{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PUVWLZJCSY2M2L7Z2SIHJGOEZM","short_pith_number":"pith:PUVWLZJC","schema_version":"1.0","canonical_sha256":"7d2b65e5229634cd2ff9d4907499c4cb03e2a30b810a7aabd81bc0389236620c","source":{"kind":"arxiv","id":"1605.02551","version":2},"attestation_state":"computed","paper":{"title":"Axiomatics for the external numbers of nonstandard analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Bruno Dinis, Imme van den Berg","submitted_at":"2016-05-09T12:13:10Z","abstract_excerpt":"Neutrices are additive subgroups of a nonstandard model of the real numbers. An external number is the algebraic sum of a nonstandard real number and a neutrix. Due to the stability by some shifts, external numbers may be seen as mathematical models for orders of magnitude. The algebraic properties of external numbers gave rise to the so-called solids, which are extensions of ordered fields, having a restricted distributivity law. However, necessary and sufficient conditions can be given for distributivity to hold. In this article we develop an axiomatics for the external numbers. The axioms a"},"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":"1605.02551","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-05-09T12:13:10Z","cross_cats_sorted":[],"title_canon_sha256":"bb5750eab7e3587cea142c5a36a6a66714b278ebc604311c2219d938bfd71f2e","abstract_canon_sha256":"02cfaa511c359ec1e5c1a944f9b3eef7bb8fc1edd7d5223e503413cb14e9b3b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:43.829362Z","signature_b64":"Ew0mXIQKNzQEVAS/H6RPathToCli2j/rAEi/dOhS5qNP8Kl19N0j1vw6eJL6dTacIiG3zyF1MOiT0aXykjMgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d2b65e5229634cd2ff9d4907499c4cb03e2a30b810a7aabd81bc0389236620c","last_reissued_at":"2026-05-17T23:42:43.828662Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:43.828662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Axiomatics for the external numbers of nonstandard analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Bruno Dinis, Imme van den Berg","submitted_at":"2016-05-09T12:13:10Z","abstract_excerpt":"Neutrices are additive subgroups of a nonstandard model of the real numbers. An external number is the algebraic sum of a nonstandard real number and a neutrix. Due to the stability by some shifts, external numbers may be seen as mathematical models for orders of magnitude. The algebraic properties of external numbers gave rise to the so-called solids, which are extensions of ordered fields, having a restricted distributivity law. However, necessary and sufficient conditions can be given for distributivity to hold. In this article we develop an axiomatics for the external numbers. The axioms a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02551","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":"1605.02551","created_at":"2026-05-17T23:42:43.828766+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.02551v2","created_at":"2026-05-17T23:42:43.828766+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02551","created_at":"2026-05-17T23:42:43.828766+00:00"},{"alias_kind":"pith_short_12","alias_value":"PUVWLZJCSY2M","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PUVWLZJCSY2M2L7Z","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PUVWLZJC","created_at":"2026-05-18T12:30:39.010887+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PUVWLZJCSY2M2L7Z2SIHJGOEZM","json":"https://pith.science/pith/PUVWLZJCSY2M2L7Z2SIHJGOEZM.json","graph_json":"https://pith.science/api/pith-number/PUVWLZJCSY2M2L7Z2SIHJGOEZM/graph.json","events_json":"https://pith.science/api/pith-number/PUVWLZJCSY2M2L7Z2SIHJGOEZM/events.json","paper":"https://pith.science/paper/PUVWLZJC"},"agent_actions":{"view_html":"https://pith.science/pith/PUVWLZJCSY2M2L7Z2SIHJGOEZM","download_json":"https://pith.science/pith/PUVWLZJCSY2M2L7Z2SIHJGOEZM.json","view_paper":"https://pith.science/paper/PUVWLZJC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.02551&json=true","fetch_graph":"https://pith.science/api/pith-number/PUVWLZJCSY2M2L7Z2SIHJGOEZM/graph.json","fetch_events":"https://pith.science/api/pith-number/PUVWLZJCSY2M2L7Z2SIHJGOEZM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PUVWLZJCSY2M2L7Z2SIHJGOEZM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PUVWLZJCSY2M2L7Z2SIHJGOEZM/action/storage_attestation","attest_author":"https://pith.science/pith/PUVWLZJCSY2M2L7Z2SIHJGOEZM/action/author_attestation","sign_citation":"https://pith.science/pith/PUVWLZJCSY2M2L7Z2SIHJGOEZM/action/citation_signature","submit_replication":"https://pith.science/pith/PUVWLZJCSY2M2L7Z2SIHJGOEZM/action/replication_record"}},"created_at":"2026-05-17T23:42:43.828766+00:00","updated_at":"2026-05-17T23:42:43.828766+00:00"}