{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KJVLLH7ZVMHQ2IYQ3OWDZNOD3E","short_pith_number":"pith:KJVLLH7Z","canonical_record":{"source":{"id":"1407.4586","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-07-17T07:33:22Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"456d3565d8f41a71a02dcfab377f03b4464ab1ddd760f20f2d84dccbc05a8948","abstract_canon_sha256":"449ff48de9558c72062a3e8d89f60cce03d225a9fbe0425f43b156900da5519c"},"schema_version":"1.0"},"canonical_sha256":"526ab59ff9ab0f0d2310dbac3cb5c3d9311bee8f04fb7f459f3511cc5a4a7700","source":{"kind":"arxiv","id":"1407.4586","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4586","created_at":"2026-05-18T02:28:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4586v2","created_at":"2026-05-18T02:28:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4586","created_at":"2026-05-18T02:28:53Z"},{"alias_kind":"pith_short_12","alias_value":"KJVLLH7ZVMHQ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KJVLLH7ZVMHQ2IYQ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KJVLLH7Z","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KJVLLH7ZVMHQ2IYQ3OWDZNOD3E","target":"record","payload":{"canonical_record":{"source":{"id":"1407.4586","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-07-17T07:33:22Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"456d3565d8f41a71a02dcfab377f03b4464ab1ddd760f20f2d84dccbc05a8948","abstract_canon_sha256":"449ff48de9558c72062a3e8d89f60cce03d225a9fbe0425f43b156900da5519c"},"schema_version":"1.0"},"canonical_sha256":"526ab59ff9ab0f0d2310dbac3cb5c3d9311bee8f04fb7f459f3511cc5a4a7700","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:53.955097Z","signature_b64":"kKyS5KXRw840ebto6Rx9L5Gzm/nsaClz2/Obab/aAk/zJmJINQ/A9PShe/s0SzBW44lFGImsMX0aKV1zIBYNBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"526ab59ff9ab0f0d2310dbac3cb5c3d9311bee8f04fb7f459f3511cc5a4a7700","last_reissued_at":"2026-05-18T02:28:53.954704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:53.954704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.4586","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":"2026-05-18T02:28:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xi1V8o72JmNhDWq4+olGrJTqQ0nU45l6+cYT5t6e9m1yHW2EGTlYJBSCKk7JKqxc2U9/NH+0+qlTZJQmlIuRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:23:18.060958Z"},"content_sha256":"3a7b3414c27a6a19851473f16a98e06f3a536ab721e4d95033eb75aa1e5d2035","schema_version":"1.0","event_id":"sha256:3a7b3414c27a6a19851473f16a98e06f3a536ab721e4d95033eb75aa1e5d2035"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KJVLLH7ZVMHQ2IYQ3OWDZNOD3E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new convergence proof for the higher-order power method and generalizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.OC","authors_text":"Andr\\'e Uschmajew","submitted_at":"2014-07-17T07:33:22Z","abstract_excerpt":"A proof for the point-wise convergence of the factors in the higher-order power method for tensors towards a critical point is given. It is obtained by applying established results from the theory of \\L{}ojasiewicz inequalities to the equivalent, unconstrained alternating least squares algorithm for best rank-one tensor approximation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4586","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":"2026-05-18T02:28:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qkwCWur7n66M/shxz0DlUktX2ukPk6r4zrspDPceW58vAgwXnHuddwPXztO966abBOxADpsZSZ0md0eMbuvbBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:23:18.061616Z"},"content_sha256":"236b593771f7df4d46c9abae44e7eacbe6f542f3b20d38bb322f87484895601d","schema_version":"1.0","event_id":"sha256:236b593771f7df4d46c9abae44e7eacbe6f542f3b20d38bb322f87484895601d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJVLLH7ZVMHQ2IYQ3OWDZNOD3E/bundle.json","state_url":"https://pith.science/pith/KJVLLH7ZVMHQ2IYQ3OWDZNOD3E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJVLLH7ZVMHQ2IYQ3OWDZNOD3E/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":"2026-05-26T12:23:18Z","links":{"resolver":"https://pith.science/pith/KJVLLH7ZVMHQ2IYQ3OWDZNOD3E","bundle":"https://pith.science/pith/KJVLLH7ZVMHQ2IYQ3OWDZNOD3E/bundle.json","state":"https://pith.science/pith/KJVLLH7ZVMHQ2IYQ3OWDZNOD3E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJVLLH7ZVMHQ2IYQ3OWDZNOD3E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KJVLLH7ZVMHQ2IYQ3OWDZNOD3E","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":"449ff48de9558c72062a3e8d89f60cce03d225a9fbe0425f43b156900da5519c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-07-17T07:33:22Z","title_canon_sha256":"456d3565d8f41a71a02dcfab377f03b4464ab1ddd760f20f2d84dccbc05a8948"},"schema_version":"1.0","source":{"id":"1407.4586","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4586","created_at":"2026-05-18T02:28:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4586v2","created_at":"2026-05-18T02:28:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4586","created_at":"2026-05-18T02:28:53Z"},{"alias_kind":"pith_short_12","alias_value":"KJVLLH7ZVMHQ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KJVLLH7ZVMHQ2IYQ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KJVLLH7Z","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:236b593771f7df4d46c9abae44e7eacbe6f542f3b20d38bb322f87484895601d","target":"graph","created_at":"2026-05-18T02:28:53Z","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":"A proof for the point-wise convergence of the factors in the higher-order power method for tensors towards a critical point is given. It is obtained by applying established results from the theory of \\L{}ojasiewicz inequalities to the equivalent, unconstrained alternating least squares algorithm for best rank-one tensor approximation.","authors_text":"Andr\\'e Uschmajew","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-07-17T07:33:22Z","title":"A new convergence proof for the higher-order power method and generalizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4586","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":"sha256:3a7b3414c27a6a19851473f16a98e06f3a536ab721e4d95033eb75aa1e5d2035","target":"record","created_at":"2026-05-18T02:28:53Z","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":"449ff48de9558c72062a3e8d89f60cce03d225a9fbe0425f43b156900da5519c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-07-17T07:33:22Z","title_canon_sha256":"456d3565d8f41a71a02dcfab377f03b4464ab1ddd760f20f2d84dccbc05a8948"},"schema_version":"1.0","source":{"id":"1407.4586","kind":"arxiv","version":2}},"canonical_sha256":"526ab59ff9ab0f0d2310dbac3cb5c3d9311bee8f04fb7f459f3511cc5a4a7700","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"526ab59ff9ab0f0d2310dbac3cb5c3d9311bee8f04fb7f459f3511cc5a4a7700","first_computed_at":"2026-05-18T02:28:53.954704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:53.954704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kKyS5KXRw840ebto6Rx9L5Gzm/nsaClz2/Obab/aAk/zJmJINQ/A9PShe/s0SzBW44lFGImsMX0aKV1zIBYNBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:53.955097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4586","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a7b3414c27a6a19851473f16a98e06f3a536ab721e4d95033eb75aa1e5d2035","sha256:236b593771f7df4d46c9abae44e7eacbe6f542f3b20d38bb322f87484895601d"],"state_sha256":"a5dacb2f27f91832fdf7b1be5d73daad4815ae414ae48faff094b1dc5d706a34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ev/7459Z4bNS+8uolBMWenbqk89V+nCmS4hg/jwPMpiByStBEGBwkoxYgTA7e+2ROoDLVd+koVHPmzqVslcKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:23:18.065083Z","bundle_sha256":"b2e1ccd171f3101f2d3271717c5a6efeafe33a986266b9c5a647b20519d15843"}}