{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HWOEAECCARNJ3JJ5YRH6AAQRKZ","short_pith_number":"pith:HWOEAECC","canonical_record":{"source":{"id":"1807.11217","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-30T08:07:57Z","cross_cats_sorted":[],"title_canon_sha256":"ed0e0f6c3ee4b21d84ec4a06fbda6f0144d9bcb7ef181e85c46b5add5e7800ab","abstract_canon_sha256":"2fc2606636659ca2c8991e3f31facdcebd38f6f066cdd183a361fb23fa4344f9"},"schema_version":"1.0"},"canonical_sha256":"3d9c401042045a9da53dc44fe00211567a146325cfd503d9b49f3c3d38545b59","source":{"kind":"arxiv","id":"1807.11217","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11217","created_at":"2026-05-18T00:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11217v2","created_at":"2026-05-18T00:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11217","created_at":"2026-05-18T00:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"HWOEAECCARNJ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HWOEAECCARNJ3JJ5","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HWOEAECC","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HWOEAECCARNJ3JJ5YRH6AAQRKZ","target":"record","payload":{"canonical_record":{"source":{"id":"1807.11217","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-30T08:07:57Z","cross_cats_sorted":[],"title_canon_sha256":"ed0e0f6c3ee4b21d84ec4a06fbda6f0144d9bcb7ef181e85c46b5add5e7800ab","abstract_canon_sha256":"2fc2606636659ca2c8991e3f31facdcebd38f6f066cdd183a361fb23fa4344f9"},"schema_version":"1.0"},"canonical_sha256":"3d9c401042045a9da53dc44fe00211567a146325cfd503d9b49f3c3d38545b59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:45.186817Z","signature_b64":"PQDoXywoavor3dghQ25mJQb5mEJOOrgMNtNj8W8nxvCcJkvbN7NNA8DYC5/8F9ZNSrRjKyxNVSraSbc5/OUTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d9c401042045a9da53dc44fe00211567a146325cfd503d9b49f3c3d38545b59","last_reissued_at":"2026-05-18T00:05:45.186076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:45.186076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.11217","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":"2026-05-18T00:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pGe1YN+SWwE1vE57/MCZ9ODBzwQTL4LMWTa6ar/noRE8NHpfApySRlE39WLL4PGqU6bpBZjU7EBRWbyTWADJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:13:23.881400Z"},"content_sha256":"8eb1c6958426242af82c9cfe3bb2725f0d25c08574c415fc7473906006b0fbf3","schema_version":"1.0","event_id":"sha256:8eb1c6958426242af82c9cfe3bb2725f0d25c08574c415fc7473906006b0fbf3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HWOEAECCARNJ3JJ5YRH6AAQRKZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$p$-adic dynamical systems of the function $\\dfrac{ax}{x^2+a}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"I.A. Sattarov, S. Yam, U.A. Rozikov","submitted_at":"2018-07-30T08:07:57Z","abstract_excerpt":"We show that any $(1,2)$-rational function with a unique fixed point is topologically conjugate to a $(2,2)$-rational function or to the function $f(x)={ax\\over x^2+a}$. The case $(2,2)$ was studied in our previous paper, here we study the dynamical systems generated by the function $f$ on the set of complex $p$-adic field $\\mathbb C_p$. We show that the unique fixed point is indifferent and therefore the convergence of the trajectories is not the typical case for the dynamical systems. We construct the corresponding Siegel disk of these dynamical systems. We determine a sufficiently small set"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11217","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":"2026-05-18T00:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WcuuZdnwXCR56B631yaB8Fq4m4IvaBOv2M6TXeK7cOpoUk0MWt/DO06CFQeJBLkgyx2QRrAahGu4B4fJranGAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:13:23.881784Z"},"content_sha256":"3ed832d6cbfba8efe6c2eb393e0b09e5678b9521364348a32e623c57d87f1184","schema_version":"1.0","event_id":"sha256:3ed832d6cbfba8efe6c2eb393e0b09e5678b9521364348a32e623c57d87f1184"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HWOEAECCARNJ3JJ5YRH6AAQRKZ/bundle.json","state_url":"https://pith.science/pith/HWOEAECCARNJ3JJ5YRH6AAQRKZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HWOEAECCARNJ3JJ5YRH6AAQRKZ/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":"2026-05-26T07:13:23Z","links":{"resolver":"https://pith.science/pith/HWOEAECCARNJ3JJ5YRH6AAQRKZ","bundle":"https://pith.science/pith/HWOEAECCARNJ3JJ5YRH6AAQRKZ/bundle.json","state":"https://pith.science/pith/HWOEAECCARNJ3JJ5YRH6AAQRKZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HWOEAECCARNJ3JJ5YRH6AAQRKZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HWOEAECCARNJ3JJ5YRH6AAQRKZ","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":"2fc2606636659ca2c8991e3f31facdcebd38f6f066cdd183a361fb23fa4344f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-30T08:07:57Z","title_canon_sha256":"ed0e0f6c3ee4b21d84ec4a06fbda6f0144d9bcb7ef181e85c46b5add5e7800ab"},"schema_version":"1.0","source":{"id":"1807.11217","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11217","created_at":"2026-05-18T00:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11217v2","created_at":"2026-05-18T00:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11217","created_at":"2026-05-18T00:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"HWOEAECCARNJ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HWOEAECCARNJ3JJ5","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HWOEAECC","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:3ed832d6cbfba8efe6c2eb393e0b09e5678b9521364348a32e623c57d87f1184","target":"graph","created_at":"2026-05-18T00:05:45Z","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":"We show that any $(1,2)$-rational function with a unique fixed point is topologically conjugate to a $(2,2)$-rational function or to the function $f(x)={ax\\over x^2+a}$. The case $(2,2)$ was studied in our previous paper, here we study the dynamical systems generated by the function $f$ on the set of complex $p$-adic field $\\mathbb C_p$. We show that the unique fixed point is indifferent and therefore the convergence of the trajectories is not the typical case for the dynamical systems. We construct the corresponding Siegel disk of these dynamical systems. We determine a sufficiently small set","authors_text":"I.A. Sattarov, S. Yam, U.A. Rozikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-30T08:07:57Z","title":"$p$-adic dynamical systems of the function $\\dfrac{ax}{x^2+a}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11217","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":"sha256:8eb1c6958426242af82c9cfe3bb2725f0d25c08574c415fc7473906006b0fbf3","target":"record","created_at":"2026-05-18T00:05:45Z","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":"2fc2606636659ca2c8991e3f31facdcebd38f6f066cdd183a361fb23fa4344f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-30T08:07:57Z","title_canon_sha256":"ed0e0f6c3ee4b21d84ec4a06fbda6f0144d9bcb7ef181e85c46b5add5e7800ab"},"schema_version":"1.0","source":{"id":"1807.11217","kind":"arxiv","version":2}},"canonical_sha256":"3d9c401042045a9da53dc44fe00211567a146325cfd503d9b49f3c3d38545b59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d9c401042045a9da53dc44fe00211567a146325cfd503d9b49f3c3d38545b59","first_computed_at":"2026-05-18T00:05:45.186076Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:45.186076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PQDoXywoavor3dghQ25mJQb5mEJOOrgMNtNj8W8nxvCcJkvbN7NNA8DYC5/8F9ZNSrRjKyxNVSraSbc5/OUTBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:45.186817Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.11217","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8eb1c6958426242af82c9cfe3bb2725f0d25c08574c415fc7473906006b0fbf3","sha256:3ed832d6cbfba8efe6c2eb393e0b09e5678b9521364348a32e623c57d87f1184"],"state_sha256":"71752d653a17479a1b91a506cdc486265b34c67272b9bd77c14309b225161586"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jRM6V6/gkgbpnVzB/U6pPF+7KoS+TMo5jJEygucfnDuEf+tgHm55ZPVFsR62m3NZUPCLsKP3olbbylhIo0DhAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:13:23.884812Z","bundle_sha256":"a21860e722f9adc042e1a635cfde29448625c46ea12da136805c5becfb77f209"}}