{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EZA53UVOLP7LVC6KCFG6UJKBI3","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":"389720cd81912166ca4b05e51db4742e000230e5715c054d4e41a4b9657593b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-17T10:14:57Z","title_canon_sha256":"773ed7e6f6dfbcec6c8328aa372874a0f2437c16fd5d38fa7d026e1c0a4eca85"},"schema_version":"1.0","source":{"id":"1207.3933","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3933","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3933v1","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3933","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"EZA53UVOLP7L","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EZA53UVOLP7LVC6K","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EZA53UVO","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:08104c91aa93f53197e630d4c02a68d23031d2ff57c439687a05876be6596152","target":"graph","created_at":"2026-05-18T03:50:49Z","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"},"paper":{"abstract_excerpt":"In earlier papers we have developed an algebraic theory of discrete tomography. In those papers the structure of the functions $f: A \\to \\{0,1\\}$ and $f: A \\to \\mathbb{Z}$ having given line sums in certain directions have been analyzed. Here $A$ was a block in $\\mathbb{Z}^n$ with sides parallel to the axes. In the present paper we assume that there is noise in the measurements and (only) that $A$ is an arbitrary or convex finite set in $\\mathbb{Z}^n$. We derive generalizations of earlier results. Furthermore we apply a method of Beck and Fiala to obtain results of he following type: if the lin","authors_text":"Lajos Hajdu, Rob Tijdeman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-17T10:14:57Z","title":"Bounds for approximate discrete tomography solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3933","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:dfbf87211ed908474f6b460dc97d148ddf45071a38d85ebac04cc8538c7fcbf4","target":"record","created_at":"2026-05-18T03:50:49Z","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":"389720cd81912166ca4b05e51db4742e000230e5715c054d4e41a4b9657593b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-17T10:14:57Z","title_canon_sha256":"773ed7e6f6dfbcec6c8328aa372874a0f2437c16fd5d38fa7d026e1c0a4eca85"},"schema_version":"1.0","source":{"id":"1207.3933","kind":"arxiv","version":1}},"canonical_sha256":"2641ddd2ae5bfeba8bca114dea254146e9d491a50956b7e39e4c81822287f558","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2641ddd2ae5bfeba8bca114dea254146e9d491a50956b7e39e4c81822287f558","first_computed_at":"2026-05-18T03:50:49.466305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:49.466305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fa4SL3AzwHUX0qksq8OLJo2FB1BiwRJ9OgzPN64ML3PqEcTDNmqTnKslYMfVlYMhQZDdKdzhfP/X0zWXFKMWAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:49.466976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3933","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfbf87211ed908474f6b460dc97d148ddf45071a38d85ebac04cc8538c7fcbf4","sha256:08104c91aa93f53197e630d4c02a68d23031d2ff57c439687a05876be6596152"],"state_sha256":"c167a5fa3b73c24c07fc1aae35ec42ad70d69b17083a72817288e3b24c0ab980"}