{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CJQK3ZTKBCLJZ4ZK7HOGKYPF4E","short_pith_number":"pith:CJQK3ZTK","canonical_record":{"source":{"id":"1706.03631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-12T13:41:49Z","cross_cats_sorted":[],"title_canon_sha256":"de8becfad4537d4a637c6b1b873f5b9ab3eeec5383bc7d608627d77af8ec1c8c","abstract_canon_sha256":"c4b11c0bd3dd076739c7c6427f8bd24854a70125b29812b283d5ef059eeb2c1e"},"schema_version":"1.0"},"canonical_sha256":"1260ade66a08969cf32af9dc6561e5e1340ed2c39faa28ec2f912d0ac5996254","source":{"kind":"arxiv","id":"1706.03631","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03631","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03631v2","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03631","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"pith_short_12","alias_value":"CJQK3ZTKBCLJ","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CJQK3ZTKBCLJZ4ZK","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CJQK3ZTK","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CJQK3ZTKBCLJZ4ZK7HOGKYPF4E","target":"record","payload":{"canonical_record":{"source":{"id":"1706.03631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-12T13:41:49Z","cross_cats_sorted":[],"title_canon_sha256":"de8becfad4537d4a637c6b1b873f5b9ab3eeec5383bc7d608627d77af8ec1c8c","abstract_canon_sha256":"c4b11c0bd3dd076739c7c6427f8bd24854a70125b29812b283d5ef059eeb2c1e"},"schema_version":"1.0"},"canonical_sha256":"1260ade66a08969cf32af9dc6561e5e1340ed2c39faa28ec2f912d0ac5996254","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:29.927848Z","signature_b64":"3zBhmPd/IYS4v6GkKW6GS+Z0MDRQXJtnBpFxY2z9gExuQQKvW9GIi45IOE+oqgaMlTcNpW+ycxdYzS0y7lXZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1260ade66a08969cf32af9dc6561e5e1340ed2c39faa28ec2f912d0ac5996254","last_reissued_at":"2026-05-17T23:55:29.927302Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:29.927302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.03631","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j2Nz0LpJFGeb1u8otgz4dg4a+oqS6srXzxY2O9ZOTcGZa6jN9766c5otlXyLXPxon1uf6Qh3LTrR/r72wUPXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:31:35.956995Z"},"content_sha256":"c6d69712dcfa0afead16777ccfb5ee1369307145d29798509c4b7da934df3b1b","schema_version":"1.0","event_id":"sha256:c6d69712dcfa0afead16777ccfb5ee1369307145d29798509c4b7da934df3b1b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CJQK3ZTKBCLJZ4ZK7HOGKYPF4E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hankel tensor decompositions and ranks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jiawang Nie, Ke Ye","submitted_at":"2017-06-12T13:41:49Z","abstract_excerpt":"Hankel tensors are generalizations of Hankel matrices. This article studies the relations among various ranks of Hankel tensors. We give an algorithm that can compute the Vandermonde ranks and decompositions for all Hankel tensors. For a generic $n$-dimensional Hankel tensor of even order or order three, we prove that the the cp rank, symmetric rank, border rank, symmetric border rank, and Vandermonde rank all coincide with each other. In particular, this implies that the Comon's conjecture is true for generic Hankel tensors when the order is even or three. Some open questions are also posed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03631","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":""},"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":"2026-05-17T23:55:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qPdJ5Cdr/CIUG0lzNlXWUsgZCHIUVoxVUirXjlCSSPOau8jlxyBm/SQgqBajoKcismAapAOYTY2QXHKbt7FSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:31:35.957358Z"},"content_sha256":"28b9fbee08da2937986b475953f177f4984cbc793ffea327d24b7ba6a65ea21e","schema_version":"1.0","event_id":"sha256:28b9fbee08da2937986b475953f177f4984cbc793ffea327d24b7ba6a65ea21e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJQK3ZTKBCLJZ4ZK7HOGKYPF4E/bundle.json","state_url":"https://pith.science/pith/CJQK3ZTKBCLJZ4ZK7HOGKYPF4E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJQK3ZTKBCLJZ4ZK7HOGKYPF4E/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":"2026-06-02T13:31:35Z","links":{"resolver":"https://pith.science/pith/CJQK3ZTKBCLJZ4ZK7HOGKYPF4E","bundle":"https://pith.science/pith/CJQK3ZTKBCLJZ4ZK7HOGKYPF4E/bundle.json","state":"https://pith.science/pith/CJQK3ZTKBCLJZ4ZK7HOGKYPF4E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJQK3ZTKBCLJZ4ZK7HOGKYPF4E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CJQK3ZTKBCLJZ4ZK7HOGKYPF4E","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":"c4b11c0bd3dd076739c7c6427f8bd24854a70125b29812b283d5ef059eeb2c1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-12T13:41:49Z","title_canon_sha256":"de8becfad4537d4a637c6b1b873f5b9ab3eeec5383bc7d608627d77af8ec1c8c"},"schema_version":"1.0","source":{"id":"1706.03631","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03631","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03631v2","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03631","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"pith_short_12","alias_value":"CJQK3ZTKBCLJ","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CJQK3ZTKBCLJZ4ZK","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CJQK3ZTK","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:28b9fbee08da2937986b475953f177f4984cbc793ffea327d24b7ba6a65ea21e","target":"graph","created_at":"2026-05-17T23:55:29Z","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":"Hankel tensors are generalizations of Hankel matrices. This article studies the relations among various ranks of Hankel tensors. We give an algorithm that can compute the Vandermonde ranks and decompositions for all Hankel tensors. For a generic $n$-dimensional Hankel tensor of even order or order three, we prove that the the cp rank, symmetric rank, border rank, symmetric border rank, and Vandermonde rank all coincide with each other. In particular, this implies that the Comon's conjecture is true for generic Hankel tensors when the order is even or three. Some open questions are also posed.","authors_text":"Jiawang Nie, Ke Ye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-12T13:41:49Z","title":"Hankel tensor decompositions and ranks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03631","kind":"arxiv","version":2},"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:c6d69712dcfa0afead16777ccfb5ee1369307145d29798509c4b7da934df3b1b","target":"record","created_at":"2026-05-17T23:55:29Z","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":"c4b11c0bd3dd076739c7c6427f8bd24854a70125b29812b283d5ef059eeb2c1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-12T13:41:49Z","title_canon_sha256":"de8becfad4537d4a637c6b1b873f5b9ab3eeec5383bc7d608627d77af8ec1c8c"},"schema_version":"1.0","source":{"id":"1706.03631","kind":"arxiv","version":2}},"canonical_sha256":"1260ade66a08969cf32af9dc6561e5e1340ed2c39faa28ec2f912d0ac5996254","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1260ade66a08969cf32af9dc6561e5e1340ed2c39faa28ec2f912d0ac5996254","first_computed_at":"2026-05-17T23:55:29.927302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:29.927302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3zBhmPd/IYS4v6GkKW6GS+Z0MDRQXJtnBpFxY2z9gExuQQKvW9GIi45IOE+oqgaMlTcNpW+ycxdYzS0y7lXZBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:29.927848Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.03631","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6d69712dcfa0afead16777ccfb5ee1369307145d29798509c4b7da934df3b1b","sha256:28b9fbee08da2937986b475953f177f4984cbc793ffea327d24b7ba6a65ea21e"],"state_sha256":"ed9f1085eacaba1d16e50f3b6201e66965f43068fea9ef76b007420e33cdb5b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HAD4sK2cgATnWsiDtKJIJ53UlqrW7DwmixLdVectVKSrDizl5wtukmgepzBsZbRHd9Tzmidyg3YZ1tDlSGrZCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:31:35.959706Z","bundle_sha256":"04af5af2bc18ef29dad328eb33c0d4cecf742ace133284d91a1bdd6d68b5a656"}}