{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:V4HW2P2F2JLU2URHHPSU64RO7E","short_pith_number":"pith:V4HW2P2F","schema_version":"1.0","canonical_sha256":"af0f6d3f45d2574d52273be54f722ef902eb456bc186f254d98c02465d9b05c7","source":{"kind":"arxiv","id":"2404.03627","version":1},"attestation_state":"computed","paper":{"title":"Injective norm of real and complex random tensors I: From spin glasses to geometric entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"math.PR","authors_text":"Benjamin McKenna, Stephane Dartois","submitted_at":"2024-04-04T17:49:23Z","abstract_excerpt":"The injective norm is a natural generalization to tensors of the operator norm of a matrix. In quantum information, the injective norm is one important measure of genuine multipartite entanglement of quantum states, where it is known as the geometric entanglement. In this paper, we give a high-probability upper bound on the injective norm of real and complex Gaussian random tensors, corresponding to a lower bound on the geometric entanglement of random quantum states, and to a bound on the ground-state energy of a particular multispecies spherical spin glass model. For some cases of our model,"},"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":"2404.03627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-04-04T17:49:23Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"95b09096d7ff8829593474cafa7bc9f85091f7b3054f4adb051e20d81f75109a","abstract_canon_sha256":"ddfafe22d287ea1c957dbc7d86686f1cfbe0b4945b326701d6017f7038d00b7d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:04:28.492234Z","signature_b64":"3zLuT8UCIiL+M5vr4eeLNuz9dUa+ldV0sqVgDSE/DUnsySnNOcpPWACTUj8qse4UIsEJD6Go25rxE1c2TKqUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af0f6d3f45d2574d52273be54f722ef902eb456bc186f254d98c02465d9b05c7","last_reissued_at":"2026-07-05T08:04:28.491827Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:04:28.491827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Injective norm of real and complex random tensors I: From spin glasses to geometric entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"math.PR","authors_text":"Benjamin McKenna, Stephane Dartois","submitted_at":"2024-04-04T17:49:23Z","abstract_excerpt":"The injective norm is a natural generalization to tensors of the operator norm of a matrix. In quantum information, the injective norm is one important measure of genuine multipartite entanglement of quantum states, where it is known as the geometric entanglement. In this paper, we give a high-probability upper bound on the injective norm of real and complex Gaussian random tensors, corresponding to a lower bound on the geometric entanglement of random quantum states, and to a bound on the ground-state energy of a particular multispecies spherical spin glass model. For some cases of our model,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.03627","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.03627/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":"2404.03627","created_at":"2026-07-05T08:04:28.491881+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.03627v1","created_at":"2026-07-05T08:04:28.491881+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.03627","created_at":"2026-07-05T08:04:28.491881+00:00"},{"alias_kind":"pith_short_12","alias_value":"V4HW2P2F2JLU","created_at":"2026-07-05T08:04:28.491881+00:00"},{"alias_kind":"pith_short_16","alias_value":"V4HW2P2F2JLU2URH","created_at":"2026-07-05T08:04:28.491881+00:00"},{"alias_kind":"pith_short_8","alias_value":"V4HW2P2F","created_at":"2026-07-05T08:04:28.491881+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.09804","citing_title":"Joint distributions of eigenvectors of symmetric random tensors","ref_index":34,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V4HW2P2F2JLU2URHHPSU64RO7E","json":"https://pith.science/pith/V4HW2P2F2JLU2URHHPSU64RO7E.json","graph_json":"https://pith.science/api/pith-number/V4HW2P2F2JLU2URHHPSU64RO7E/graph.json","events_json":"https://pith.science/api/pith-number/V4HW2P2F2JLU2URHHPSU64RO7E/events.json","paper":"https://pith.science/paper/V4HW2P2F"},"agent_actions":{"view_html":"https://pith.science/pith/V4HW2P2F2JLU2URHHPSU64RO7E","download_json":"https://pith.science/pith/V4HW2P2F2JLU2URHHPSU64RO7E.json","view_paper":"https://pith.science/paper/V4HW2P2F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.03627&json=true","fetch_graph":"https://pith.science/api/pith-number/V4HW2P2F2JLU2URHHPSU64RO7E/graph.json","fetch_events":"https://pith.science/api/pith-number/V4HW2P2F2JLU2URHHPSU64RO7E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V4HW2P2F2JLU2URHHPSU64RO7E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V4HW2P2F2JLU2URHHPSU64RO7E/action/storage_attestation","attest_author":"https://pith.science/pith/V4HW2P2F2JLU2URHHPSU64RO7E/action/author_attestation","sign_citation":"https://pith.science/pith/V4HW2P2F2JLU2URHHPSU64RO7E/action/citation_signature","submit_replication":"https://pith.science/pith/V4HW2P2F2JLU2URHHPSU64RO7E/action/replication_record"}},"created_at":"2026-07-05T08:04:28.491881+00:00","updated_at":"2026-07-05T08:04:28.491881+00:00"}