{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:QM2D2RFWXXU446PTWDT4NFYUUH","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":"393c7c21cac691ac96c5f2f22255011d55bd538eb82fa3f918e5df80a1a5c170","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-01-11T18:39:38Z","title_canon_sha256":"99462451f0a41d001d3e4e418135501301e27c60da18158ae64047dd8ec1abf4"},"schema_version":"1.0","source":{"id":"2301.04635","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.04635","created_at":"2026-07-05T05:34:05Z"},{"alias_kind":"arxiv_version","alias_value":"2301.04635v2","created_at":"2026-07-05T05:34:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.04635","created_at":"2026-07-05T05:34:05Z"},{"alias_kind":"pith_short_12","alias_value":"QM2D2RFWXXU4","created_at":"2026-07-05T05:34:05Z"},{"alias_kind":"pith_short_16","alias_value":"QM2D2RFWXXU446PT","created_at":"2026-07-05T05:34:05Z"},{"alias_kind":"pith_short_8","alias_value":"QM2D2RFW","created_at":"2026-07-05T05:34:05Z"}],"graph_snapshots":[{"event_id":"sha256:25fc1408ce393a8e5e72f72d9574b77e3dd546df6e477ba81ca1ff4c6102853a","target":"graph","created_at":"2026-07-05T05:34:05Z","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/2301.04635/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $A$ be a multiset with elements in an abelian group. Let $FS(A)$ be the multiset containing the $2^{|A|}$ sums of all subsets of $A$.\n  We study the reconstruction problem ``Given $FS(A)$, is it possible to identify $A$?'', and we give a satisfactory answer for all abelian groups. We prove that, up to identifying multisets through a natural equivalence relation, the function $A \\mapsto FS(A)$ is injective (and thus the reconstruction problem is solvable) if and only if every order $n$ of a torsion element of the abelian group satisfies a certain number-theoretical property linked to the mu","authors_text":"Andrea Ciprietti, Federico Glaudo","cross_cats":["math.CO","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-01-11T18:39:38Z","title":"On The Determination of Sets By Their Subset Sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.04635","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":"sha256:1b65f453ed57845f7c0ae935ae5c7bf511767aabeec511bfe7556fabbb2717dc","target":"record","created_at":"2026-07-05T05:34:05Z","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":"393c7c21cac691ac96c5f2f22255011d55bd538eb82fa3f918e5df80a1a5c170","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-01-11T18:39:38Z","title_canon_sha256":"99462451f0a41d001d3e4e418135501301e27c60da18158ae64047dd8ec1abf4"},"schema_version":"1.0","source":{"id":"2301.04635","kind":"arxiv","version":2}},"canonical_sha256":"83343d44b6bde9ce79f3b0e7c69714a1ff9045f38c271398d946177bbedcaebd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83343d44b6bde9ce79f3b0e7c69714a1ff9045f38c271398d946177bbedcaebd","first_computed_at":"2026-07-05T05:34:05.011896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:34:05.011896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r715c7T2YRjY6vexL5IvHq50KVDqjD0rJPn8WZvALENJChugGDDQVt1Z0GGUiQCeM9IYuGVQ2mFMTXL7gc7HCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:34:05.012347Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.04635","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b65f453ed57845f7c0ae935ae5c7bf511767aabeec511bfe7556fabbb2717dc","sha256:25fc1408ce393a8e5e72f72d9574b77e3dd546df6e477ba81ca1ff4c6102853a"],"state_sha256":"381400203d3a71bd8ea567ac2109cabe37d99fb01148163528e3b71b70d14b5f"}