{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:TOIN4FQ64YACRUHWGK245A5KTJ","short_pith_number":"pith:TOIN4FQ6","schema_version":"1.0","canonical_sha256":"9b90de161ee60028d0f632b5ce83aa9a791999998d030a2d4367c7e17f2bcede","source":{"kind":"arxiv","id":"1007.0744","version":2},"attestation_state":"computed","paper":{"title":"Pre-images of quadratic dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Benjamin Hutz, Benjamin Krause, Trevor Hyde","submitted_at":"2010-07-05T18:49:53Z","abstract_excerpt":"For a quadratic endomorphism of the affine line defined over the rationals we consider the problem of bounding the number of rational points that eventually land at a given constant after iteration, called pre-images of the constant. In the article \"Uniform Bounds on Pre-Images Under Quadratic Dynamical Systems,\" it was shown that the number of rational pre-images is bounded as one varies the morphism in a certain one-dimensional family. Explicit values of the constant for pre-images of zero and -1 defined over the rational numbers were addressed in subsequent articles. This article addresses "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1007.0744","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-07-05T18:49:53Z","cross_cats_sorted":[],"title_canon_sha256":"bdb24451df3e585719459bc04d036a120cef7c8ede023f0b9175fd1509dfd8dc","abstract_canon_sha256":"e69f67c804f97c950aa367ef8d97ae5ad1ece61a361c7a74d899c8c1081210f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:02.373362Z","signature_b64":"vf7iimTh0oC7mhOV15Ve2okdjgz9vClpGgm9OGwL8ST6TA7nS3iNE6ikpWDjrjxg+pwETBgPLZmJ7LKFPgf5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b90de161ee60028d0f632b5ce83aa9a791999998d030a2d4367c7e17f2bcede","last_reissued_at":"2026-05-18T04:22:02.372902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:02.372902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pre-images of quadratic dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Benjamin Hutz, Benjamin Krause, Trevor Hyde","submitted_at":"2010-07-05T18:49:53Z","abstract_excerpt":"For a quadratic endomorphism of the affine line defined over the rationals we consider the problem of bounding the number of rational points that eventually land at a given constant after iteration, called pre-images of the constant. In the article \"Uniform Bounds on Pre-Images Under Quadratic Dynamical Systems,\" it was shown that the number of rational pre-images is bounded as one varies the morphism in a certain one-dimensional family. Explicit values of the constant for pre-images of zero and -1 defined over the rational numbers were addressed in subsequent articles. This article addresses "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0744","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1007.0744","created_at":"2026-05-18T04:22:02.372961+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.0744v2","created_at":"2026-05-18T04:22:02.372961+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0744","created_at":"2026-05-18T04:22:02.372961+00:00"},{"alias_kind":"pith_short_12","alias_value":"TOIN4FQ64YAC","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"TOIN4FQ64YACRUHW","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"TOIN4FQ6","created_at":"2026-05-18T12:26:13.927090+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TOIN4FQ64YACRUHWGK245A5KTJ","json":"https://pith.science/pith/TOIN4FQ64YACRUHWGK245A5KTJ.json","graph_json":"https://pith.science/api/pith-number/TOIN4FQ64YACRUHWGK245A5KTJ/graph.json","events_json":"https://pith.science/api/pith-number/TOIN4FQ64YACRUHWGK245A5KTJ/events.json","paper":"https://pith.science/paper/TOIN4FQ6"},"agent_actions":{"view_html":"https://pith.science/pith/TOIN4FQ64YACRUHWGK245A5KTJ","download_json":"https://pith.science/pith/TOIN4FQ64YACRUHWGK245A5KTJ.json","view_paper":"https://pith.science/paper/TOIN4FQ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.0744&json=true","fetch_graph":"https://pith.science/api/pith-number/TOIN4FQ64YACRUHWGK245A5KTJ/graph.json","fetch_events":"https://pith.science/api/pith-number/TOIN4FQ64YACRUHWGK245A5KTJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TOIN4FQ64YACRUHWGK245A5KTJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TOIN4FQ64YACRUHWGK245A5KTJ/action/storage_attestation","attest_author":"https://pith.science/pith/TOIN4FQ64YACRUHWGK245A5KTJ/action/author_attestation","sign_citation":"https://pith.science/pith/TOIN4FQ64YACRUHWGK245A5KTJ/action/citation_signature","submit_replication":"https://pith.science/pith/TOIN4FQ64YACRUHWGK245A5KTJ/action/replication_record"}},"created_at":"2026-05-18T04:22:02.372961+00:00","updated_at":"2026-05-18T04:22:02.372961+00:00"}