{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:STUSJCWNWDJWMRKRW6ZNTPYI7R","short_pith_number":"pith:STUSJCWN","schema_version":"1.0","canonical_sha256":"94e9248acdb0d3664551b7b2d9bf08fc751d4e2c4a20ad4119e1d6a19fb9c1b4","source":{"kind":"arxiv","id":"2606.24491","version":1},"attestation_state":"computed","paper":{"title":"Randomized Estimation of T-Eigenvalues of T-SPD Tensors: A Two-Sided Bracket","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hemant Sharma, Nachiketa Mishra","submitted_at":"2026-06-23T12:24:13Z","abstract_excerpt":"In earlier work \\cite{sharma2025} we developed deterministic analytical bounds on the T-eigenvalues of symmetric positive definite (SPD) third-order tensors under the Kilmer--Martin T-product: the trace--determinant (TDet) bounds via the AM--GM inequality, and the trace-dependent (TDep) bounds generalizing Samuelson's inequality. While these bounds are cheap and guaranteed-valid, their relative gap grows as $\\sqrt{d-1}$ in the tensor dimension $d = np$, limiting their usefulness for large tensors.\n  This paper develops randomized estimators for the extreme T-eigenvalues of T-SPD tensors that c"},"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":"2606.24491","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-23T12:24:13Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6589f2b3d7ab65a182f249aa0b9c8ea947a003d511ee3a32e13ae518a40d6820","abstract_canon_sha256":"985e5e8d7649bda426f0cfc6e20ddc20492bf99411931612948e4c1368b83ccd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:15:32.062396Z","signature_b64":"ZehQB6GdYsVygjtWFu+XWmpuRLABJls7CT3PKPLA8M3uvSaVTXDA/fJcHyWe5Lqjq3sVYlw9N+ll0KiQQ1YGAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94e9248acdb0d3664551b7b2d9bf08fc751d4e2c4a20ad4119e1d6a19fb9c1b4","last_reissued_at":"2026-06-24T01:15:32.062008Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:15:32.062008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Randomized Estimation of T-Eigenvalues of T-SPD Tensors: A Two-Sided Bracket","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hemant Sharma, Nachiketa Mishra","submitted_at":"2026-06-23T12:24:13Z","abstract_excerpt":"In earlier work \\cite{sharma2025} we developed deterministic analytical bounds on the T-eigenvalues of symmetric positive definite (SPD) third-order tensors under the Kilmer--Martin T-product: the trace--determinant (TDet) bounds via the AM--GM inequality, and the trace-dependent (TDep) bounds generalizing Samuelson's inequality. While these bounds are cheap and guaranteed-valid, their relative gap grows as $\\sqrt{d-1}$ in the tensor dimension $d = np$, limiting their usefulness for large tensors.\n  This paper develops randomized estimators for the extreme T-eigenvalues of T-SPD tensors that c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24491","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/2606.24491/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":"2606.24491","created_at":"2026-06-24T01:15:32.062073+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.24491v1","created_at":"2026-06-24T01:15:32.062073+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24491","created_at":"2026-06-24T01:15:32.062073+00:00"},{"alias_kind":"pith_short_12","alias_value":"STUSJCWNWDJW","created_at":"2026-06-24T01:15:32.062073+00:00"},{"alias_kind":"pith_short_16","alias_value":"STUSJCWNWDJWMRKR","created_at":"2026-06-24T01:15:32.062073+00:00"},{"alias_kind":"pith_short_8","alias_value":"STUSJCWN","created_at":"2026-06-24T01:15:32.062073+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/STUSJCWNWDJWMRKRW6ZNTPYI7R","json":"https://pith.science/pith/STUSJCWNWDJWMRKRW6ZNTPYI7R.json","graph_json":"https://pith.science/api/pith-number/STUSJCWNWDJWMRKRW6ZNTPYI7R/graph.json","events_json":"https://pith.science/api/pith-number/STUSJCWNWDJWMRKRW6ZNTPYI7R/events.json","paper":"https://pith.science/paper/STUSJCWN"},"agent_actions":{"view_html":"https://pith.science/pith/STUSJCWNWDJWMRKRW6ZNTPYI7R","download_json":"https://pith.science/pith/STUSJCWNWDJWMRKRW6ZNTPYI7R.json","view_paper":"https://pith.science/paper/STUSJCWN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.24491&json=true","fetch_graph":"https://pith.science/api/pith-number/STUSJCWNWDJWMRKRW6ZNTPYI7R/graph.json","fetch_events":"https://pith.science/api/pith-number/STUSJCWNWDJWMRKRW6ZNTPYI7R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/STUSJCWNWDJWMRKRW6ZNTPYI7R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/STUSJCWNWDJWMRKRW6ZNTPYI7R/action/storage_attestation","attest_author":"https://pith.science/pith/STUSJCWNWDJWMRKRW6ZNTPYI7R/action/author_attestation","sign_citation":"https://pith.science/pith/STUSJCWNWDJWMRKRW6ZNTPYI7R/action/citation_signature","submit_replication":"https://pith.science/pith/STUSJCWNWDJWMRKRW6ZNTPYI7R/action/replication_record"}},"created_at":"2026-06-24T01:15:32.062073+00:00","updated_at":"2026-06-24T01:15:32.062073+00:00"}