{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:ZJQ3BJR7I44K375UYQTE6NMLUJ","short_pith_number":"pith:ZJQ3BJR7","canonical_record":{"source":{"id":"math/0611500","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-11-16T15:01:22Z","cross_cats_sorted":[],"title_canon_sha256":"bbde7e98d44f5a3ea2df85c596c2cd73241ca9493c37953c30bce070063ad302","abstract_canon_sha256":"f69e34069e0477734b6c6a8ede904c65c3a9f9e0afd783b7af9a50065cb2d89e"},"schema_version":"1.0"},"canonical_sha256":"ca61b0a63f4738adffb4c4264f358ba27264d4f5f6072cace41ece8b669b193d","source":{"kind":"arxiv","id":"math/0611500","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611500","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611500v7","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611500","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"ZJQ3BJR7I44K","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZJQ3BJR7I44K375U","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZJQ3BJR7","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:ZJQ3BJR7I44K375UYQTE6NMLUJ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0611500","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-11-16T15:01:22Z","cross_cats_sorted":[],"title_canon_sha256":"bbde7e98d44f5a3ea2df85c596c2cd73241ca9493c37953c30bce070063ad302","abstract_canon_sha256":"f69e34069e0477734b6c6a8ede904c65c3a9f9e0afd783b7af9a50065cb2d89e"},"schema_version":"1.0"},"canonical_sha256":"ca61b0a63f4738adffb4c4264f358ba27264d4f5f6072cace41ece8b669b193d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:51.582866Z","signature_b64":"m4XkZWuvxpav2zQFRNYTC+2h/47b6qyxq2ump/vCg/0JQK2sd3rvJm1xaL4E0mKVK3Vx/e1mm3HPqCN8r/KtCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca61b0a63f4738adffb4c4264f358ba27264d4f5f6072cace41ece8b669b193d","last_reissued_at":"2026-05-18T04:36:51.582371Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:51.582371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0611500","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pWma0ujypVuFYIT47EyiL9Ej3FqhKS9TtHfC/wByv5EQ/yU/NgVxt8eshu9JWd2rzj0lgAtIY49OcBcXTxCxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:04:36.010762Z"},"content_sha256":"211e578af1786ee7550b0fc748ec8e33a73aa157750d4a2df8f48fd9bcb44517","schema_version":"1.0","event_id":"sha256:211e578af1786ee7550b0fc748ec8e33a73aa157750d4a2df8f48fd9bcb44517"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:ZJQ3BJR7I44K375UYQTE6NMLUJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cycles of free words in several independent random permutations with restricted cycle lengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"CMAP), Florent Benaych-Georges (PMA","submitted_at":"2006-11-16T15:01:22Z","abstract_excerpt":"In this text, we consider random permutations which can be written as free words in several independent random permutations: firstly, we fix a non trivial word $w$ in letters $g_1,g_1^{-1},..., g_k,g_k^{-1}$, secondly, for all $n$, we introduce a $k$-tuple $s_1(n),..., s_k(n)$ of independent random permutations of $\\{1,..., n\\}$, and the random permutation $\\sigma_n$ we are going to consider is the one obtained by replacing each letter $g_i$ in $w$ by $s_i(n)$. For example, for $w=g_1g_2g_3g_2^{-1}$, $\\sigma_n=s_1(n)\\circ s_2(n)\\circ s_3(n)\\circ s_2(n)^{-1}$. Moreover, we restrict the set of p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611500","kind":"arxiv","version":7},"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":"2026-05-18T04:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M4xdjHNpf6vIY+03XjFekB8vWhgsN/SmTtnW5oqReq9UCgndlFSSYdApz7atlrfrzyR2yZ21BqHEmkA/B95KAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:04:36.011114Z"},"content_sha256":"46cdf044121301cf2878ace4fa22ff016dc4a0923d618d371342ffddcda7d030","schema_version":"1.0","event_id":"sha256:46cdf044121301cf2878ace4fa22ff016dc4a0923d618d371342ffddcda7d030"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZJQ3BJR7I44K375UYQTE6NMLUJ/bundle.json","state_url":"https://pith.science/pith/ZJQ3BJR7I44K375UYQTE6NMLUJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZJQ3BJR7I44K375UYQTE6NMLUJ/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":"2026-06-03T09:04:36Z","links":{"resolver":"https://pith.science/pith/ZJQ3BJR7I44K375UYQTE6NMLUJ","bundle":"https://pith.science/pith/ZJQ3BJR7I44K375UYQTE6NMLUJ/bundle.json","state":"https://pith.science/pith/ZJQ3BJR7I44K375UYQTE6NMLUJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZJQ3BJR7I44K375UYQTE6NMLUJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:ZJQ3BJR7I44K375UYQTE6NMLUJ","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":"f69e34069e0477734b6c6a8ede904c65c3a9f9e0afd783b7af9a50065cb2d89e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-11-16T15:01:22Z","title_canon_sha256":"bbde7e98d44f5a3ea2df85c596c2cd73241ca9493c37953c30bce070063ad302"},"schema_version":"1.0","source":{"id":"math/0611500","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611500","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611500v7","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611500","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"ZJQ3BJR7I44K","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZJQ3BJR7I44K375U","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZJQ3BJR7","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:46cdf044121301cf2878ace4fa22ff016dc4a0923d618d371342ffddcda7d030","target":"graph","created_at":"2026-05-18T04:36:51Z","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":"In this text, we consider random permutations which can be written as free words in several independent random permutations: firstly, we fix a non trivial word $w$ in letters $g_1,g_1^{-1},..., g_k,g_k^{-1}$, secondly, for all $n$, we introduce a $k$-tuple $s_1(n),..., s_k(n)$ of independent random permutations of $\\{1,..., n\\}$, and the random permutation $\\sigma_n$ we are going to consider is the one obtained by replacing each letter $g_i$ in $w$ by $s_i(n)$. For example, for $w=g_1g_2g_3g_2^{-1}$, $\\sigma_n=s_1(n)\\circ s_2(n)\\circ s_3(n)\\circ s_2(n)^{-1}$. Moreover, we restrict the set of p","authors_text":"CMAP), Florent Benaych-Georges (PMA","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-11-16T15:01:22Z","title":"Cycles of free words in several independent random permutations with restricted cycle lengths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611500","kind":"arxiv","version":7},"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":"sha256:211e578af1786ee7550b0fc748ec8e33a73aa157750d4a2df8f48fd9bcb44517","target":"record","created_at":"2026-05-18T04:36:51Z","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":"f69e34069e0477734b6c6a8ede904c65c3a9f9e0afd783b7af9a50065cb2d89e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-11-16T15:01:22Z","title_canon_sha256":"bbde7e98d44f5a3ea2df85c596c2cd73241ca9493c37953c30bce070063ad302"},"schema_version":"1.0","source":{"id":"math/0611500","kind":"arxiv","version":7}},"canonical_sha256":"ca61b0a63f4738adffb4c4264f358ba27264d4f5f6072cace41ece8b669b193d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca61b0a63f4738adffb4c4264f358ba27264d4f5f6072cace41ece8b669b193d","first_computed_at":"2026-05-18T04:36:51.582371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:51.582371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m4XkZWuvxpav2zQFRNYTC+2h/47b6qyxq2ump/vCg/0JQK2sd3rvJm1xaL4E0mKVK3Vx/e1mm3HPqCN8r/KtCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:51.582866Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0611500","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:211e578af1786ee7550b0fc748ec8e33a73aa157750d4a2df8f48fd9bcb44517","sha256:46cdf044121301cf2878ace4fa22ff016dc4a0923d618d371342ffddcda7d030"],"state_sha256":"7593a235568ab3a9909058dde0f62b931b6b9c5741185d2374aaf85e3ea7e6f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lIisgtpFaREr32MEZkN5vzNcETUDRqk0/X1I2NIxrt+yvSY4/mkQdCtX2YidjUkA7mpO0ZTZe/sDAXc6sVNvBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:04:36.013127Z","bundle_sha256":"cdbe016ba4501e71435db0694ecec22863760dc53edf7b5ed5626cd99f9e3b4e"}}