{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YUPC5L5D2Z2YS6TBHQUVXOLOXB","short_pith_number":"pith:YUPC5L5D","schema_version":"1.0","canonical_sha256":"c51e2eafa3d675897a613c295bb96eb86dddc2dee57bd3c01597b5922a44968a","source":{"kind":"arxiv","id":"1405.7113","version":4},"attestation_state":"computed","paper":{"title":"Scaled-free objects II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Will Grilliette","submitted_at":"2014-05-28T04:15:35Z","abstract_excerpt":"This work creates two categories of \"array-weighted sets\" for the purposes of constructing universal matrix-normed spaces and algebras. These universal objects have the analogous universal property to the free vector space, lifting maps completely bounded on a generation set to a completely bounded linear map of the matrix-normed space.\n  Moreover, the universal matrix-normed algebra is used to prove the existence of a free product for matrix-normed algebras using algebraic methods."},"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":"1405.7113","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-28T04:15:35Z","cross_cats_sorted":[],"title_canon_sha256":"55c0afe5e0446ec25f29f41aee64a35118382acdab3fad84e36bbc169c270543","abstract_canon_sha256":"e9b9d086896756e21c93a4fb3892db602acb8f1d2c2edde6c1481abbb1ff8c13"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:09.832478Z","signature_b64":"AM1jWHXcIAxPu+tIEuYqdBWcqm3jWBWa+lbRYZjGg7PvxSajYPrZwjabRVyV2RwrISZPLXxQRSIPr3mojT97AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c51e2eafa3d675897a613c295bb96eb86dddc2dee57bd3c01597b5922a44968a","last_reissued_at":"2026-05-18T00:43:09.831762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:09.831762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scaled-free objects II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Will Grilliette","submitted_at":"2014-05-28T04:15:35Z","abstract_excerpt":"This work creates two categories of \"array-weighted sets\" for the purposes of constructing universal matrix-normed spaces and algebras. These universal objects have the analogous universal property to the free vector space, lifting maps completely bounded on a generation set to a completely bounded linear map of the matrix-normed space.\n  Moreover, the universal matrix-normed algebra is used to prove the existence of a free product for matrix-normed algebras using algebraic methods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7113","kind":"arxiv","version":4},"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":"1405.7113","created_at":"2026-05-18T00:43:09.831879+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.7113v4","created_at":"2026-05-18T00:43:09.831879+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7113","created_at":"2026-05-18T00:43:09.831879+00:00"},{"alias_kind":"pith_short_12","alias_value":"YUPC5L5D2Z2Y","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YUPC5L5D2Z2YS6TB","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YUPC5L5D","created_at":"2026-05-18T12:28:57.508820+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/YUPC5L5D2Z2YS6TBHQUVXOLOXB","json":"https://pith.science/pith/YUPC5L5D2Z2YS6TBHQUVXOLOXB.json","graph_json":"https://pith.science/api/pith-number/YUPC5L5D2Z2YS6TBHQUVXOLOXB/graph.json","events_json":"https://pith.science/api/pith-number/YUPC5L5D2Z2YS6TBHQUVXOLOXB/events.json","paper":"https://pith.science/paper/YUPC5L5D"},"agent_actions":{"view_html":"https://pith.science/pith/YUPC5L5D2Z2YS6TBHQUVXOLOXB","download_json":"https://pith.science/pith/YUPC5L5D2Z2YS6TBHQUVXOLOXB.json","view_paper":"https://pith.science/paper/YUPC5L5D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.7113&json=true","fetch_graph":"https://pith.science/api/pith-number/YUPC5L5D2Z2YS6TBHQUVXOLOXB/graph.json","fetch_events":"https://pith.science/api/pith-number/YUPC5L5D2Z2YS6TBHQUVXOLOXB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YUPC5L5D2Z2YS6TBHQUVXOLOXB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YUPC5L5D2Z2YS6TBHQUVXOLOXB/action/storage_attestation","attest_author":"https://pith.science/pith/YUPC5L5D2Z2YS6TBHQUVXOLOXB/action/author_attestation","sign_citation":"https://pith.science/pith/YUPC5L5D2Z2YS6TBHQUVXOLOXB/action/citation_signature","submit_replication":"https://pith.science/pith/YUPC5L5D2Z2YS6TBHQUVXOLOXB/action/replication_record"}},"created_at":"2026-05-18T00:43:09.831879+00:00","updated_at":"2026-05-18T00:43:09.831879+00:00"}