{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3KLALDXCIV2JJD5UHR6JJSLNIQ","short_pith_number":"pith:3KLALDXC","canonical_record":{"source":{"id":"2607.19252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-21T16:22:17Z","cross_cats_sorted":[],"title_canon_sha256":"86f3c60f4087b4ef2abc800c55b4c293d00444122ce8c257c84ad33a4c189514","abstract_canon_sha256":"9b999d93f5e00589a23f2f597e82e5575fb33dd52d0c09266007f1b334a0530a"},"schema_version":"1.0"},"canonical_sha256":"da96058ee24574948fb43c7c94c96d440903c3974349a2ad009e5fa613759468","source":{"kind":"arxiv","id":"2607.19252","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.19252","created_at":"2026-07-22T01:24:16Z"},{"alias_kind":"arxiv_version","alias_value":"2607.19252v1","created_at":"2026-07-22T01:24:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19252","created_at":"2026-07-22T01:24:16Z"},{"alias_kind":"pith_short_12","alias_value":"3KLALDXCIV2J","created_at":"2026-07-22T01:24:16Z"},{"alias_kind":"pith_short_16","alias_value":"3KLALDXCIV2JJD5U","created_at":"2026-07-22T01:24:16Z"},{"alias_kind":"pith_short_8","alias_value":"3KLALDXC","created_at":"2026-07-22T01:24:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3KLALDXCIV2JJD5UHR6JJSLNIQ","target":"record","payload":{"canonical_record":{"source":{"id":"2607.19252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-21T16:22:17Z","cross_cats_sorted":[],"title_canon_sha256":"86f3c60f4087b4ef2abc800c55b4c293d00444122ce8c257c84ad33a4c189514","abstract_canon_sha256":"9b999d93f5e00589a23f2f597e82e5575fb33dd52d0c09266007f1b334a0530a"},"schema_version":"1.0"},"canonical_sha256":"da96058ee24574948fb43c7c94c96d440903c3974349a2ad009e5fa613759468","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T01:24:16.442153Z","signature_b64":"HlZn1MRRUXtfFY9/CpJ1XT7J6UuUKyQcWAzAeDlv8IaXYaNq79Y4vDykuOvK1YnsVnXt1xqtxRx5G3ta/2pPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da96058ee24574948fb43c7c94c96d440903c3974349a2ad009e5fa613759468","last_reissued_at":"2026-07-22T01:24:16.441441Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T01:24:16.441441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.19252","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":"2026-07-22T01:24:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"77LslylLx4Q5zgoX5dh4WHB3mAOQzeuw9PNNF41/Skw4dwNpe6GTQQVfnun4Jn5N4EcCFttjJtDvDLFqPyNNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:45:59.553283Z"},"content_sha256":"810d4c6ff274e457851245507df1a47a24ece8e72f462c688de3320b7258b230","schema_version":"1.0","event_id":"sha256:810d4c6ff274e457851245507df1a47a24ece8e72f462c688de3320b7258b230"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3KLALDXCIV2JJD5UHR6JJSLNIQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Archimedean Rigidity and Uniformity for Common Preperiodic Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chen Gong, Jit Wu Yap","submitted_at":"2026-07-21T16:22:17Z","abstract_excerpt":"Let $k$ be an algebraically closed, complete non-Archimedean field of residue characteristic $0$. Let $f$ be a polynomial of degree at least $2$ over $k$ which does not have potential good reduction. We prove that if $g$ is any other polynomial with the same Julia set, then $f$ and $g$ must be dynamically related.\n  As a consequence, we show that for any two complex polynomials $f,g$ of degree at least $2$, either their sets of preperiodic points coincide, or the number of their common preperiodic points is uniformly bounded above by a constant depending only on the degrees, thereby answering "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19252","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.19252/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-22T01:24:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IUKgiJEKe5Up0DMTrvhmwrdKWBIsknzbSCktQXlc/7v09zAshjjf280XC8FkACTFsTTAqByjv8avO5aVNdAWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:45:59.553787Z"},"content_sha256":"7e7c8e37499f6982adf91bb7fca2af4e1554d3ee72ab9c01cc99e436a5b00f2e","schema_version":"1.0","event_id":"sha256:7e7c8e37499f6982adf91bb7fca2af4e1554d3ee72ab9c01cc99e436a5b00f2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3KLALDXCIV2JJD5UHR6JJSLNIQ/bundle.json","state_url":"https://pith.science/pith/3KLALDXCIV2JJD5UHR6JJSLNIQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3KLALDXCIV2JJD5UHR6JJSLNIQ/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":"2026-08-12T15:45:59Z","links":{"resolver":"https://pith.science/pith/3KLALDXCIV2JJD5UHR6JJSLNIQ","bundle":"https://pith.science/pith/3KLALDXCIV2JJD5UHR6JJSLNIQ/bundle.json","state":"https://pith.science/pith/3KLALDXCIV2JJD5UHR6JJSLNIQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3KLALDXCIV2JJD5UHR6JJSLNIQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3KLALDXCIV2JJD5UHR6JJSLNIQ","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":"9b999d93f5e00589a23f2f597e82e5575fb33dd52d0c09266007f1b334a0530a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-21T16:22:17Z","title_canon_sha256":"86f3c60f4087b4ef2abc800c55b4c293d00444122ce8c257c84ad33a4c189514"},"schema_version":"1.0","source":{"id":"2607.19252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.19252","created_at":"2026-07-22T01:24:16Z"},{"alias_kind":"arxiv_version","alias_value":"2607.19252v1","created_at":"2026-07-22T01:24:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19252","created_at":"2026-07-22T01:24:16Z"},{"alias_kind":"pith_short_12","alias_value":"3KLALDXCIV2J","created_at":"2026-07-22T01:24:16Z"},{"alias_kind":"pith_short_16","alias_value":"3KLALDXCIV2JJD5U","created_at":"2026-07-22T01:24:16Z"},{"alias_kind":"pith_short_8","alias_value":"3KLALDXC","created_at":"2026-07-22T01:24:16Z"}],"graph_snapshots":[{"event_id":"sha256:7e7c8e37499f6982adf91bb7fca2af4e1554d3ee72ab9c01cc99e436a5b00f2e","target":"graph","created_at":"2026-07-22T01:24:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.19252/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $k$ be an algebraically closed, complete non-Archimedean field of residue characteristic $0$. Let $f$ be a polynomial of degree at least $2$ over $k$ which does not have potential good reduction. We prove that if $g$ is any other polynomial with the same Julia set, then $f$ and $g$ must be dynamically related.\n  As a consequence, we show that for any two complex polynomials $f,g$ of degree at least $2$, either their sets of preperiodic points coincide, or the number of their common preperiodic points is uniformly bounded above by a constant depending only on the degrees, thereby answering ","authors_text":"Chen Gong, Jit Wu Yap","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-21T16:22:17Z","title":"Non-Archimedean Rigidity and Uniformity for Common Preperiodic Points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19252","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":"sha256:810d4c6ff274e457851245507df1a47a24ece8e72f462c688de3320b7258b230","target":"record","created_at":"2026-07-22T01:24:16Z","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":"9b999d93f5e00589a23f2f597e82e5575fb33dd52d0c09266007f1b334a0530a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-21T16:22:17Z","title_canon_sha256":"86f3c60f4087b4ef2abc800c55b4c293d00444122ce8c257c84ad33a4c189514"},"schema_version":"1.0","source":{"id":"2607.19252","kind":"arxiv","version":1}},"canonical_sha256":"da96058ee24574948fb43c7c94c96d440903c3974349a2ad009e5fa613759468","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da96058ee24574948fb43c7c94c96d440903c3974349a2ad009e5fa613759468","first_computed_at":"2026-07-22T01:24:16.441441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T01:24:16.441441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HlZn1MRRUXtfFY9/CpJ1XT7J6UuUKyQcWAzAeDlv8IaXYaNq79Y4vDykuOvK1YnsVnXt1xqtxRx5G3ta/2pPDw==","signature_status":"signed_v1","signed_at":"2026-07-22T01:24:16.442153Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.19252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:810d4c6ff274e457851245507df1a47a24ece8e72f462c688de3320b7258b230","sha256:7e7c8e37499f6982adf91bb7fca2af4e1554d3ee72ab9c01cc99e436a5b00f2e"],"state_sha256":"8a001193775321c2215c9afc6389950bcd5d46f85bcd3865958e91438ae66544"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ozcL2/8sEUNbdjeuDbzfSGnZYP+20eMMANAotSeXcDhhSjSgRGN6cNHrjuPjl+n50A8vSaQT8862DHCdIYYeCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T15:45:59.557964Z","bundle_sha256":"7380ea78d24df039cdfc2027d1a8fb055c601bd8bf7e90d416bb4f55f673e0f7"}}