{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GGPNSJLVFXLSCYA34LL5STAAHV","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":"d455989ff3b5d4aa0cc301f05e730a70623f27c20e6b6c2ea9df0861afc1ec0c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-16T13:03:59Z","title_canon_sha256":"cd6cf0b5192c4a9e9519d67cf6207627080b62e8db44295f33684bb8a18e8e04"},"schema_version":"1.0","source":{"id":"2606.17884","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17884","created_at":"2026-06-19T16:10:42Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17884v1","created_at":"2026-06-19T16:10:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17884","created_at":"2026-06-19T16:10:42Z"},{"alias_kind":"pith_short_12","alias_value":"GGPNSJLVFXLS","created_at":"2026-06-19T16:10:42Z"},{"alias_kind":"pith_short_16","alias_value":"GGPNSJLVFXLSCYA3","created_at":"2026-06-19T16:10:42Z"},{"alias_kind":"pith_short_8","alias_value":"GGPNSJLV","created_at":"2026-06-19T16:10:42Z"}],"graph_snapshots":[{"event_id":"sha256:82b005c9842080d154896344e6bf94fdf262e4504ba5a765c2a27a1f87c84581","target":"graph","created_at":"2026-06-19T16:10:42Z","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/2606.17884/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define naive atomic decompositions of smooth projective varieties. We show that they satisfy a naive version of Iritani's blowup formula in several examples that are complicated enough to show most interesting features of the general theory while being simple enough to be computable by elementary methods.","authors_text":"Christian B\\\"ohning, Hans-Christian Graf von Bothmer, Zac Su'a","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-16T13:03:59Z","title":"Naive atoms of blowups: examples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17884","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":"sha256:510cb0684d34ff11caed74a78bef70dd097ee231422c5183d57b100846527e88","target":"record","created_at":"2026-06-19T16:10:42Z","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":"d455989ff3b5d4aa0cc301f05e730a70623f27c20e6b6c2ea9df0861afc1ec0c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-16T13:03:59Z","title_canon_sha256":"cd6cf0b5192c4a9e9519d67cf6207627080b62e8db44295f33684bb8a18e8e04"},"schema_version":"1.0","source":{"id":"2606.17884","kind":"arxiv","version":1}},"canonical_sha256":"319ed925752dd721601be2d7d94c003d4dfa1ff927b401c02824b27699b9f8e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"319ed925752dd721601be2d7d94c003d4dfa1ff927b401c02824b27699b9f8e5","first_computed_at":"2026-06-19T16:10:42.630405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:42.630405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SE96uyqgNk9/At/bPHb99XbS/VD/8Ye4c7bpre5hw4Eqt8wN9H0XBMy0EyacJagNKXtB43e6nOBG/AskRyKhDQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:42.630811Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17884","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:510cb0684d34ff11caed74a78bef70dd097ee231422c5183d57b100846527e88","sha256:82b005c9842080d154896344e6bf94fdf262e4504ba5a765c2a27a1f87c84581"],"state_sha256":"c7a9b4e47a9f4458febf12314e0b3d445ef3dd111a4c89d1c559d00a3b97c339"}