{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:G3PAIGU2MRRBSCXV6Z4OLDKOUT","short_pith_number":"pith:G3PAIGU2","canonical_record":{"source":{"id":"1505.06581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-25T09:45:42Z","cross_cats_sorted":[],"title_canon_sha256":"0a9deee2a58b89f9075086b0a6e7ccd82cf50e857e6ca6c2da895b165c3cfbef","abstract_canon_sha256":"8899066ef396071b0d7b79af05b98db6688ba26e13d6257f45d2d901c89a5d80"},"schema_version":"1.0"},"canonical_sha256":"36de041a9a6462190af5f678e58d4ea4d8f28ff13bb3154f0d9d125b14de4b05","source":{"kind":"arxiv","id":"1505.06581","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06581","created_at":"2026-05-18T01:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06581v1","created_at":"2026-05-18T01:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06581","created_at":"2026-05-18T01:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"G3PAIGU2MRRB","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G3PAIGU2MRRBSCXV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G3PAIGU2","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:G3PAIGU2MRRBSCXV6Z4OLDKOUT","target":"record","payload":{"canonical_record":{"source":{"id":"1505.06581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-25T09:45:42Z","cross_cats_sorted":[],"title_canon_sha256":"0a9deee2a58b89f9075086b0a6e7ccd82cf50e857e6ca6c2da895b165c3cfbef","abstract_canon_sha256":"8899066ef396071b0d7b79af05b98db6688ba26e13d6257f45d2d901c89a5d80"},"schema_version":"1.0"},"canonical_sha256":"36de041a9a6462190af5f678e58d4ea4d8f28ff13bb3154f0d9d125b14de4b05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:46.861121Z","signature_b64":"inw7CjtOMdiDBAtYXaTjWJccBxbj8ROYQNcN/cHXCpqsxhX88+/0XyNXn9Tc6BhXcsKUQDtsETUuSno88p6yCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36de041a9a6462190af5f678e58d4ea4d8f28ff13bb3154f0d9d125b14de4b05","last_reissued_at":"2026-05-18T01:09:46.860441Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:46.860441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.06581","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":"2026-05-18T01:09:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wIIA1r8HQMTMyZNg9eSyz0g7H31Sy80b5MviHE5IPZ+AD9vWN5EqWT4K6kzFntwL8BQu4fflzKaj98zNanfGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:34:50.219821Z"},"content_sha256":"9226968281587767b5131ddbc59817f5b4729d99f5f85a9054300003def9d64e","schema_version":"1.0","event_id":"sha256:9226968281587767b5131ddbc59817f5b4729d99f5f85a9054300003def9d64e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:G3PAIGU2MRRBSCXV6Z4OLDKOUT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simple permutations with order $4n + 2$ by means of Pasting and Reversing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Oscar E. Mart\\'inez-Castiblanco, Primitivo B. Acosta-Hum\\'anez","submitted_at":"2015-05-25T09:45:42Z","abstract_excerpt":"The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Hum\\'anez \\& Bernhardt (power of two). It is well known that Sharkovskii's theorem shows the relationship between the cardinal of the set of periodic points of a continuous map, but simple permutations will show the behaviour of those periodic points. Recently Abdulla et al studied the structure of minimal $4n+2$-orbits of the continuous endomorphisms on the real line. This paper studies some combinatorial dynamics structures of permutations of mixed order $4n+2$, describing its genealogy, using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06581","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":"2026-05-18T01:09:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V7xTjmNcxS+5i6ooSqLl+BfFCWdr1csXCeC3C+t4kkAhAUuPp2w4OQrkmgqfe0Ew8c27xO92zWPx6WGzQ7ivDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:34:50.220969Z"},"content_sha256":"8ae76ac8c819b26ee4cf36ed193d328e4272fdd0885c7bbdb13ed26c9a8fc078","schema_version":"1.0","event_id":"sha256:8ae76ac8c819b26ee4cf36ed193d328e4272fdd0885c7bbdb13ed26c9a8fc078"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G3PAIGU2MRRBSCXV6Z4OLDKOUT/bundle.json","state_url":"https://pith.science/pith/G3PAIGU2MRRBSCXV6Z4OLDKOUT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G3PAIGU2MRRBSCXV6Z4OLDKOUT/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":"2026-05-25T16:34:50Z","links":{"resolver":"https://pith.science/pith/G3PAIGU2MRRBSCXV6Z4OLDKOUT","bundle":"https://pith.science/pith/G3PAIGU2MRRBSCXV6Z4OLDKOUT/bundle.json","state":"https://pith.science/pith/G3PAIGU2MRRBSCXV6Z4OLDKOUT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G3PAIGU2MRRBSCXV6Z4OLDKOUT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:G3PAIGU2MRRBSCXV6Z4OLDKOUT","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":"8899066ef396071b0d7b79af05b98db6688ba26e13d6257f45d2d901c89a5d80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-25T09:45:42Z","title_canon_sha256":"0a9deee2a58b89f9075086b0a6e7ccd82cf50e857e6ca6c2da895b165c3cfbef"},"schema_version":"1.0","source":{"id":"1505.06581","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06581","created_at":"2026-05-18T01:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06581v1","created_at":"2026-05-18T01:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06581","created_at":"2026-05-18T01:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"G3PAIGU2MRRB","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G3PAIGU2MRRBSCXV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G3PAIGU2","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:8ae76ac8c819b26ee4cf36ed193d328e4272fdd0885c7bbdb13ed26c9a8fc078","target":"graph","created_at":"2026-05-18T01:09:46Z","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":"The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Hum\\'anez \\& Bernhardt (power of two). It is well known that Sharkovskii's theorem shows the relationship between the cardinal of the set of periodic points of a continuous map, but simple permutations will show the behaviour of those periodic points. Recently Abdulla et al studied the structure of minimal $4n+2$-orbits of the continuous endomorphisms on the real line. This paper studies some combinatorial dynamics structures of permutations of mixed order $4n+2$, describing its genealogy, using","authors_text":"Oscar E. Mart\\'inez-Castiblanco, Primitivo B. Acosta-Hum\\'anez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-25T09:45:42Z","title":"Simple permutations with order $4n + 2$ by means of Pasting and Reversing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06581","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":"sha256:9226968281587767b5131ddbc59817f5b4729d99f5f85a9054300003def9d64e","target":"record","created_at":"2026-05-18T01:09:46Z","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":"8899066ef396071b0d7b79af05b98db6688ba26e13d6257f45d2d901c89a5d80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-25T09:45:42Z","title_canon_sha256":"0a9deee2a58b89f9075086b0a6e7ccd82cf50e857e6ca6c2da895b165c3cfbef"},"schema_version":"1.0","source":{"id":"1505.06581","kind":"arxiv","version":1}},"canonical_sha256":"36de041a9a6462190af5f678e58d4ea4d8f28ff13bb3154f0d9d125b14de4b05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36de041a9a6462190af5f678e58d4ea4d8f28ff13bb3154f0d9d125b14de4b05","first_computed_at":"2026-05-18T01:09:46.860441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:46.860441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"inw7CjtOMdiDBAtYXaTjWJccBxbj8ROYQNcN/cHXCpqsxhX88+/0XyNXn9Tc6BhXcsKUQDtsETUuSno88p6yCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:46.861121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06581","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9226968281587767b5131ddbc59817f5b4729d99f5f85a9054300003def9d64e","sha256:8ae76ac8c819b26ee4cf36ed193d328e4272fdd0885c7bbdb13ed26c9a8fc078"],"state_sha256":"6a1e0ca65b8860e86eb6d8fe7bc29845bcc188ed7abe0669e413b62f7f92d315"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KIJgUeM0Ym8WcgZkpDzzyaYiL1tppbebXBhh6uXIqkWYcr8XnClS+CNXbeIE6ZrrtR3F8FOJKXmOxLh67Ea3DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:34:50.224669Z","bundle_sha256":"b5cc66961c85f16f66da5ab06313b0f05cc7e08d76cb7752309d919a83ff1dc8"}}