{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4IIBQO6TDCKKO4EHPECC3WQRYU","short_pith_number":"pith:4IIBQO6T","schema_version":"1.0","canonical_sha256":"e210183bd31894a7708779042dda11c523bb05b7d8064a3065bbb17497c112fc","source":{"kind":"arxiv","id":"1504.02941","version":1},"attestation_state":"computed","paper":{"title":"The Archimedean Projection Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jeff Dodd, Michael Harrison, Vincent Coll","submitted_at":"2015-04-12T07:45:07Z","abstract_excerpt":"Let $H$ be a hypersurface in $\\mathbb R^n$ and let $\\pi$ be an orthogonal projection in $\\mathbb R^n$ restricted to $H$. We say that $H$ satisfies the $Archimedean$ $projection$ $property$ corresponding to $\\pi$ if there exists a constant $C$ such that $Vol(\\pi^{-1}(U)) = C \\cdot Vol(U)$ for every measurable $U$ in the range of $\\pi$. It is well-known that the $(n-1)$-dimensional sphere, as a hypersurface in $\\mathbb R^n$, satisfies the Archimedean projection property corresponding to any codimension 2 orthogonal projection in $\\mathbb R^n$, the range of any such projection being an $(n-2)$-di"},"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":"1504.02941","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-12T07:45:07Z","cross_cats_sorted":[],"title_canon_sha256":"a1eb169404301da4c54e9871ab74bbaefe83321954046b85b1be335ef9a35905","abstract_canon_sha256":"eceb18a39fed30ba972e14663ab70892c1876506a0ddfd209b6a7db45362a37c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:59.605017Z","signature_b64":"M/v4zck+sxJDUpVjEOBLnV5iQDFCxOyM75iQIqyxFkpsKoyIoGx4egJ8sOJucRM8Edo+KqaxNuuvZCQWHOe0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e210183bd31894a7708779042dda11c523bb05b7d8064a3065bbb17497c112fc","last_reissued_at":"2026-05-18T02:18:59.604342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:59.604342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Archimedean Projection Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jeff Dodd, Michael Harrison, Vincent Coll","submitted_at":"2015-04-12T07:45:07Z","abstract_excerpt":"Let $H$ be a hypersurface in $\\mathbb R^n$ and let $\\pi$ be an orthogonal projection in $\\mathbb R^n$ restricted to $H$. We say that $H$ satisfies the $Archimedean$ $projection$ $property$ corresponding to $\\pi$ if there exists a constant $C$ such that $Vol(\\pi^{-1}(U)) = C \\cdot Vol(U)$ for every measurable $U$ in the range of $\\pi$. It is well-known that the $(n-1)$-dimensional sphere, as a hypersurface in $\\mathbb R^n$, satisfies the Archimedean projection property corresponding to any codimension 2 orthogonal projection in $\\mathbb R^n$, the range of any such projection being an $(n-2)$-di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02941","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":"1504.02941","created_at":"2026-05-18T02:18:59.604448+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.02941v1","created_at":"2026-05-18T02:18:59.604448+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02941","created_at":"2026-05-18T02:18:59.604448+00:00"},{"alias_kind":"pith_short_12","alias_value":"4IIBQO6TDCKK","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4IIBQO6TDCKKO4EH","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4IIBQO6T","created_at":"2026-05-18T12:29:05.191682+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/4IIBQO6TDCKKO4EHPECC3WQRYU","json":"https://pith.science/pith/4IIBQO6TDCKKO4EHPECC3WQRYU.json","graph_json":"https://pith.science/api/pith-number/4IIBQO6TDCKKO4EHPECC3WQRYU/graph.json","events_json":"https://pith.science/api/pith-number/4IIBQO6TDCKKO4EHPECC3WQRYU/events.json","paper":"https://pith.science/paper/4IIBQO6T"},"agent_actions":{"view_html":"https://pith.science/pith/4IIBQO6TDCKKO4EHPECC3WQRYU","download_json":"https://pith.science/pith/4IIBQO6TDCKKO4EHPECC3WQRYU.json","view_paper":"https://pith.science/paper/4IIBQO6T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.02941&json=true","fetch_graph":"https://pith.science/api/pith-number/4IIBQO6TDCKKO4EHPECC3WQRYU/graph.json","fetch_events":"https://pith.science/api/pith-number/4IIBQO6TDCKKO4EHPECC3WQRYU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4IIBQO6TDCKKO4EHPECC3WQRYU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4IIBQO6TDCKKO4EHPECC3WQRYU/action/storage_attestation","attest_author":"https://pith.science/pith/4IIBQO6TDCKKO4EHPECC3WQRYU/action/author_attestation","sign_citation":"https://pith.science/pith/4IIBQO6TDCKKO4EHPECC3WQRYU/action/citation_signature","submit_replication":"https://pith.science/pith/4IIBQO6TDCKKO4EHPECC3WQRYU/action/replication_record"}},"created_at":"2026-05-18T02:18:59.604448+00:00","updated_at":"2026-05-18T02:18:59.604448+00:00"}