{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZQT3B6OQ57G2SLQILQQJYRGKJG","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":"4c8888539a217d3e0e41961219adb1a536648972075a96a0321ee10a6e3e0631","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-24T17:46:52Z","title_canon_sha256":"59123ce49492ff5203513007bc17471d8fb01f90301c8d4fc4f9fc83efcd2e79"},"schema_version":"1.0","source":{"id":"2508.17463","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.17463","created_at":"2026-07-05T11:58:41Z"},{"alias_kind":"arxiv_version","alias_value":"2508.17463v1","created_at":"2026-07-05T11:58:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.17463","created_at":"2026-07-05T11:58:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZQT3B6OQ57G2","created_at":"2026-07-05T11:58:41Z"},{"alias_kind":"pith_short_16","alias_value":"ZQT3B6OQ57G2SLQI","created_at":"2026-07-05T11:58:41Z"},{"alias_kind":"pith_short_8","alias_value":"ZQT3B6OQ","created_at":"2026-07-05T11:58:41Z"}],"graph_snapshots":[{"event_id":"sha256:a8991f35dd8857455180e2c9096a510589b073c334c37bb5cb45f799d9f9e539","target":"graph","created_at":"2026-07-05T11:58:41Z","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/2508.17463/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The modular curves in the family $X_1(N)$ for natural numbers $N$ parametrize elliptic curves over the complex numbers with a distinguished point of order $N$. The purpose of this paper is to better understand how to calculate the degrees of points on $X_1(\\ell^n)$ for a prime $\\ell$ and arbitrary positive integer $n$. In analogy with the definition of the level of a Galois representation, we construct a new definition: the level of a fiber of a closed point on a modular curve. Using this definition, we prove that, under certain conditions, if the degree of a point on $X_1(\\ell^{k+1})$ is as l","authors_text":"Hailey Maxwell","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-24T17:46:52Z","title":"Computing the Level of a Fiber for Points on Modular Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.17463","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":"sha256:3ff6fa5ff4186cba1d191aeb2ce85af0d696893307844973370849143894094d","target":"record","created_at":"2026-07-05T11:58:41Z","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":"4c8888539a217d3e0e41961219adb1a536648972075a96a0321ee10a6e3e0631","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-24T17:46:52Z","title_canon_sha256":"59123ce49492ff5203513007bc17471d8fb01f90301c8d4fc4f9fc83efcd2e79"},"schema_version":"1.0","source":{"id":"2508.17463","kind":"arxiv","version":1}},"canonical_sha256":"cc27b0f9d0efcda92e085c209c44ca49b1011684e1156f96bd726dd1aed3091d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc27b0f9d0efcda92e085c209c44ca49b1011684e1156f96bd726dd1aed3091d","first_computed_at":"2026-07-05T11:58:41.861413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:58:41.861413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sKlgeFJxVyNFxTG6RAaKMyWyIp6UDzTMu8FOY33fG8DNfcQUktdQsa4rEUTTYLglUsM8Re/gd0QauvN0/bRMDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:58:41.861818Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.17463","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ff6fa5ff4186cba1d191aeb2ce85af0d696893307844973370849143894094d","sha256:a8991f35dd8857455180e2c9096a510589b073c334c37bb5cb45f799d9f9e539"],"state_sha256":"fa31fc7073e261a0921b086e86a9376743c3bc8f401d7c8c00265625b73270cc"}