{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SWUNDHRYNNGVPQ232A3CMIH5LS","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":"b439dca6cc3436f3b5c7ab1d19a269e97242d1999a590860f9afface8653f5fb","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-31T15:39:57Z","title_canon_sha256":"0755ad3bb639e231296732856e2b7e890841507c04b618c5f402d352a4b48c95"},"schema_version":"1.0","source":{"id":"2606.01299","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01299","created_at":"2026-06-02T02:04:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01299v1","created_at":"2026-06-02T02:04:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01299","created_at":"2026-06-02T02:04:29Z"},{"alias_kind":"pith_short_12","alias_value":"SWUNDHRYNNGV","created_at":"2026-06-02T02:04:29Z"},{"alias_kind":"pith_short_16","alias_value":"SWUNDHRYNNGVPQ23","created_at":"2026-06-02T02:04:29Z"},{"alias_kind":"pith_short_8","alias_value":"SWUNDHRY","created_at":"2026-06-02T02:04:29Z"}],"graph_snapshots":[{"event_id":"sha256:000daad22dedbedea86b797138bed1a49a4d2fd9b83180ab1f40936dee5126de","target":"graph","created_at":"2026-06-02T02:04:29Z","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/2606.01299/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the interaction between the group law on an abelian variety and the additive structure induced on its image under a morphism to a projective space. Let $A/F$ be an abelian variety, $f:A \\rightarrow \\mathbb{P}^n$ be a morphism which is finite onto its image, and $\\Gamma \\subseteq A(F)$ be a finite-rank subgroup. We show that for any affine chart $\\mathbb{A}^n \\subseteq \\mathbb{P}^n$ and any finite subset $X \\subseteq f(\\Gamma) \\cap \\mathbb{A}^n$, the energy satisfies $E(X) \\ll \\lvert X \\rvert^2$ and the sumset satisfies $\\lvert X+X \\rvert \\gg \\lvert X \\rvert^2$. Thus images of finite-r","authors_text":"Seokhyun Choi","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-31T15:39:57Z","title":"Additive Rigidity for Images of Rational Points on Abelian Varieties II: The General Case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01299","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:c40380d0f910ea2cbdab167a929797bcbbd137c8c2df74f0be2526098332bc0f","target":"record","created_at":"2026-06-02T02:04:29Z","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":"b439dca6cc3436f3b5c7ab1d19a269e97242d1999a590860f9afface8653f5fb","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-31T15:39:57Z","title_canon_sha256":"0755ad3bb639e231296732856e2b7e890841507c04b618c5f402d352a4b48c95"},"schema_version":"1.0","source":{"id":"2606.01299","kind":"arxiv","version":1}},"canonical_sha256":"95a8d19e386b4d57c35bd0362620fd5cb586f266f6730f7bc8269aded805bccf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95a8d19e386b4d57c35bd0362620fd5cb586f266f6730f7bc8269aded805bccf","first_computed_at":"2026-06-02T02:04:29.440178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:29.440178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qmzCc4vwNE7G8KxypS8VEXB2tg3vvAVo/Q1SgQ3CPNJ4dDcdmnO4G+fKcPtSnP3WHUfHTuHwOEfr/jjCedk8DA==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:29.441205Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.01299","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c40380d0f910ea2cbdab167a929797bcbbd137c8c2df74f0be2526098332bc0f","sha256:000daad22dedbedea86b797138bed1a49a4d2fd9b83180ab1f40936dee5126de"],"state_sha256":"23839359c5e55d68a8d33ebf566afcb028d2af433f9b6565b1228775a394b7d6"}