{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:B33NOODACU5TEW46BC2MH3EDZW","short_pith_number":"pith:B33NOODA","schema_version":"1.0","canonical_sha256":"0ef6d73860153b325b9e08b4c3ec83cdb4963abb1ca241224a8c698af68e5b5d","source":{"kind":"arxiv","id":"1111.3880","version":3},"attestation_state":"computed","paper":{"title":"Hom-polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.MG"],"primary_cat":"math.CO","authors_text":"Joseph Gubeladze, Mark Contois, Tristram Bogart","submitted_at":"2011-11-16T17:32:54Z","abstract_excerpt":"We study the polytopes of affine maps between two polytopes -- the hom-polytopes. The hom-polytope functor has a left adjoint -- tensor product polytopes. The analogy with the category of vector spaces is limited, as we illustrate by a series of explicit examples exhibiting various extremal properties. The main challenge for hom-polytopes is to determine their vertices. A polytopal analogue of the rank-nullity theorem amounts to understanding how the vertex maps behave relative to their surjective and injective factors. This leads to interesting classes of surjective maps. In the last two sect"},"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":"1111.3880","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-16T17:32:54Z","cross_cats_sorted":["math.CT","math.MG"],"title_canon_sha256":"80eaa8b037e5b3defa9e464ae3431834770159f7e0d98a997c48dbb839b15bef","abstract_canon_sha256":"27324ba32b0ec754fbe0bf0c34500ff05b30b59898b2c5d372c8a504f754b15c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:23.385807Z","signature_b64":"1wz/v6UHTjPNiICmPrBDhKGGn+NCQBqX4iOQhop4KhqprYQeXa+Sj1KP0piyKpcmypF1VdrG6s/Y8tnm7A0JBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ef6d73860153b325b9e08b4c3ec83cdb4963abb1ca241224a8c698af68e5b5d","last_reissued_at":"2026-05-18T03:55:23.385019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:23.385019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hom-polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.MG"],"primary_cat":"math.CO","authors_text":"Joseph Gubeladze, Mark Contois, Tristram Bogart","submitted_at":"2011-11-16T17:32:54Z","abstract_excerpt":"We study the polytopes of affine maps between two polytopes -- the hom-polytopes. The hom-polytope functor has a left adjoint -- tensor product polytopes. The analogy with the category of vector spaces is limited, as we illustrate by a series of explicit examples exhibiting various extremal properties. The main challenge for hom-polytopes is to determine their vertices. A polytopal analogue of the rank-nullity theorem amounts to understanding how the vertex maps behave relative to their surjective and injective factors. This leads to interesting classes of surjective maps. In the last two sect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3880","kind":"arxiv","version":3},"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":"1111.3880","created_at":"2026-05-18T03:55:23.385148+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.3880v3","created_at":"2026-05-18T03:55:23.385148+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3880","created_at":"2026-05-18T03:55:23.385148+00:00"},{"alias_kind":"pith_short_12","alias_value":"B33NOODACU5T","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"B33NOODACU5TEW46","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"B33NOODA","created_at":"2026-05-18T12:26:24.575870+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/B33NOODACU5TEW46BC2MH3EDZW","json":"https://pith.science/pith/B33NOODACU5TEW46BC2MH3EDZW.json","graph_json":"https://pith.science/api/pith-number/B33NOODACU5TEW46BC2MH3EDZW/graph.json","events_json":"https://pith.science/api/pith-number/B33NOODACU5TEW46BC2MH3EDZW/events.json","paper":"https://pith.science/paper/B33NOODA"},"agent_actions":{"view_html":"https://pith.science/pith/B33NOODACU5TEW46BC2MH3EDZW","download_json":"https://pith.science/pith/B33NOODACU5TEW46BC2MH3EDZW.json","view_paper":"https://pith.science/paper/B33NOODA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.3880&json=true","fetch_graph":"https://pith.science/api/pith-number/B33NOODACU5TEW46BC2MH3EDZW/graph.json","fetch_events":"https://pith.science/api/pith-number/B33NOODACU5TEW46BC2MH3EDZW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B33NOODACU5TEW46BC2MH3EDZW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B33NOODACU5TEW46BC2MH3EDZW/action/storage_attestation","attest_author":"https://pith.science/pith/B33NOODACU5TEW46BC2MH3EDZW/action/author_attestation","sign_citation":"https://pith.science/pith/B33NOODACU5TEW46BC2MH3EDZW/action/citation_signature","submit_replication":"https://pith.science/pith/B33NOODACU5TEW46BC2MH3EDZW/action/replication_record"}},"created_at":"2026-05-18T03:55:23.385148+00:00","updated_at":"2026-05-18T03:55:23.385148+00:00"}