{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:T6ZXIMYB2WZ7DQAYHSVF5KCZZQ","short_pith_number":"pith:T6ZXIMYB","canonical_record":{"source":{"id":"2606.29057","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-27T19:31:04Z","cross_cats_sorted":["math.AG","math.DS"],"title_canon_sha256":"8d83cf3636b0f71500b9763bc9cdfcd4745741e06409acf8f6526d4938f45bd4","abstract_canon_sha256":"17f4a104889b52b3b5e370fcb71a9055b024936740fa88c51c0b3e569801ffad"},"schema_version":"1.0"},"canonical_sha256":"9fb3743301d5b3f1c0183caa5ea859cc068f1e2a65c4055203d5cddb0ee696bf","source":{"kind":"arxiv","id":"2606.29057","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29057","created_at":"2026-06-30T01:17:51Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29057v1","created_at":"2026-06-30T01:17:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29057","created_at":"2026-06-30T01:17:51Z"},{"alias_kind":"pith_short_12","alias_value":"T6ZXIMYB2WZ7","created_at":"2026-06-30T01:17:51Z"},{"alias_kind":"pith_short_16","alias_value":"T6ZXIMYB2WZ7DQAY","created_at":"2026-06-30T01:17:51Z"},{"alias_kind":"pith_short_8","alias_value":"T6ZXIMYB","created_at":"2026-06-30T01:17:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:T6ZXIMYB2WZ7DQAYHSVF5KCZZQ","target":"record","payload":{"canonical_record":{"source":{"id":"2606.29057","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-27T19:31:04Z","cross_cats_sorted":["math.AG","math.DS"],"title_canon_sha256":"8d83cf3636b0f71500b9763bc9cdfcd4745741e06409acf8f6526d4938f45bd4","abstract_canon_sha256":"17f4a104889b52b3b5e370fcb71a9055b024936740fa88c51c0b3e569801ffad"},"schema_version":"1.0"},"canonical_sha256":"9fb3743301d5b3f1c0183caa5ea859cc068f1e2a65c4055203d5cddb0ee696bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:17:51.065410Z","signature_b64":"78Y3CtQm8wT2L1oREV5cskOVQPn0G61FITDZ6TQ0EkDI/x4vLHPKsUpvrNdhsBWvvWrbHUB+LVp5Oz+CECSDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fb3743301d5b3f1c0183caa5ea859cc068f1e2a65c4055203d5cddb0ee696bf","last_reissued_at":"2026-06-30T01:17:51.064946Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:17:51.064946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.29057","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-30T01:17:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1T1rl5h4oScCRzGJgTw9XeepH/6Q7j/Huqua3nhxiOZymnxQdXUo7VJLkNXp67VGS2iyKeWvD5Ofw+plcr0bAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T11:55:37.962274Z"},"content_sha256":"54af741a3bf1d8ad6a1566ef5f3e76fac2748747ecd835e89f500980a1ea1182","schema_version":"1.0","event_id":"sha256:54af741a3bf1d8ad6a1566ef5f3e76fac2748747ecd835e89f500980a1ea1182"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:T6ZXIMYB2WZ7DQAYHSVF5KCZZQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Dense Orbit Transversality for Endomorphisms of Abelian Varieties","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AG","math.DS"],"primary_cat":"math.NT","authors_text":"Kaiwen Lu","submitted_at":"2026-06-27T19:31:04Z","abstract_excerpt":"Let $X/K$ be a smooth projective variety defined over a number field and $f:X\\to X$ be a morphism defined over $K$. Assuming there exists a point in $X(K)$ whose $f$-orbit is Zariski dense in $X$ and up to replacing $K$ by a finite extension, Pasten and Silverman studied the distribution of grand $(f,K)$-orbits and proved that many sets of representatives of grand $(f,K)$-orbits on various classes of varieties are Zariski dense. In particular, they showed that if $X$ is a geometrically simple abelian variety, then all such sets of representatives are Zariski dense. We demonstrate the existence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29057","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29057/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-30T01:17:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xoQHD3zlO/hFmczhOEgGFBMmla86WW2BkQd0n/KTDjT0saOHrv5lTRE0yAvZ/nvPG5nOKSrPP3iNLA4bhhwZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T11:55:37.962805Z"},"content_sha256":"a5ab010c3b021f45bffc1523eea19c464c0b94753ab510cd7fbd21ecdbb9e493","schema_version":"1.0","event_id":"sha256:a5ab010c3b021f45bffc1523eea19c464c0b94753ab510cd7fbd21ecdbb9e493"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T6ZXIMYB2WZ7DQAYHSVF5KCZZQ/bundle.json","state_url":"https://pith.science/pith/T6ZXIMYB2WZ7DQAYHSVF5KCZZQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T6ZXIMYB2WZ7DQAYHSVF5KCZZQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-23T11:55:37Z","links":{"resolver":"https://pith.science/pith/T6ZXIMYB2WZ7DQAYHSVF5KCZZQ","bundle":"https://pith.science/pith/T6ZXIMYB2WZ7DQAYHSVF5KCZZQ/bundle.json","state":"https://pith.science/pith/T6ZXIMYB2WZ7DQAYHSVF5KCZZQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T6ZXIMYB2WZ7DQAYHSVF5KCZZQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:T6ZXIMYB2WZ7DQAYHSVF5KCZZQ","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":"17f4a104889b52b3b5e370fcb71a9055b024936740fa88c51c0b3e569801ffad","cross_cats_sorted":["math.AG","math.DS"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-27T19:31:04Z","title_canon_sha256":"8d83cf3636b0f71500b9763bc9cdfcd4745741e06409acf8f6526d4938f45bd4"},"schema_version":"1.0","source":{"id":"2606.29057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29057","created_at":"2026-06-30T01:17:51Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29057v1","created_at":"2026-06-30T01:17:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29057","created_at":"2026-06-30T01:17:51Z"},{"alias_kind":"pith_short_12","alias_value":"T6ZXIMYB2WZ7","created_at":"2026-06-30T01:17:51Z"},{"alias_kind":"pith_short_16","alias_value":"T6ZXIMYB2WZ7DQAY","created_at":"2026-06-30T01:17:51Z"},{"alias_kind":"pith_short_8","alias_value":"T6ZXIMYB","created_at":"2026-06-30T01:17:51Z"}],"graph_snapshots":[{"event_id":"sha256:a5ab010c3b021f45bffc1523eea19c464c0b94753ab510cd7fbd21ecdbb9e493","target":"graph","created_at":"2026-06-30T01:17:51Z","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/2606.29057/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X/K$ be a smooth projective variety defined over a number field and $f:X\\to X$ be a morphism defined over $K$. Assuming there exists a point in $X(K)$ whose $f$-orbit is Zariski dense in $X$ and up to replacing $K$ by a finite extension, Pasten and Silverman studied the distribution of grand $(f,K)$-orbits and proved that many sets of representatives of grand $(f,K)$-orbits on various classes of varieties are Zariski dense. In particular, they showed that if $X$ is a geometrically simple abelian variety, then all such sets of representatives are Zariski dense. We demonstrate the existence","authors_text":"Kaiwen Lu","cross_cats":["math.AG","math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-27T19:31:04Z","title":"On Dense Orbit Transversality for Endomorphisms of Abelian Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29057","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":"sha256:54af741a3bf1d8ad6a1566ef5f3e76fac2748747ecd835e89f500980a1ea1182","target":"record","created_at":"2026-06-30T01:17:51Z","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":"17f4a104889b52b3b5e370fcb71a9055b024936740fa88c51c0b3e569801ffad","cross_cats_sorted":["math.AG","math.DS"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-27T19:31:04Z","title_canon_sha256":"8d83cf3636b0f71500b9763bc9cdfcd4745741e06409acf8f6526d4938f45bd4"},"schema_version":"1.0","source":{"id":"2606.29057","kind":"arxiv","version":1}},"canonical_sha256":"9fb3743301d5b3f1c0183caa5ea859cc068f1e2a65c4055203d5cddb0ee696bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fb3743301d5b3f1c0183caa5ea859cc068f1e2a65c4055203d5cddb0ee696bf","first_computed_at":"2026-06-30T01:17:51.064946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:17:51.064946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"78Y3CtQm8wT2L1oREV5cskOVQPn0G61FITDZ6TQ0EkDI/x4vLHPKsUpvrNdhsBWvvWrbHUB+LVp5Oz+CECSDAQ==","signature_status":"signed_v1","signed_at":"2026-06-30T01:17:51.065410Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.29057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54af741a3bf1d8ad6a1566ef5f3e76fac2748747ecd835e89f500980a1ea1182","sha256:a5ab010c3b021f45bffc1523eea19c464c0b94753ab510cd7fbd21ecdbb9e493"],"state_sha256":"c6d9c864a1901aa24745b2742d449cafe7bbbc59b783ff61e0f7bd23cea634c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/F9taqVFK2kuDyA6ocFtHh0drzmrhXiaxajBvDSIwsGCsSi8OPOkkNv0tnoYI+i/cOshgR87E41EeOqt57w6BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T11:55:37.967544Z","bundle_sha256":"9be7fa8e2651d34eada651e34101ad28b80206fd60ad68b7db0514ca82aefdc4"}}