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We show that there exists an infinite dimensional separable Hilbert space $\\mathcal{H}$ and a semigroup $\\alpha:=\\{\\alpha_x\\}_{x \\in P}$ of unital normal $*$-endomorphisms of $B(\\mathcal{H})$ such that $E$ is isomorphic to the product system associated to $\\alpha$."},"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":"1710.04649","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-10-12T04:40:47Z","cross_cats_sorted":[],"title_canon_sha256":"df800f03a7c12e9c77f9030a5054ab312c4017197251410f3221a835ff9809ae","abstract_canon_sha256":"9aac7bedc10ee11f3fef3037c3578d1a16648e7aa381669b1b5aa5c0c70f80f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:23:52.258512Z","signature_b64":"NchlL+5UwIAVqQufGymhkeroFkhJKM6cS2UwrD3JCYlCQSGSL7KoLQFfglUIRtmjA3PBgXQqO98/m/HQXKCJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d651955669b5bc0c9c342ea78759ff5d7b4f71a07c31e2f77db3ad96bc0e26a","last_reissued_at":"2026-07-05T01:23:52.258113Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:23:52.258113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the existence of $E_{0}$-semigroups -- the multiparameter case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"S.P.Murugan, S.Sundar","submitted_at":"2017-10-12T04:40:47Z","abstract_excerpt":"Let $P \\subset \\mathbb{R}^{d}$ be a closed convex cone. 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We show that there exists an infinite dimensional separable Hilbert space $\\mathcal{H}$ and a semigroup $\\alpha:=\\{\\alpha_x\\}_{x \\in P}$ of unital normal $*$-endomorphisms of $B(\\mathcal{H})$ such that $E$ is isomorphic to the product system associated to $\\alpha$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04649","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1710.04649/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1710.04649","created_at":"2026-07-05T01:23:52.258173+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.04649v2","created_at":"2026-07-05T01:23:52.258173+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04649","created_at":"2026-07-05T01:23:52.258173+00:00"},{"alias_kind":"pith_short_12","alias_value":"DVSRSVLGTNN4","created_at":"2026-07-05T01:23:52.258173+00:00"},{"alias_kind":"pith_short_16","alias_value":"DVSRSVLGTNN4BSOD","created_at":"2026-07-05T01:23:52.258173+00:00"},{"alias_kind":"pith_short_8","alias_value":"DVSRSVLG","created_at":"2026-07-05T01:23:52.258173+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/DVSRSVLGTNN4BSODILVHQ5M76X","json":"https://pith.science/pith/DVSRSVLGTNN4BSODILVHQ5M76X.json","graph_json":"https://pith.science/api/pith-number/DVSRSVLGTNN4BSODILVHQ5M76X/graph.json","events_json":"https://pith.science/api/pith-number/DVSRSVLGTNN4BSODILVHQ5M76X/events.json","paper":"https://pith.science/paper/DVSRSVLG"},"agent_actions":{"view_html":"https://pith.science/pith/DVSRSVLGTNN4BSODILVHQ5M76X","download_json":"https://pith.science/pith/DVSRSVLGTNN4BSODILVHQ5M76X.json","view_paper":"https://pith.science/paper/DVSRSVLG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.04649&json=true","fetch_graph":"https://pith.science/api/pith-number/DVSRSVLGTNN4BSODILVHQ5M76X/graph.json","fetch_events":"https://pith.science/api/pith-number/DVSRSVLGTNN4BSODILVHQ5M76X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DVSRSVLGTNN4BSODILVHQ5M76X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DVSRSVLGTNN4BSODILVHQ5M76X/action/storage_attestation","attest_author":"https://pith.science/pith/DVSRSVLGTNN4BSODILVHQ5M76X/action/author_attestation","sign_citation":"https://pith.science/pith/DVSRSVLGTNN4BSODILVHQ5M76X/action/citation_signature","submit_replication":"https://pith.science/pith/DVSRSVLGTNN4BSODILVHQ5M76X/action/replication_record"}},"created_at":"2026-07-05T01:23:52.258173+00:00","updated_at":"2026-07-05T01:23:52.258173+00:00"}