{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:G74XEFL3KXEHLO6TCBKAQR7WE6","short_pith_number":"pith:G74XEFL3","schema_version":"1.0","canonical_sha256":"37f972157b55c875bbd310540847f627b84583a0563f0545be9ec571697486d4","source":{"kind":"arxiv","id":"1512.06258","version":1},"attestation_state":"computed","paper":{"title":"p-adic variation of unit root L-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"C. Douglas Haessig, Steven Sperber","submitted_at":"2015-12-19T14:57:58Z","abstract_excerpt":"Dwork's conjecture, now proven by Wan, states that unit root L-functions \"coming from geometry\" are p-adic meromorphic. In this paper we study the p-adic variation of a family of unit root L-functions coming from a suitable family of toric exponential sums. In this setting, we find that the unit root L-functions each have a unique p-adic unit root. We then study the variation of this unit root over the family of unit root L-functions. Surprisingly, we find that this unit root behaves similarly to the classical case of families of exponential sums. That is, the unit root is essentially a ratio "},"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":"1512.06258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-19T14:57:58Z","cross_cats_sorted":[],"title_canon_sha256":"79e9bc7724ec9cbe3d9ffd375bbb1bbcb244baa4066725512f1756dc77870a88","abstract_canon_sha256":"1162d0a324b794ad4d02fb71c85f697ced62f70924629bd7dc7b6915de0f8c4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:09.170468Z","signature_b64":"7i5RyeTPV++DD+6uZ/USILotX1j72aeEdp9gwRsphIpb9osULiVfD1iBnh0zvnOVZwQzgkShUyS7ja/TNialDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37f972157b55c875bbd310540847f627b84583a0563f0545be9ec571697486d4","last_reissued_at":"2026-05-18T00:46:09.170030Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:09.170030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"p-adic variation of unit root L-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"C. Douglas Haessig, Steven Sperber","submitted_at":"2015-12-19T14:57:58Z","abstract_excerpt":"Dwork's conjecture, now proven by Wan, states that unit root L-functions \"coming from geometry\" are p-adic meromorphic. In this paper we study the p-adic variation of a family of unit root L-functions coming from a suitable family of toric exponential sums. In this setting, we find that the unit root L-functions each have a unique p-adic unit root. We then study the variation of this unit root over the family of unit root L-functions. Surprisingly, we find that this unit root behaves similarly to the classical case of families of exponential sums. That is, the unit root is essentially a ratio "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06258","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":""},"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":"1512.06258","created_at":"2026-05-18T00:46:09.170093+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.06258v1","created_at":"2026-05-18T00:46:09.170093+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06258","created_at":"2026-05-18T00:46:09.170093+00:00"},{"alias_kind":"pith_short_12","alias_value":"G74XEFL3KXEH","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"G74XEFL3KXEHLO6T","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"G74XEFL3","created_at":"2026-05-18T12:29:22.688609+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/G74XEFL3KXEHLO6TCBKAQR7WE6","json":"https://pith.science/pith/G74XEFL3KXEHLO6TCBKAQR7WE6.json","graph_json":"https://pith.science/api/pith-number/G74XEFL3KXEHLO6TCBKAQR7WE6/graph.json","events_json":"https://pith.science/api/pith-number/G74XEFL3KXEHLO6TCBKAQR7WE6/events.json","paper":"https://pith.science/paper/G74XEFL3"},"agent_actions":{"view_html":"https://pith.science/pith/G74XEFL3KXEHLO6TCBKAQR7WE6","download_json":"https://pith.science/pith/G74XEFL3KXEHLO6TCBKAQR7WE6.json","view_paper":"https://pith.science/paper/G74XEFL3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.06258&json=true","fetch_graph":"https://pith.science/api/pith-number/G74XEFL3KXEHLO6TCBKAQR7WE6/graph.json","fetch_events":"https://pith.science/api/pith-number/G74XEFL3KXEHLO6TCBKAQR7WE6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G74XEFL3KXEHLO6TCBKAQR7WE6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G74XEFL3KXEHLO6TCBKAQR7WE6/action/storage_attestation","attest_author":"https://pith.science/pith/G74XEFL3KXEHLO6TCBKAQR7WE6/action/author_attestation","sign_citation":"https://pith.science/pith/G74XEFL3KXEHLO6TCBKAQR7WE6/action/citation_signature","submit_replication":"https://pith.science/pith/G74XEFL3KXEHLO6TCBKAQR7WE6/action/replication_record"}},"created_at":"2026-05-18T00:46:09.170093+00:00","updated_at":"2026-05-18T00:46:09.170093+00:00"}