{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:6HBSVH5RQOCTXS4LLYR66H576S","short_pith_number":"pith:6HBSVH5R","canonical_record":{"source":{"id":"2602.04654","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-02-04T15:29:23Z","cross_cats_sorted":[],"title_canon_sha256":"915de959c9e17e83cbd6e88b49b0f2bed5b77ff9778813ad45de97fe092462fd","abstract_canon_sha256":"dd7e0b422e13a1ebc427bbda5c473cd70821b5b18d6e6fc7a0d39a837457b46b"},"schema_version":"1.0"},"canonical_sha256":"f1c32a9fb183853bcb8b5e23ef1fbff498d6ac716bc7d34d7a9d68ffd1c04a25","source":{"kind":"arxiv","id":"2602.04654","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.04654","created_at":"2026-06-01T01:02:32Z"},{"alias_kind":"arxiv_version","alias_value":"2602.04654v2","created_at":"2026-06-01T01:02:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.04654","created_at":"2026-06-01T01:02:32Z"},{"alias_kind":"pith_short_12","alias_value":"6HBSVH5RQOCT","created_at":"2026-06-01T01:02:32Z"},{"alias_kind":"pith_short_16","alias_value":"6HBSVH5RQOCTXS4L","created_at":"2026-06-01T01:02:32Z"},{"alias_kind":"pith_short_8","alias_value":"6HBSVH5R","created_at":"2026-06-01T01:02:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:6HBSVH5RQOCTXS4LLYR66H576S","target":"record","payload":{"canonical_record":{"source":{"id":"2602.04654","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-02-04T15:29:23Z","cross_cats_sorted":[],"title_canon_sha256":"915de959c9e17e83cbd6e88b49b0f2bed5b77ff9778813ad45de97fe092462fd","abstract_canon_sha256":"dd7e0b422e13a1ebc427bbda5c473cd70821b5b18d6e6fc7a0d39a837457b46b"},"schema_version":"1.0"},"canonical_sha256":"f1c32a9fb183853bcb8b5e23ef1fbff498d6ac716bc7d34d7a9d68ffd1c04a25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:02:32.192106Z","signature_b64":"dfc/iinvW0uPlkMhr9MGQe2xVYpQ9eIhknVJOPJatPYBHsNxZCZMfKRyGV3TC/6YDutZF5LnwAD7ot85TLxpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1c32a9fb183853bcb8b5e23ef1fbff498d6ac716bc7d34d7a9d68ffd1c04a25","last_reissued_at":"2026-06-01T01:02:32.190857Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:02:32.190857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.04654","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-01T01:02:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mQ020iCE5FqETVxz9xCcafwh1v6oHNWc/f6JRTBa0XHqMkOX9OPOAtjp+gEpoL0rNKDL9AuCLqC0vk4akgjsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T14:31:42.852248Z"},"content_sha256":"9db1a2350889c779372a2ca7c9f61f71c16765bab0421c9b88e96dc790b3b2a8","schema_version":"1.0","event_id":"sha256:9db1a2350889c779372a2ca7c9f61f71c16765bab0421c9b88e96dc790b3b2a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:6HBSVH5RQOCTXS4LLYR66H576S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the density of rational lines on diagonal cubic hypersurfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kiseok Yeon","submitted_at":"2026-02-04T15:29:23Z","abstract_excerpt":"In this paper, we establish the asymptotic estimates for the rational lines on diagonal cubic hypersurfaces defined by $\\sum_{i=1}^sc_ix^3_i=0$ with $c_i\\in\\mathbb{Z}\\setminus \\{0\\},$ provided that $s\\geq 19.$ This improves the previously known bound $s\\geq 21$ required to obtain such asymptotic estimates. Our approach develops a multidimensional shifting variables argument together with a pruning argument, and exploits the recent progress on the Parsell-Vinogradov system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.04654","kind":"arxiv","version":2},"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/2602.04654/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":"2026-06-01T01:02:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"il2tz4yw3eo0LEAFrpBA6m3ld2KXSvv3AaWjiolGoxO2ZQ52LBFZoq9y7Oh++dqLxNyXx0XgcP7oiDwc/YX5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T14:31:42.852628Z"},"content_sha256":"e0973cef1b3d0790de5ae297de03aad13de4f5f92feeadbcc038a0990961f679","schema_version":"1.0","event_id":"sha256:e0973cef1b3d0790de5ae297de03aad13de4f5f92feeadbcc038a0990961f679"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6HBSVH5RQOCTXS4LLYR66H576S/bundle.json","state_url":"https://pith.science/pith/6HBSVH5RQOCTXS4LLYR66H576S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6HBSVH5RQOCTXS4LLYR66H576S/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":"2026-06-28T14:31:42Z","links":{"resolver":"https://pith.science/pith/6HBSVH5RQOCTXS4LLYR66H576S","bundle":"https://pith.science/pith/6HBSVH5RQOCTXS4LLYR66H576S/bundle.json","state":"https://pith.science/pith/6HBSVH5RQOCTXS4LLYR66H576S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6HBSVH5RQOCTXS4LLYR66H576S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6HBSVH5RQOCTXS4LLYR66H576S","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":"dd7e0b422e13a1ebc427bbda5c473cd70821b5b18d6e6fc7a0d39a837457b46b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-02-04T15:29:23Z","title_canon_sha256":"915de959c9e17e83cbd6e88b49b0f2bed5b77ff9778813ad45de97fe092462fd"},"schema_version":"1.0","source":{"id":"2602.04654","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.04654","created_at":"2026-06-01T01:02:32Z"},{"alias_kind":"arxiv_version","alias_value":"2602.04654v2","created_at":"2026-06-01T01:02:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.04654","created_at":"2026-06-01T01:02:32Z"},{"alias_kind":"pith_short_12","alias_value":"6HBSVH5RQOCT","created_at":"2026-06-01T01:02:32Z"},{"alias_kind":"pith_short_16","alias_value":"6HBSVH5RQOCTXS4L","created_at":"2026-06-01T01:02:32Z"},{"alias_kind":"pith_short_8","alias_value":"6HBSVH5R","created_at":"2026-06-01T01:02:32Z"}],"graph_snapshots":[{"event_id":"sha256:e0973cef1b3d0790de5ae297de03aad13de4f5f92feeadbcc038a0990961f679","target":"graph","created_at":"2026-06-01T01:02:32Z","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/2602.04654/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we establish the asymptotic estimates for the rational lines on diagonal cubic hypersurfaces defined by $\\sum_{i=1}^sc_ix^3_i=0$ with $c_i\\in\\mathbb{Z}\\setminus \\{0\\},$ provided that $s\\geq 19.$ This improves the previously known bound $s\\geq 21$ required to obtain such asymptotic estimates. Our approach develops a multidimensional shifting variables argument together with a pruning argument, and exploits the recent progress on the Parsell-Vinogradov system.","authors_text":"Kiseok Yeon","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-02-04T15:29:23Z","title":"On the density of rational lines on diagonal cubic hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.04654","kind":"arxiv","version":2},"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":"sha256:9db1a2350889c779372a2ca7c9f61f71c16765bab0421c9b88e96dc790b3b2a8","target":"record","created_at":"2026-06-01T01:02:32Z","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":"dd7e0b422e13a1ebc427bbda5c473cd70821b5b18d6e6fc7a0d39a837457b46b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-02-04T15:29:23Z","title_canon_sha256":"915de959c9e17e83cbd6e88b49b0f2bed5b77ff9778813ad45de97fe092462fd"},"schema_version":"1.0","source":{"id":"2602.04654","kind":"arxiv","version":2}},"canonical_sha256":"f1c32a9fb183853bcb8b5e23ef1fbff498d6ac716bc7d34d7a9d68ffd1c04a25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1c32a9fb183853bcb8b5e23ef1fbff498d6ac716bc7d34d7a9d68ffd1c04a25","first_computed_at":"2026-06-01T01:02:32.190857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T01:02:32.190857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dfc/iinvW0uPlkMhr9MGQe2xVYpQ9eIhknVJOPJatPYBHsNxZCZMfKRyGV3TC/6YDutZF5LnwAD7ot85TLxpDw==","signature_status":"signed_v1","signed_at":"2026-06-01T01:02:32.192106Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.04654","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9db1a2350889c779372a2ca7c9f61f71c16765bab0421c9b88e96dc790b3b2a8","sha256:e0973cef1b3d0790de5ae297de03aad13de4f5f92feeadbcc038a0990961f679"],"state_sha256":"a47711c7f0ec2f0b2fd11fa8b741fd99fd6b57d6f9a1acceed90f7ed15bce99a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SR8lp9swB9R0EEA3WRDycVN5TZIYyw/5C4UCRsfFX4p8Ke5AGPt93ieAmQ3jvGGOkmNZlFD5AnJ5iyqDm/4iAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T14:31:42.854505Z","bundle_sha256":"e18b6874ceac4d0dd74dc9491381d5e6a3e9c5bc4da5776f31ae62cdbe8b2509"}}