{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FE55B5KJ6G2HKGKWOVJHBD24WT","short_pith_number":"pith:FE55B5KJ","canonical_record":{"source":{"id":"1506.00983","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-02T18:37:08Z","cross_cats_sorted":[],"title_canon_sha256":"bac983cd99e295c0cca18efd82b776b6d5e0e41bb58cfa2274539ed6614a8bb9","abstract_canon_sha256":"257a3c2469c9749f639e28b56f84d152288d1a355815c53542d3bc9571eafec8"},"schema_version":"1.0"},"canonical_sha256":"293bd0f549f1b47519567552708f5cb4d4f239375652a59650c6b7800b335869","source":{"kind":"arxiv","id":"1506.00983","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00983","created_at":"2026-05-18T01:59:33Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00983v1","created_at":"2026-05-18T01:59:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00983","created_at":"2026-05-18T01:59:33Z"},{"alias_kind":"pith_short_12","alias_value":"FE55B5KJ6G2H","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FE55B5KJ6G2HKGKW","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FE55B5KJ","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FE55B5KJ6G2HKGKWOVJHBD24WT","target":"record","payload":{"canonical_record":{"source":{"id":"1506.00983","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-02T18:37:08Z","cross_cats_sorted":[],"title_canon_sha256":"bac983cd99e295c0cca18efd82b776b6d5e0e41bb58cfa2274539ed6614a8bb9","abstract_canon_sha256":"257a3c2469c9749f639e28b56f84d152288d1a355815c53542d3bc9571eafec8"},"schema_version":"1.0"},"canonical_sha256":"293bd0f549f1b47519567552708f5cb4d4f239375652a59650c6b7800b335869","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:33.954082Z","signature_b64":"mjsd6r0sM4ZvNuQyPEny4tgUAXbAf9NSUHLAkcwyKPVV+rAVbx2T7IGba8ubbMCQ+LIded8CJK0dfyEiE09ZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"293bd0f549f1b47519567552708f5cb4d4f239375652a59650c6b7800b335869","last_reissued_at":"2026-05-18T01:59:33.953450Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:33.953450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.00983","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tw8A1TJU45OJ9ogs980f6Fwjpa3dBS3UQZjqi42V2K8NfHMgPwFzvnRVfyN1ta48DL7JmNxqhPbaUvYT8Lu/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:08:31.872230Z"},"content_sha256":"83ff9612b5aa06aa6ae9bbc61633718189ae1d5e69ec92da7b0eb7e9aa3dd1b4","schema_version":"1.0","event_id":"sha256:83ff9612b5aa06aa6ae9bbc61633718189ae1d5e69ec92da7b0eb7e9aa3dd1b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FE55B5KJ6G2HKGKWOVJHBD24WT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the maximum number of Latin transversals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Roman Glebov, Zur Luria","submitted_at":"2015-06-02T18:37:08Z","abstract_excerpt":"Let $T(n)$ denote the maximal number of transversals in an order-$n$ Latin square. Improving on the bounds obtained by McKay et al., Taranenko recently proved that $T(n) \\leq \\left((1+o(1))\\frac{n}{e^2}\\right)^{n}$, and conjectured that this bound is tight.\n  We prove via a probabilistic construction that indeed $T(n) = \\left((1+o(1))\\frac{n}{e^2}\\right)^{n}$. Until the present paper, no superexponential lower bound for $T(n)$ was known. We also give a simpler proof of the upper bound."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00983","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OgdPTqGaFEdOHdd8C5IPDdMTUVNcwGDbKuIKkOyMgAw+bW6ZzHmt17y7afv185qgwsNYrqduAEhBbcXvJqf+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:08:31.872604Z"},"content_sha256":"3a5cf9618727376335a7f421f48e4e6661f1f90459e4efddaa9672e5b3317183","schema_version":"1.0","event_id":"sha256:3a5cf9618727376335a7f421f48e4e6661f1f90459e4efddaa9672e5b3317183"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FE55B5KJ6G2HKGKWOVJHBD24WT/bundle.json","state_url":"https://pith.science/pith/FE55B5KJ6G2HKGKWOVJHBD24WT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FE55B5KJ6G2HKGKWOVJHBD24WT/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":"2026-05-30T15:08:31Z","links":{"resolver":"https://pith.science/pith/FE55B5KJ6G2HKGKWOVJHBD24WT","bundle":"https://pith.science/pith/FE55B5KJ6G2HKGKWOVJHBD24WT/bundle.json","state":"https://pith.science/pith/FE55B5KJ6G2HKGKWOVJHBD24WT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FE55B5KJ6G2HKGKWOVJHBD24WT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FE55B5KJ6G2HKGKWOVJHBD24WT","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":"257a3c2469c9749f639e28b56f84d152288d1a355815c53542d3bc9571eafec8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-02T18:37:08Z","title_canon_sha256":"bac983cd99e295c0cca18efd82b776b6d5e0e41bb58cfa2274539ed6614a8bb9"},"schema_version":"1.0","source":{"id":"1506.00983","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00983","created_at":"2026-05-18T01:59:33Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00983v1","created_at":"2026-05-18T01:59:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00983","created_at":"2026-05-18T01:59:33Z"},{"alias_kind":"pith_short_12","alias_value":"FE55B5KJ6G2H","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FE55B5KJ6G2HKGKW","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FE55B5KJ","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:3a5cf9618727376335a7f421f48e4e6661f1f90459e4efddaa9672e5b3317183","target":"graph","created_at":"2026-05-18T01:59:33Z","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":"Let $T(n)$ denote the maximal number of transversals in an order-$n$ Latin square. Improving on the bounds obtained by McKay et al., Taranenko recently proved that $T(n) \\leq \\left((1+o(1))\\frac{n}{e^2}\\right)^{n}$, and conjectured that this bound is tight.\n  We prove via a probabilistic construction that indeed $T(n) = \\left((1+o(1))\\frac{n}{e^2}\\right)^{n}$. Until the present paper, no superexponential lower bound for $T(n)$ was known. We also give a simpler proof of the upper bound.","authors_text":"Roman Glebov, Zur Luria","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-02T18:37:08Z","title":"On the maximum number of Latin transversals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00983","kind":"arxiv","version":1},"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":"sha256:83ff9612b5aa06aa6ae9bbc61633718189ae1d5e69ec92da7b0eb7e9aa3dd1b4","target":"record","created_at":"2026-05-18T01:59:33Z","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":"257a3c2469c9749f639e28b56f84d152288d1a355815c53542d3bc9571eafec8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-02T18:37:08Z","title_canon_sha256":"bac983cd99e295c0cca18efd82b776b6d5e0e41bb58cfa2274539ed6614a8bb9"},"schema_version":"1.0","source":{"id":"1506.00983","kind":"arxiv","version":1}},"canonical_sha256":"293bd0f549f1b47519567552708f5cb4d4f239375652a59650c6b7800b335869","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"293bd0f549f1b47519567552708f5cb4d4f239375652a59650c6b7800b335869","first_computed_at":"2026-05-18T01:59:33.953450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:33.953450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mjsd6r0sM4ZvNuQyPEny4tgUAXbAf9NSUHLAkcwyKPVV+rAVbx2T7IGba8ubbMCQ+LIded8CJK0dfyEiE09ZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:33.954082Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.00983","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83ff9612b5aa06aa6ae9bbc61633718189ae1d5e69ec92da7b0eb7e9aa3dd1b4","sha256:3a5cf9618727376335a7f421f48e4e6661f1f90459e4efddaa9672e5b3317183"],"state_sha256":"13f1a40b876db1233abf2ebdf4030c2f063a144d06f93c8baf21a4732341394c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sGgMnpbStqoI340TP3R02fOdmCZhJQ9jDsIjTG/pXgZUOs4WBoCSkmNa1Ql7DveqZ12AvZ8grIV+qfDG0WZZBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:08:31.874805Z","bundle_sha256":"22240cfaccb06490e3c2a445cc4e814bea8e6d4f48c1189a10fa165d26f2f732"}}