{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZQ55YCFY4YHENBKSSOZB5Y7KBH","short_pith_number":"pith:ZQ55YCFY","schema_version":"1.0","canonical_sha256":"cc3bdc08b8e60e46855293b21ee3ea09e9e6dcf0addb1bc674d8d3b350172122","source":{"kind":"arxiv","id":"1708.03894","version":1},"attestation_state":"computed","paper":{"title":"Product cones in dense pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Pantelis E. Eleftheriou","submitted_at":"2017-08-13T12:14:41Z","abstract_excerpt":"Let $\\mathcal M=\\langle M, <, +, \\dots\\rangle$ be an o-minimal expansion of an ordered group, and $P\\subseteq M$ a dense set such that certain tameness conditions hold. We introduce the notion of a `product cone' in $\\widetilde{\\mathcal M}=\\langle \\cal M, P\\rangle$, and prove: if $\\mathcal M$ expands a real closed field, then $\\widetilde{\\mathcal M}$ admits a product cone decomposition. If $\\mathcal M$ is linear, then it does not. In particular, we settle a question from [10]."},"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":"1708.03894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-13T12:14:41Z","cross_cats_sorted":[],"title_canon_sha256":"12351a8c158d9ad445eb7948a4a962e026b19d7d5665d7777d68478f9b2cf80a","abstract_canon_sha256":"f5f249a5de672018b3b53b5f7409e3024498cedb60d42b82d9e00704d5db0ef9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:07.594023Z","signature_b64":"ivMx+nQ1g85Z3jclnnLNuYmpJ3DHQMG61O6gV+M8kZAw+eVCjn4YpgZvzKdGM6aI8yeZhMuzsAGavKfKj+xqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc3bdc08b8e60e46855293b21ee3ea09e9e6dcf0addb1bc674d8d3b350172122","last_reissued_at":"2026-05-18T00:38:07.593554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:07.593554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Product cones in dense pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Pantelis E. Eleftheriou","submitted_at":"2017-08-13T12:14:41Z","abstract_excerpt":"Let $\\mathcal M=\\langle M, <, +, \\dots\\rangle$ be an o-minimal expansion of an ordered group, and $P\\subseteq M$ a dense set such that certain tameness conditions hold. We introduce the notion of a `product cone' in $\\widetilde{\\mathcal M}=\\langle \\cal M, P\\rangle$, and prove: if $\\mathcal M$ expands a real closed field, then $\\widetilde{\\mathcal M}$ admits a product cone decomposition. If $\\mathcal M$ is linear, then it does not. In particular, we settle a question from [10]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03894","kind":"arxiv","version":1},"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":"1708.03894","created_at":"2026-05-18T00:38:07.593629+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.03894v1","created_at":"2026-05-18T00:38:07.593629+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03894","created_at":"2026-05-18T00:38:07.593629+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZQ55YCFY4YHE","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZQ55YCFY4YHENBKS","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZQ55YCFY","created_at":"2026-05-18T12:31:59.375834+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/ZQ55YCFY4YHENBKSSOZB5Y7KBH","json":"https://pith.science/pith/ZQ55YCFY4YHENBKSSOZB5Y7KBH.json","graph_json":"https://pith.science/api/pith-number/ZQ55YCFY4YHENBKSSOZB5Y7KBH/graph.json","events_json":"https://pith.science/api/pith-number/ZQ55YCFY4YHENBKSSOZB5Y7KBH/events.json","paper":"https://pith.science/paper/ZQ55YCFY"},"agent_actions":{"view_html":"https://pith.science/pith/ZQ55YCFY4YHENBKSSOZB5Y7KBH","download_json":"https://pith.science/pith/ZQ55YCFY4YHENBKSSOZB5Y7KBH.json","view_paper":"https://pith.science/paper/ZQ55YCFY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.03894&json=true","fetch_graph":"https://pith.science/api/pith-number/ZQ55YCFY4YHENBKSSOZB5Y7KBH/graph.json","fetch_events":"https://pith.science/api/pith-number/ZQ55YCFY4YHENBKSSOZB5Y7KBH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZQ55YCFY4YHENBKSSOZB5Y7KBH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZQ55YCFY4YHENBKSSOZB5Y7KBH/action/storage_attestation","attest_author":"https://pith.science/pith/ZQ55YCFY4YHENBKSSOZB5Y7KBH/action/author_attestation","sign_citation":"https://pith.science/pith/ZQ55YCFY4YHENBKSSOZB5Y7KBH/action/citation_signature","submit_replication":"https://pith.science/pith/ZQ55YCFY4YHENBKSSOZB5Y7KBH/action/replication_record"}},"created_at":"2026-05-18T00:38:07.593629+00:00","updated_at":"2026-05-18T00:38:07.593629+00:00"}