{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:XJH2KT6SVZWPAIGF57OWQ2OTHP","short_pith_number":"pith:XJH2KT6S","schema_version":"1.0","canonical_sha256":"ba4fa54fd2ae6cf020c5efdd6869d33be5192f581a792695a9faf9e546fd77ff","source":{"kind":"arxiv","id":"1301.6208","version":2},"attestation_state":"computed","paper":{"title":"Additive systems and a theorem of de Bruijn","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Melvyn B. Nathanson","submitted_at":"2013-01-26T03:57:38Z","abstract_excerpt":"This paper gives a complete proof of a theorem of de Bruijn that classifies additive systems for the nonnegative integers, that is, families $\\mca = (A_i)_{i\\in I}$ of sets of nonnegative integers, each set containing 0, such that every nonnegative integer can be written uniquely in the form $\\sum_{i\\in I} a_i$ with $a_i \\in A_i$ for all $i$ and $a_i \\neq 0$ for only finitely many $i$. All indecomposable additive systems are determined."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.6208","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-26T03:57:38Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a93d80643454a9eeaff5f0a893d9aba81df05b9a1410e8af20ee616bb5bea597","abstract_canon_sha256":"5f1550cddcfc73b1489e53a6e0297a198bc0f0ec829f02b40348b2715d0f70ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:32.387166Z","signature_b64":"Pv1+aUu9rkTuV5UyB+D8GflokZYndo+NGlP2Qi1xG+dKzzWPOSJRFewapvxRejbrze1qrq9/hFCVoZIcANbLDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba4fa54fd2ae6cf020c5efdd6869d33be5192f581a792695a9faf9e546fd77ff","last_reissued_at":"2026-05-18T03:03:32.386661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:32.386661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Additive systems and a theorem of de Bruijn","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Melvyn B. Nathanson","submitted_at":"2013-01-26T03:57:38Z","abstract_excerpt":"This paper gives a complete proof of a theorem of de Bruijn that classifies additive systems for the nonnegative integers, that is, families $\\mca = (A_i)_{i\\in I}$ of sets of nonnegative integers, each set containing 0, such that every nonnegative integer can be written uniquely in the form $\\sum_{i\\in I} a_i$ with $a_i \\in A_i$ for all $i$ and $a_i \\neq 0$ for only finitely many $i$. All indecomposable additive systems are determined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6208","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.6208","created_at":"2026-05-18T03:03:32.386727+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.6208v2","created_at":"2026-05-18T03:03:32.386727+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6208","created_at":"2026-05-18T03:03:32.386727+00:00"},{"alias_kind":"pith_short_12","alias_value":"XJH2KT6SVZWP","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XJH2KT6SVZWPAIGF","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XJH2KT6S","created_at":"2026-05-18T12:28:06.772260+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.17285","citing_title":"Additive systems for $\\mathbb{Z}$ are undecidable","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XJH2KT6SVZWPAIGF57OWQ2OTHP","json":"https://pith.science/pith/XJH2KT6SVZWPAIGF57OWQ2OTHP.json","graph_json":"https://pith.science/api/pith-number/XJH2KT6SVZWPAIGF57OWQ2OTHP/graph.json","events_json":"https://pith.science/api/pith-number/XJH2KT6SVZWPAIGF57OWQ2OTHP/events.json","paper":"https://pith.science/paper/XJH2KT6S"},"agent_actions":{"view_html":"https://pith.science/pith/XJH2KT6SVZWPAIGF57OWQ2OTHP","download_json":"https://pith.science/pith/XJH2KT6SVZWPAIGF57OWQ2OTHP.json","view_paper":"https://pith.science/paper/XJH2KT6S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.6208&json=true","fetch_graph":"https://pith.science/api/pith-number/XJH2KT6SVZWPAIGF57OWQ2OTHP/graph.json","fetch_events":"https://pith.science/api/pith-number/XJH2KT6SVZWPAIGF57OWQ2OTHP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XJH2KT6SVZWPAIGF57OWQ2OTHP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XJH2KT6SVZWPAIGF57OWQ2OTHP/action/storage_attestation","attest_author":"https://pith.science/pith/XJH2KT6SVZWPAIGF57OWQ2OTHP/action/author_attestation","sign_citation":"https://pith.science/pith/XJH2KT6SVZWPAIGF57OWQ2OTHP/action/citation_signature","submit_replication":"https://pith.science/pith/XJH2KT6SVZWPAIGF57OWQ2OTHP/action/replication_record"}},"created_at":"2026-05-18T03:03:32.386727+00:00","updated_at":"2026-05-18T03:03:32.386727+00:00"}