41Z","title":"${\\rm{TS}}(v,\\lambda)$ with cyclic 2-intersecting Gray codes: $v\\equiv 0$ or $4\\pmod{12}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00535","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0fe4f55e6302fa39ff2fef2758c46b4c32c92ea0cc18fa79806981dd03a45543","target":"record","created_at":"2026-05-17T23:56:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d20ed6a546983146ac6dd1c945ab8bd70c4d49897dc99b853746a43d34a5fc73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-01T20:05:41Z","title_canon_sha256":"d29f3eb3b9d73c23e4942e9573016f051b289c64b4d30c6be83bcdfbe552ceca"},"schema_version":"1.0","source":{"id":"1805.00535","kind":"arxiv","version":2}},"canonical_sha256":"76af204d666a0f16fc2525fbc180ebd8709fb94ea4e7f073cb35bbea2aaa659f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76af204d666a0f16fc2525fbc180ebd8709fb94ea4e7f073cb35bbea2aaa659f","first_computed_at":"2026-05-17T23:56:41.368143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:41.368143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o+jloSl4k1ZAYt1iIJWaxkmP9jiUL75raWXwu5rtZsBpdc2YnrByEUL9eudjX7lVhOepQihaB2ak5rJuni/gAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:41.368598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00535","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fe4f55e6302fa39ff2fef2758c46b4c32c92ea0cc18fa79806981dd03a45543","sha256:23b0cfe75667538c0fdbd15affa96ea7175b9b812411dabd935f7ce6d07810c8"],"state_sha256":"a4077d05a8cda47174d747386503c9d9462acdb523411352fbf1415608f3681e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fOdbytmbSlvZ0EMhcjThKorTXWUg7Q3MQnHrCG9GIj0xz7YuvkkYoTEFQA3ynNSNUo6cAHzsz2a608S1xqZpBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:03:25.315409Z","bundle_sha256":"a010a998094b197884f7cc2aa288bbf3ae62c8271edd5e033c6af4707d832666"}}