{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:KOG2RAZBYH3ACIIWHRYWILLIVD","short_pith_number":"pith:KOG2RAZB","canonical_record":{"source":{"id":"2206.07879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-06-16T02:12:33Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"1f3744bddfb9678e8bad982ac6411ea7c03489d2d60637727c23e1e937725895","abstract_canon_sha256":"8b26132bfd2b31beb5586fbbc6a380c112d43ade39e4af978792636702c774c2"},"schema_version":"1.0"},"canonical_sha256":"538da88321c1f60121163c71642d68a8d45ddd65b4f4240e66aac017b301e916","source":{"kind":"arxiv","id":"2206.07879","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.07879","created_at":"2026-07-05T04:32:19Z"},{"alias_kind":"arxiv_version","alias_value":"2206.07879v1","created_at":"2026-07-05T04:32:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.07879","created_at":"2026-07-05T04:32:19Z"},{"alias_kind":"pith_short_12","alias_value":"KOG2RAZBYH3A","created_at":"2026-07-05T04:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"KOG2RAZBYH3ACIIW","created_at":"2026-07-05T04:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"KOG2RAZB","created_at":"2026-07-05T04:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:KOG2RAZBYH3ACIIWHRYWILLIVD","target":"record","payload":{"canonical_record":{"source":{"id":"2206.07879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-06-16T02:12:33Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"1f3744bddfb9678e8bad982ac6411ea7c03489d2d60637727c23e1e937725895","abstract_canon_sha256":"8b26132bfd2b31beb5586fbbc6a380c112d43ade39e4af978792636702c774c2"},"schema_version":"1.0"},"canonical_sha256":"538da88321c1f60121163c71642d68a8d45ddd65b4f4240e66aac017b301e916","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:32:19.313307Z","signature_b64":"x47RrgFOuSJJq6TpurU1vMmFq38YoGXjhs7uhl9w3D5qE23h2z/Xgz7DrAHNJbHQA/U5vlxyFG3krDwY+JatBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"538da88321c1f60121163c71642d68a8d45ddd65b4f4240e66aac017b301e916","last_reissued_at":"2026-07-05T04:32:19.312887Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:32:19.312887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.07879","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:32:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tahf8ixB8H7FD9VeF9UQ6Y4iePCOPwfSuIz3Tl/r80pFxsWlm4rqdW7nRj7PNEa2g739IUI33EMfSPL/JQB/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T22:06:00.803806Z"},"content_sha256":"fbb460e9dfc87078177dab40fa8ed87d026665a13b2dad079a4fb7cd209719d7","schema_version":"1.0","event_id":"sha256:fbb460e9dfc87078177dab40fa8ed87d026665a13b2dad079a4fb7cd209719d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:KOG2RAZBYH3ACIIWHRYWILLIVD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extreme ratio between spectral and Frobenius norms of nonnegative tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Shengyu Cao, Simai He, Zhening Li, Zhen Wang","submitted_at":"2022-06-16T02:12:33Z","abstract_excerpt":"One of the fundamental problems in multilinear algebra, the minimum ratio between the spectral and Frobenius norms of tensors, has received considerable attention in recent years. While most values are unknown for real and complex tensors, the asymptotic order of magnitude and tight lower bounds have been established. However, little is known about nonnegative tensors. In this paper, we present an almost complete picture of the ratio for nonnegative tensors. In particular, we provide a tight lower bound that can be achieved by a wide class of nonnegative tensors under a simple necessary and su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.07879","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/2206.07879/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:32:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ew0+pX1XCssDO7EDoz4XHB0PzXzKxYGr9YQh4hKhhSmmHn470hNlZ0acgTmOZnohgPxwBqOQBMRMs+IWI9TvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T22:06:00.804175Z"},"content_sha256":"78a7e58c02d49369e8f161ca42689e49393d142bac1701eddfd6bcd1aaef0e9c","schema_version":"1.0","event_id":"sha256:78a7e58c02d49369e8f161ca42689e49393d142bac1701eddfd6bcd1aaef0e9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KOG2RAZBYH3ACIIWHRYWILLIVD/bundle.json","state_url":"https://pith.science/pith/KOG2RAZBYH3ACIIWHRYWILLIVD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KOG2RAZBYH3ACIIWHRYWILLIVD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-08T22:06:00Z","links":{"resolver":"https://pith.science/pith/KOG2RAZBYH3ACIIWHRYWILLIVD","bundle":"https://pith.science/pith/KOG2RAZBYH3ACIIWHRYWILLIVD/bundle.json","state":"https://pith.science/pith/KOG2RAZBYH3ACIIWHRYWILLIVD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KOG2RAZBYH3ACIIWHRYWILLIVD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:KOG2RAZBYH3ACIIWHRYWILLIVD","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":"8b26132bfd2b31beb5586fbbc6a380c112d43ade39e4af978792636702c774c2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-06-16T02:12:33Z","title_canon_sha256":"1f3744bddfb9678e8bad982ac6411ea7c03489d2d60637727c23e1e937725895"},"schema_version":"1.0","source":{"id":"2206.07879","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.07879","created_at":"2026-07-05T04:32:19Z"},{"alias_kind":"arxiv_version","alias_value":"2206.07879v1","created_at":"2026-07-05T04:32:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.07879","created_at":"2026-07-05T04:32:19Z"},{"alias_kind":"pith_short_12","alias_value":"KOG2RAZBYH3A","created_at":"2026-07-05T04:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"KOG2RAZBYH3ACIIW","created_at":"2026-07-05T04:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"KOG2RAZB","created_at":"2026-07-05T04:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:78a7e58c02d49369e8f161ca42689e49393d142bac1701eddfd6bcd1aaef0e9c","target":"graph","created_at":"2026-07-05T04:32:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.07879/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"One of the fundamental problems in multilinear algebra, the minimum ratio between the spectral and Frobenius norms of tensors, has received considerable attention in recent years. While most values are unknown for real and complex tensors, the asymptotic order of magnitude and tight lower bounds have been established. However, little is known about nonnegative tensors. In this paper, we present an almost complete picture of the ratio for nonnegative tensors. In particular, we provide a tight lower bound that can be achieved by a wide class of nonnegative tensors under a simple necessary and su","authors_text":"Shengyu Cao, Simai He, Zhening Li, Zhen Wang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-06-16T02:12:33Z","title":"Extreme ratio between spectral and Frobenius norms of nonnegative tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.07879","kind":"arxiv","version":1},"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:fbb460e9dfc87078177dab40fa8ed87d026665a13b2dad079a4fb7cd209719d7","target":"record","created_at":"2026-07-05T04:32:19Z","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":"8b26132bfd2b31beb5586fbbc6a380c112d43ade39e4af978792636702c774c2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-06-16T02:12:33Z","title_canon_sha256":"1f3744bddfb9678e8bad982ac6411ea7c03489d2d60637727c23e1e937725895"},"schema_version":"1.0","source":{"id":"2206.07879","kind":"arxiv","version":1}},"canonical_sha256":"538da88321c1f60121163c71642d68a8d45ddd65b4f4240e66aac017b301e916","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"538da88321c1f60121163c71642d68a8d45ddd65b4f4240e66aac017b301e916","first_computed_at":"2026-07-05T04:32:19.312887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:32:19.312887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x47RrgFOuSJJq6TpurU1vMmFq38YoGXjhs7uhl9w3D5qE23h2z/Xgz7DrAHNJbHQA/U5vlxyFG3krDwY+JatBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:32:19.313307Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.07879","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbb460e9dfc87078177dab40fa8ed87d026665a13b2dad079a4fb7cd209719d7","sha256:78a7e58c02d49369e8f161ca42689e49393d142bac1701eddfd6bcd1aaef0e9c"],"state_sha256":"22eae8c902df9124133903518d107d5ed6d007cc1ae1ca1e1e08382d98b97d49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CTnXE3+q5K03LGZwjBJnP1zmna9SvwwRIXoQ0G91Wt8eeQMaB7GHTKwlu6dDeKw/0omYRgfZPk+XW0B5BHA7Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T22:06:00.806309Z","bundle_sha256":"8561a5ac8e938985061fbe29959764947d4f8c5bc67a5e646e442a9aeabce8f1"}}