{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FLYJIHLAJUUJY4JD544RU5SIDR","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":"bc79f515848372db73bd7ba9ab2f0e54a5d7d09f9642130fb1ed89bafc5df991","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-30T22:19:19Z","title_canon_sha256":"563283f05e077808330910669bd6f93bbbff5e2fd3632418fc76b21f0bc5a08b"},"schema_version":"1.0","source":{"id":"2607.00232","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00232","created_at":"2026-07-02T00:18:40Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00232v1","created_at":"2026-07-02T00:18:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00232","created_at":"2026-07-02T00:18:40Z"},{"alias_kind":"pith_short_12","alias_value":"FLYJIHLAJUUJ","created_at":"2026-07-02T00:18:40Z"},{"alias_kind":"pith_short_16","alias_value":"FLYJIHLAJUUJY4JD","created_at":"2026-07-02T00:18:40Z"},{"alias_kind":"pith_short_8","alias_value":"FLYJIHLA","created_at":"2026-07-02T00:18:40Z"}],"graph_snapshots":[{"event_id":"sha256:f1dc2aef8837e45f8f0a9df5b9e96fa62e2018a48ede3da73d9d71f9b84694cd","target":"graph","created_at":"2026-07-02T00:18:40Z","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/2607.00232/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove that the \\'{e}tale fundamental group of the N\\'{e}ron model of an abelian variety over a number field $K$ is the semidirect product of a finite group with the \\'{e}tale fundamental group of the ring of integers of $K.$ We prove this by studying how the Faltings height of an abelian variety changes under covers that spread out to finite \\'{e}tale covers of its N\\'{e}ron model. We then strengthen this result for elliptic curves. Using Merel's torsion theorem, we show the size of this finite group can be uniformly bounded for a fixed number field. We conclude by giving the","authors_text":"Frank Lu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-30T22:19:19Z","title":"Finiteness for \\'{E}tale Fundamental Groups of N\\'{e}ron Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00232","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":"sha256:44a01317774f96413cb84ab10b06fef9e4c368b3e8e187b3cc212779e444463d","target":"record","created_at":"2026-07-02T00:18:40Z","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":"bc79f515848372db73bd7ba9ab2f0e54a5d7d09f9642130fb1ed89bafc5df991","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-30T22:19:19Z","title_canon_sha256":"563283f05e077808330910669bd6f93bbbff5e2fd3632418fc76b21f0bc5a08b"},"schema_version":"1.0","source":{"id":"2607.00232","kind":"arxiv","version":1}},"canonical_sha256":"2af0941d604d289c7123ef391a76481c6d0e31fdee8edd61b1d9c46b20196b79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2af0941d604d289c7123ef391a76481c6d0e31fdee8edd61b1d9c46b20196b79","first_computed_at":"2026-07-02T00:18:40.307914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T00:18:40.307914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AWj5WrC9r9L1fLBDVTJWmnGCMUfNYp5bGN7wREiePmOxvg7J8EMcu9ehkI6LJwAqT4dzQhkErWky16f5eW1tBQ==","signature_status":"signed_v1","signed_at":"2026-07-02T00:18:40.308423Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00232","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44a01317774f96413cb84ab10b06fef9e4c368b3e8e187b3cc212779e444463d","sha256:f1dc2aef8837e45f8f0a9df5b9e96fa62e2018a48ede3da73d9d71f9b84694cd"],"state_sha256":"94e48e7f6af87802accb46080abe1aa91ce1de30475e12b8647a063f871c8353"}