{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:U2XU6GEYVLJLJHZW3V67J2MG5A","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":"9566ab297261e0d5b65dd0bf11c470ac426d08288d1fcc18d2b05e8e78d97792","cross_cats_sorted":["cs.NA","math.AC","math.AG"],"license":"","primary_cat":"math.NA","submitted_at":"2006-02-01T19:48:33Z","title_canon_sha256":"5e049b47c31b2b63f651fd5d7f86861eaee0eb0d4f70a450e4e5dc602fa77815"},"schema_version":"1.0","source":{"id":"math/0602019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0602019","created_at":"2026-06-03T22:06:18Z"},{"alias_kind":"arxiv_version","alias_value":"math/0602019v1","created_at":"2026-06-03T22:06:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0602019","created_at":"2026-06-03T22:06:18Z"},{"alias_kind":"pith_short_12","alias_value":"U2XU6GEYVLJL","created_at":"2026-06-03T22:06:18Z"},{"alias_kind":"pith_short_16","alias_value":"U2XU6GEYVLJLJHZW","created_at":"2026-06-03T22:06:18Z"},{"alias_kind":"pith_short_8","alias_value":"U2XU6GEY","created_at":"2026-06-03T22:06:18Z"}],"graph_snapshots":[{"event_id":"sha256:7fd8a1dbef619a53a222a321e7d17c87b6bbb2a2ed5b7c761f85a8651c083723","target":"graph","created_at":"2026-06-03T22:06:18Z","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/math/0602019/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we want to revisit results of Dahmen and Micchelli on box-splines which we reinterpret and make more precise. We compare these ideas with the work of Brion, Szenes, Vergne and others on polytopes and partition functions.","authors_text":"C. De Concini, C. Procesi","cross_cats":["cs.NA","math.AC","math.AG"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2006-02-01T19:48:33Z","title":"The algebra of the box spline"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602019","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":"sha256:1abecfce49a69d5ce9a31531f61cdcbd63789c28e3885bf43ddf31b122db230f","target":"record","created_at":"2026-06-03T22:06:18Z","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":"9566ab297261e0d5b65dd0bf11c470ac426d08288d1fcc18d2b05e8e78d97792","cross_cats_sorted":["cs.NA","math.AC","math.AG"],"license":"","primary_cat":"math.NA","submitted_at":"2006-02-01T19:48:33Z","title_canon_sha256":"5e049b47c31b2b63f651fd5d7f86861eaee0eb0d4f70a450e4e5dc602fa77815"},"schema_version":"1.0","source":{"id":"math/0602019","kind":"arxiv","version":1}},"canonical_sha256":"a6af4f1898aad2b49f36dd7df4e986e807c94428f17ec54f8a9d736313bba769","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6af4f1898aad2b49f36dd7df4e986e807c94428f17ec54f8a9d736313bba769","first_computed_at":"2026-06-03T22:06:18.888949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:18.888949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3uXLlb23M4wD5b6o0DYV6TakPPpm7FtQ8wYq002jeZLCLlAj/hfZZ0m5eI3XGmn0UC8YAcDPaVYxi3+miyUoCA==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:18.889350Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0602019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1abecfce49a69d5ce9a31531f61cdcbd63789c28e3885bf43ddf31b122db230f","sha256:7fd8a1dbef619a53a222a321e7d17c87b6bbb2a2ed5b7c761f85a8651c083723"],"state_sha256":"9c6f38aa86e8c1793c98b3ffcc3c69673136b502ae581ce802f48a6e178a8c76"}