{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4NNVIQIJ3VNDXSBFJ3RBPWYL4K","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":"298c67ca62dca7e77e9d1d2d9f74ad3aa5719b3bb9dce26d801e2bab0340b649","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-30T22:04:05Z","title_canon_sha256":"7744979973d085792c3066bf77c2dcdc3f99c0ffc043c029e042ebd8780bd4a7"},"schema_version":"1.0","source":{"id":"1605.00172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00172","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00172v1","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00172","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"pith_short_12","alias_value":"4NNVIQIJ3VND","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4NNVIQIJ3VNDXSBF","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4NNVIQIJ","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:7d0e102b390cdda3fd9d233d158efeb5abb330b41dc039edcf710d14f9db71ea","target":"graph","created_at":"2026-05-18T01:15:56Z","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":"Shmuel Friedland and Giorgio Ottaviani's beautiful constant term expression for the number of singular vector tuples of generic tensors is used to derive a rational generating function for these numbers, that in turn, is used to obtain an asymptotic formula for the number of such tuples for n by n by n three-dimensional tensors, and to conjecture an asymptotic formula for the general d-dimensional case. A donation of 100 dollars, in honor of the first prover, will be made to the On-line Encyclopedia of Integer Sequences.","authors_text":"Doron Zeilberger, Shalosh B. Ekhad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-30T22:04:05Z","title":"On the number of Singular Vector Tuples of Hyper-Cubical Tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00172","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:b78377bf11de1eae4d62c78532c600391524ac3fc2a64121194b6dc8a1160d03","target":"record","created_at":"2026-05-18T01:15:56Z","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":"298c67ca62dca7e77e9d1d2d9f74ad3aa5719b3bb9dce26d801e2bab0340b649","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-30T22:04:05Z","title_canon_sha256":"7744979973d085792c3066bf77c2dcdc3f99c0ffc043c029e042ebd8780bd4a7"},"schema_version":"1.0","source":{"id":"1605.00172","kind":"arxiv","version":1}},"canonical_sha256":"e35b544109dd5a3bc8254ee217db0be2a3bb8bce10027530e70745c85817f5e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e35b544109dd5a3bc8254ee217db0be2a3bb8bce10027530e70745c85817f5e6","first_computed_at":"2026-05-18T01:15:56.521194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:56.521194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LGsOB5WCWF8qUnhxSu8MGS1hjDHYjqcQfeZmqRA3Lr5hHNfiYLDRrnq1FE/OgITrezeMyIjLJ0NpfNwNzz7OBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:56.521841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b78377bf11de1eae4d62c78532c600391524ac3fc2a64121194b6dc8a1160d03","sha256:7d0e102b390cdda3fd9d233d158efeb5abb330b41dc039edcf710d14f9db71ea"],"state_sha256":"081285a7f986a54b93c12af03b1619f23e01b29655d1f1ea5937656787ba0a10"}