{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AGXPUASJGFHCO7GQQKYVTRM2ZW","short_pith_number":"pith:AGXPUASJ","canonical_record":{"source":{"id":"1711.07524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-20T20:14:03Z","cross_cats_sorted":[],"title_canon_sha256":"5a34cd1ea3c6dee3c646bd8258b7a920a67a275c740b58f63fc5d31791f8a062","abstract_canon_sha256":"df70c11d1988f05c7145b3642109017b5cc249abb7006fa93cbd81d23d5f3642"},"schema_version":"1.0"},"canonical_sha256":"01aefa0249314e277cd082b159c59acd8debb49da05db25056671295f1e88cdf","source":{"kind":"arxiv","id":"1711.07524","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07524","created_at":"2026-05-18T00:29:58Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07524v1","created_at":"2026-05-18T00:29:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07524","created_at":"2026-05-18T00:29:58Z"},{"alias_kind":"pith_short_12","alias_value":"AGXPUASJGFHC","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AGXPUASJGFHCO7GQ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AGXPUASJ","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AGXPUASJGFHCO7GQQKYVTRM2ZW","target":"record","payload":{"canonical_record":{"source":{"id":"1711.07524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-20T20:14:03Z","cross_cats_sorted":[],"title_canon_sha256":"5a34cd1ea3c6dee3c646bd8258b7a920a67a275c740b58f63fc5d31791f8a062","abstract_canon_sha256":"df70c11d1988f05c7145b3642109017b5cc249abb7006fa93cbd81d23d5f3642"},"schema_version":"1.0"},"canonical_sha256":"01aefa0249314e277cd082b159c59acd8debb49da05db25056671295f1e88cdf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:58.800330Z","signature_b64":"QVhf8gQKAu6KpiyYeBGiH6h+FJRWgm5BsNGU6oWVU3HgKvS5ibyTlKAHxbmpEmgvdbS3WvS2MHRD875jdJEICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01aefa0249314e277cd082b159c59acd8debb49da05db25056671295f1e88cdf","last_reissued_at":"2026-05-18T00:29:58.799779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:58.799779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.07524","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":"2026-05-18T00:29:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MVS1NG71V48AxuhUazZUE8keMbh6m/bgkVccCLNWzax5BiGOsmrK1CDsUGmvDM7CpIABhvVIhIzP6CY+1v1vDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:44:52.791557Z"},"content_sha256":"777afb780c085403f75918b22ba628ac66d2b00474d885de0abed497087dfa58","schema_version":"1.0","event_id":"sha256:777afb780c085403f75918b22ba628ac66d2b00474d885de0abed497087dfa58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AGXPUASJGFHCO7GQQKYVTRM2ZW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On k-neighbor separated permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Solt\\'esz, Istv\\'an Kov\\'acs","submitted_at":"2017-11-20T20:14:03Z","abstract_excerpt":"Two permutations of $[n]=\\{1,2 \\ldots n\\}$ are \\textit{$k$-neighbor separated} if there are two elements that are neighbors in one of the permutations and that are separated by exactly $k-2$ other elements in the other permutation. Let the maximal number of pairwise $k$-neighbor separated permutations of $[n]$ be denoted by $P(n,k)$. In a previous paper, the authors have determined $P(n,3)$ for every $n$, answering a question of K\\\"orner, Messuti and Simonyi affirmatively. In this paper we prove that for every fixed positive integer $\\ell $, $$P(n,2^\\ell+1) = 2^{n-o(n)}. $$ We conjecture that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07524","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":"2026-05-18T00:29:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ua6EJzar0LT2rajA61oCPWDWgD2hYzd+J+/K6V3hdx9LNXksFoSC2a3fnax2JcAhflAx8yfwdkttJ8ozHojPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:44:52.791898Z"},"content_sha256":"89a57707098486e4f7635e1bc180edcb43cb4afdac0addc30c81a9c812dcba6a","schema_version":"1.0","event_id":"sha256:89a57707098486e4f7635e1bc180edcb43cb4afdac0addc30c81a9c812dcba6a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AGXPUASJGFHCO7GQQKYVTRM2ZW/bundle.json","state_url":"https://pith.science/pith/AGXPUASJGFHCO7GQQKYVTRM2ZW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AGXPUASJGFHCO7GQQKYVTRM2ZW/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":"2026-06-01T07:44:52Z","links":{"resolver":"https://pith.science/pith/AGXPUASJGFHCO7GQQKYVTRM2ZW","bundle":"https://pith.science/pith/AGXPUASJGFHCO7GQQKYVTRM2ZW/bundle.json","state":"https://pith.science/pith/AGXPUASJGFHCO7GQQKYVTRM2ZW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AGXPUASJGFHCO7GQQKYVTRM2ZW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AGXPUASJGFHCO7GQQKYVTRM2ZW","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":"df70c11d1988f05c7145b3642109017b5cc249abb7006fa93cbd81d23d5f3642","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-20T20:14:03Z","title_canon_sha256":"5a34cd1ea3c6dee3c646bd8258b7a920a67a275c740b58f63fc5d31791f8a062"},"schema_version":"1.0","source":{"id":"1711.07524","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07524","created_at":"2026-05-18T00:29:58Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07524v1","created_at":"2026-05-18T00:29:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07524","created_at":"2026-05-18T00:29:58Z"},{"alias_kind":"pith_short_12","alias_value":"AGXPUASJGFHC","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AGXPUASJGFHCO7GQ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AGXPUASJ","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:89a57707098486e4f7635e1bc180edcb43cb4afdac0addc30c81a9c812dcba6a","target":"graph","created_at":"2026-05-18T00:29:58Z","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":"Two permutations of $[n]=\\{1,2 \\ldots n\\}$ are \\textit{$k$-neighbor separated} if there are two elements that are neighbors in one of the permutations and that are separated by exactly $k-2$ other elements in the other permutation. Let the maximal number of pairwise $k$-neighbor separated permutations of $[n]$ be denoted by $P(n,k)$. In a previous paper, the authors have determined $P(n,3)$ for every $n$, answering a question of K\\\"orner, Messuti and Simonyi affirmatively. In this paper we prove that for every fixed positive integer $\\ell $, $$P(n,2^\\ell+1) = 2^{n-o(n)}. $$ We conjecture that ","authors_text":"Daniel Solt\\'esz, Istv\\'an Kov\\'acs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-20T20:14:03Z","title":"On k-neighbor separated permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07524","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":"sha256:777afb780c085403f75918b22ba628ac66d2b00474d885de0abed497087dfa58","target":"record","created_at":"2026-05-18T00:29:58Z","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":"df70c11d1988f05c7145b3642109017b5cc249abb7006fa93cbd81d23d5f3642","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-20T20:14:03Z","title_canon_sha256":"5a34cd1ea3c6dee3c646bd8258b7a920a67a275c740b58f63fc5d31791f8a062"},"schema_version":"1.0","source":{"id":"1711.07524","kind":"arxiv","version":1}},"canonical_sha256":"01aefa0249314e277cd082b159c59acd8debb49da05db25056671295f1e88cdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01aefa0249314e277cd082b159c59acd8debb49da05db25056671295f1e88cdf","first_computed_at":"2026-05-18T00:29:58.799779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:58.799779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QVhf8gQKAu6KpiyYeBGiH6h+FJRWgm5BsNGU6oWVU3HgKvS5ibyTlKAHxbmpEmgvdbS3WvS2MHRD875jdJEICA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:58.800330Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.07524","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:777afb780c085403f75918b22ba628ac66d2b00474d885de0abed497087dfa58","sha256:89a57707098486e4f7635e1bc180edcb43cb4afdac0addc30c81a9c812dcba6a"],"state_sha256":"2471a3bd840cb11314e1bb1df5ee954fec7e5456357e7bfa5e7294167dbc46f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iPnfBwCnCeEis21xv+nzVXEPImS1eAZzXvQjFiJh/hv/el3cJVwwT5iBf+v7rde1XH7pKOPgclGsyBcVFvvIAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:44:52.793759Z","bundle_sha256":"08736cb9d3d7665d3345486c542383201fcb3e589bad9254a09832e3adcacae6"}}