{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YLGPCBHQDR6OEDFJIQ4F735XDL","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":"71d8871b4f4104edc0601dc14825c51a3672dd2c336eaa03505fbd41531e65b8","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-12T17:48:50Z","title_canon_sha256":"fccea79d920d8774fd0d4baf99458289e6abbd22bcd01e41557156d94c22a9fe"},"schema_version":"1.0","source":{"id":"2508.09114","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.09114","created_at":"2026-07-05T11:52:39Z"},{"alias_kind":"arxiv_version","alias_value":"2508.09114v1","created_at":"2026-07-05T11:52:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.09114","created_at":"2026-07-05T11:52:39Z"},{"alias_kind":"pith_short_12","alias_value":"YLGPCBHQDR6O","created_at":"2026-07-05T11:52:39Z"},{"alias_kind":"pith_short_16","alias_value":"YLGPCBHQDR6OEDFJ","created_at":"2026-07-05T11:52:39Z"},{"alias_kind":"pith_short_8","alias_value":"YLGPCBHQ","created_at":"2026-07-05T11:52:39Z"}],"graph_snapshots":[{"event_id":"sha256:605ae3ad3646d513613f541c151b89341972acab7fe8e5ee303e05a75d16b80a","target":"graph","created_at":"2026-07-05T11:52:39Z","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/2508.09114/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we explore a variety of finiteness questions for preperiodic points of morphisms. We begin by treating a group action analog of the Burnside problem for torsion groups using the p-adic arc method. We then prove some results connecting commonality of preperiodic points for elements of an automorphism group with structural properties of the group; these results are related to well-known results of Tits and Borel. We finish by proving some Northcott-type results for finite morphisms.","authors_text":"Jason P. Bell, Thomas J. Tucker","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-12T17:48:50Z","title":"Preperiodic points, finiteness, and structures of semigroups of algebraic morphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.09114","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:b5acd4ee389503d2d0d134c567cb376e4de727c92aaf2c63be9a4d6a13b7554b","target":"record","created_at":"2026-07-05T11:52:39Z","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":"71d8871b4f4104edc0601dc14825c51a3672dd2c336eaa03505fbd41531e65b8","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-12T17:48:50Z","title_canon_sha256":"fccea79d920d8774fd0d4baf99458289e6abbd22bcd01e41557156d94c22a9fe"},"schema_version":"1.0","source":{"id":"2508.09114","kind":"arxiv","version":1}},"canonical_sha256":"c2ccf104f01c7ce20ca944385fefb71adf8e47ae9135ba280a53097a9eef55a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2ccf104f01c7ce20ca944385fefb71adf8e47ae9135ba280a53097a9eef55a1","first_computed_at":"2026-07-05T11:52:39.842671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:52:39.842671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5U5BTGa08XETj1aNcTWmOqpsYqU8VPDpFUpfW5/AsfVeRnlX0clk/Pt6U+L+u8M0fqpEvJOeei3sP/n4F2IXCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:52:39.843245Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.09114","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5acd4ee389503d2d0d134c567cb376e4de727c92aaf2c63be9a4d6a13b7554b","sha256:605ae3ad3646d513613f541c151b89341972acab7fe8e5ee303e05a75d16b80a"],"state_sha256":"ca4b3c4cda5b042f6ca9d564bed3dd307027341ddecac3e85c6687dbbac2dd3f"}