{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6EYZVXPRMQF4WDNDC6TCA6BMVW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"96d8d9bf0a0acf4f760963459f8f241340d2855fbf5eb311f79241dafe4b16a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-09-28T15:59:19Z","title_canon_sha256":"972fa7bf986692247e419079304d43b3cda9040af21ab488c935c3bc6df62743"},"schema_version":"1.0","source":{"id":"1809.11107","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.11107","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"1809.11107v2","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.11107","created_at":"2026-05-18T00:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"6EYZVXPRMQF4","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6EYZVXPRMQF4WDND","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6EYZVXPR","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:ae4361860b9d7dbdcc6312840b66c39f419daa6072500973b96e7ae44f211140","target":"graph","created_at":"2026-05-18T00:02:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The notion and theory of the quantum space of all maps from a quantum space pioneered by So{\\l}tan have been mainly focused on finite-dimensional C*-algebras which are matrix algebra bundles over a finite set $S$. We propose a modification of this notion to cover the case of $C\\left( X\\right) $ for general compact Hausdorff spaces $X$ instead of finite sets $S$ while taking into account of the topology of $X$. A notion of free product of copies of a unital C*-algebra topologically indexed by a compact Hausdorff space arises naturally, and satisfies some desired functoriality.","authors_text":"Albert Jeu-Liang Sheu, Thomas Timmermann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-09-28T15:59:19Z","title":"A Note on the Quantum Family of Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.11107","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0fa51e16f668e6a91ecdd997de885d858dd6c6c12a8e199e0820d23b6c198e59","target":"record","created_at":"2026-05-18T00:02:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"96d8d9bf0a0acf4f760963459f8f241340d2855fbf5eb311f79241dafe4b16a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-09-28T15:59:19Z","title_canon_sha256":"972fa7bf986692247e419079304d43b3cda9040af21ab488c935c3bc6df62743"},"schema_version":"1.0","source":{"id":"1809.11107","kind":"arxiv","version":2}},"canonical_sha256":"f1319addf1640bcb0da317a620782cad92abff15d313b5e0204eb29cb34d19f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1319addf1640bcb0da317a620782cad92abff15d313b5e0204eb29cb34d19f0","first_computed_at":"2026-05-18T00:02:44.214433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:44.214433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jgafjaq0oCNRfUjCGxOPA1xm6B+dACof6On0OkfE3J4F3VZxfv/8SG12yxSqii+tkMbFXPIBHQ1TKNt0G7ToBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:44.214923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.11107","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fa51e16f668e6a91ecdd997de885d858dd6c6c12a8e199e0820d23b6c198e59","sha256:ae4361860b9d7dbdcc6312840b66c39f419daa6072500973b96e7ae44f211140"],"state_sha256":"eeaaa015e3d7c17fda84e6d04cbf33b5a4b8b5d53dd538e1a1348bbd847889ba"}