{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TPJP6Z3YEPEES4KEJGR7BZ7QY3","short_pith_number":"pith:TPJP6Z3Y","canonical_record":{"source":{"id":"2401.17872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-01-31T14:28:58Z","cross_cats_sorted":[],"title_canon_sha256":"4776d7a14a7e5624793b6beb7dcd02fbc26e7d05cb62c8f2bece3029811aba09","abstract_canon_sha256":"7ae5b3d395e1592ecd735b551f040a3d6650ab88cc170f853c3731a8426d4735"},"schema_version":"1.0"},"canonical_sha256":"9bd2ff677823c849714449a3f0e7f0c6ddd0d34a7de9dc86101c1bbca85b5108","source":{"kind":"arxiv","id":"2401.17872","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.17872","created_at":"2026-07-05T07:40:07Z"},{"alias_kind":"arxiv_version","alias_value":"2401.17872v2","created_at":"2026-07-05T07:40:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.17872","created_at":"2026-07-05T07:40:07Z"},{"alias_kind":"pith_short_12","alias_value":"TPJP6Z3YEPEE","created_at":"2026-07-05T07:40:07Z"},{"alias_kind":"pith_short_16","alias_value":"TPJP6Z3YEPEES4KE","created_at":"2026-07-05T07:40:07Z"},{"alias_kind":"pith_short_8","alias_value":"TPJP6Z3Y","created_at":"2026-07-05T07:40:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TPJP6Z3YEPEES4KEJGR7BZ7QY3","target":"record","payload":{"canonical_record":{"source":{"id":"2401.17872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-01-31T14:28:58Z","cross_cats_sorted":[],"title_canon_sha256":"4776d7a14a7e5624793b6beb7dcd02fbc26e7d05cb62c8f2bece3029811aba09","abstract_canon_sha256":"7ae5b3d395e1592ecd735b551f040a3d6650ab88cc170f853c3731a8426d4735"},"schema_version":"1.0"},"canonical_sha256":"9bd2ff677823c849714449a3f0e7f0c6ddd0d34a7de9dc86101c1bbca85b5108","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:40:07.419395Z","signature_b64":"f1tw9mCqb1JRm9eO4uYm8Wj04NBoH5qS4V9dbt2iyco+RFtH5OlfJuJWxctEG64NBILbWxSw4ICE4/w+TnGxDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bd2ff677823c849714449a3f0e7f0c6ddd0d34a7de9dc86101c1bbca85b5108","last_reissued_at":"2026-07-05T07:40:07.418957Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:40:07.418957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.17872","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":"2026-07-05T07:40:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J49jwEzggYGoskY9+GcNJsP+bfH9qNiCHx12LZmqaIyxZI9uXSn+aWPeVcE35hKEAYNnpNY+PMtDQIQkf00YBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:24:08.368221Z"},"content_sha256":"9214a523aea9213d79166e7ce763bf24f35468ffdfaf3bc8b8747e449e1058f1","schema_version":"1.0","event_id":"sha256:9214a523aea9213d79166e7ce763bf24f35468ffdfaf3bc8b8747e449e1058f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TPJP6Z3YEPEES4KEJGR7BZ7QY3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial compositions with large monodromy groups and applications to arithmetic dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Danny Neftin, Joachim K\\\"onig, Shai Rosenberg","submitted_at":"2024-01-31T14:28:58Z","abstract_excerpt":"For a composition $f=f_1\\circ\\cdots \\circ f_r$ of polynomials $f_i\\in \\mathbb Q[x]$ of degrees $d_i\\geq 5$ with alternating or symmetric monodromy group, we show that the monodromy group of $f$ contains the iterated wreath product $A_{d_r}\\wr \\cdots\\wr A_{d_1}$. A similar property holds more generally for polynomials that do not factor through $x^d$ or Chebyshev. We derive consequences to arithmetic dynamics regarding arboreal representations, and forward and backward orbits of such $f$. In particular, given an orbit $(a_n)_{n=0}^\\infty$ of $f$ as above, we show that for \"almost all\" $a\\in \\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.17872","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.17872/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":"2026-07-05T07:40:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k4hUgozbsJFfaO+4Uq8fhUn1ysLnaCJdTSyUHAD/y5/Bvq3YFQ/H2OwaVyWgnUx3dffOanWYWCb/HerqdH+SCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:24:08.369257Z"},"content_sha256":"97e12c9583ad40e1bae827674a7e6a63677dad80de585bec07abc35e616b97e1","schema_version":"1.0","event_id":"sha256:97e12c9583ad40e1bae827674a7e6a63677dad80de585bec07abc35e616b97e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TPJP6Z3YEPEES4KEJGR7BZ7QY3/bundle.json","state_url":"https://pith.science/pith/TPJP6Z3YEPEES4KEJGR7BZ7QY3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TPJP6Z3YEPEES4KEJGR7BZ7QY3/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":"2026-08-10T19:24:08Z","links":{"resolver":"https://pith.science/pith/TPJP6Z3YEPEES4KEJGR7BZ7QY3","bundle":"https://pith.science/pith/TPJP6Z3YEPEES4KEJGR7BZ7QY3/bundle.json","state":"https://pith.science/pith/TPJP6Z3YEPEES4KEJGR7BZ7QY3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TPJP6Z3YEPEES4KEJGR7BZ7QY3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TPJP6Z3YEPEES4KEJGR7BZ7QY3","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":"7ae5b3d395e1592ecd735b551f040a3d6650ab88cc170f853c3731a8426d4735","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-01-31T14:28:58Z","title_canon_sha256":"4776d7a14a7e5624793b6beb7dcd02fbc26e7d05cb62c8f2bece3029811aba09"},"schema_version":"1.0","source":{"id":"2401.17872","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.17872","created_at":"2026-07-05T07:40:07Z"},{"alias_kind":"arxiv_version","alias_value":"2401.17872v2","created_at":"2026-07-05T07:40:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.17872","created_at":"2026-07-05T07:40:07Z"},{"alias_kind":"pith_short_12","alias_value":"TPJP6Z3YEPEE","created_at":"2026-07-05T07:40:07Z"},{"alias_kind":"pith_short_16","alias_value":"TPJP6Z3YEPEES4KE","created_at":"2026-07-05T07:40:07Z"},{"alias_kind":"pith_short_8","alias_value":"TPJP6Z3Y","created_at":"2026-07-05T07:40:07Z"}],"graph_snapshots":[{"event_id":"sha256:97e12c9583ad40e1bae827674a7e6a63677dad80de585bec07abc35e616b97e1","target":"graph","created_at":"2026-07-05T07:40:07Z","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/2401.17872/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a composition $f=f_1\\circ\\cdots \\circ f_r$ of polynomials $f_i\\in \\mathbb Q[x]$ of degrees $d_i\\geq 5$ with alternating or symmetric monodromy group, we show that the monodromy group of $f$ contains the iterated wreath product $A_{d_r}\\wr \\cdots\\wr A_{d_1}$. A similar property holds more generally for polynomials that do not factor through $x^d$ or Chebyshev. We derive consequences to arithmetic dynamics regarding arboreal representations, and forward and backward orbits of such $f$. In particular, given an orbit $(a_n)_{n=0}^\\infty$ of $f$ as above, we show that for \"almost all\" $a\\in \\ma","authors_text":"Danny Neftin, Joachim K\\\"onig, Shai Rosenberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-01-31T14:28:58Z","title":"Polynomial compositions with large monodromy groups and applications to arithmetic dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.17872","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":"sha256:9214a523aea9213d79166e7ce763bf24f35468ffdfaf3bc8b8747e449e1058f1","target":"record","created_at":"2026-07-05T07:40:07Z","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":"7ae5b3d395e1592ecd735b551f040a3d6650ab88cc170f853c3731a8426d4735","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-01-31T14:28:58Z","title_canon_sha256":"4776d7a14a7e5624793b6beb7dcd02fbc26e7d05cb62c8f2bece3029811aba09"},"schema_version":"1.0","source":{"id":"2401.17872","kind":"arxiv","version":2}},"canonical_sha256":"9bd2ff677823c849714449a3f0e7f0c6ddd0d34a7de9dc86101c1bbca85b5108","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bd2ff677823c849714449a3f0e7f0c6ddd0d34a7de9dc86101c1bbca85b5108","first_computed_at":"2026-07-05T07:40:07.418957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:40:07.418957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f1tw9mCqb1JRm9eO4uYm8Wj04NBoH5qS4V9dbt2iyco+RFtH5OlfJuJWxctEG64NBILbWxSw4ICE4/w+TnGxDg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:40:07.419395Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.17872","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9214a523aea9213d79166e7ce763bf24f35468ffdfaf3bc8b8747e449e1058f1","sha256:97e12c9583ad40e1bae827674a7e6a63677dad80de585bec07abc35e616b97e1"],"state_sha256":"f5b57fe85297d693801c86c7231f8062888f072c4eb198577bf996a6078ccb34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dHUpLylCAfW5eulVwxCD02Gh/YrTsVSTdiDLDKaD1TU7BuHgzmxaSGF6seKMqPvJZ9rGgacTUfP/hn+Td3tCBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T19:24:08.375217Z","bundle_sha256":"6261e809c521c3ddc57b43a9f69c7a263a334e46af1b63b51967f7c9f1daf87b"}}