{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ZHCTSSOAYIDHBHVGOTYOLZ3MAV","short_pith_number":"pith:ZHCTSSOA","canonical_record":{"source":{"id":"1004.4953","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-04-28T05:02:31Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"7a03fbd162fbb82eb50f56f1335e68871aeba1be81ffa6e683b857ed33e61cee","abstract_canon_sha256":"f86aedcce2110889d93e87b8efd97cd9266e65fbe81289921c86e1cb22e7662d"},"schema_version":"1.0"},"canonical_sha256":"c9c53949c0c206709ea674f0e5e76c055d73fcb8561df4e3263c4cd9ef00151d","source":{"kind":"arxiv","id":"1004.4953","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.4953","created_at":"2026-05-18T00:13:14Z"},{"alias_kind":"arxiv_version","alias_value":"1004.4953v2","created_at":"2026-05-18T00:13:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4953","created_at":"2026-05-18T00:13:14Z"},{"alias_kind":"pith_short_12","alias_value":"ZHCTSSOAYIDH","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZHCTSSOAYIDHBHVG","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZHCTSSOA","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ZHCTSSOAYIDHBHVGOTYOLZ3MAV","target":"record","payload":{"canonical_record":{"source":{"id":"1004.4953","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-04-28T05:02:31Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"7a03fbd162fbb82eb50f56f1335e68871aeba1be81ffa6e683b857ed33e61cee","abstract_canon_sha256":"f86aedcce2110889d93e87b8efd97cd9266e65fbe81289921c86e1cb22e7662d"},"schema_version":"1.0"},"canonical_sha256":"c9c53949c0c206709ea674f0e5e76c055d73fcb8561df4e3263c4cd9ef00151d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:14.252180Z","signature_b64":"31Byt4ASbvd0TGPFwesTNIPwEWzAf9ra5XtQP6ZIHqhiKze29Nt75SDHdEyILHlBIvlve3CEbQTUcuEl9fqjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9c53949c0c206709ea674f0e5e76c055d73fcb8561df4e3263c4cd9ef00151d","last_reissued_at":"2026-05-18T00:13:14.251569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:14.251569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.4953","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":"2026-05-18T00:13:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nHaGBxSs9I2EBd9aPAqnrmkDjLxiNLlYrRqnLv8a5yvS1HUr7PsWEpdG2h+NUxtal4or56uin4Xn03ve3Aj7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T09:25:45.984016Z"},"content_sha256":"539d2f5b6169f3cb0fc76bd6dadca5d7eb947d307d623bd1f774ad2395da303b","schema_version":"1.0","event_id":"sha256:539d2f5b6169f3cb0fc76bd6dadca5d7eb947d307d623bd1f774ad2395da303b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ZHCTSSOAYIDHBHVGOTYOLZ3MAV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Number of Eigenvalues of a Tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NA","authors_text":"Bernd Sturmfels, Dustin Cartwright","submitted_at":"2010-04-28T05:02:31Z","abstract_excerpt":"Eigenvectors of tensors, as studied recently in numerical multilinear algebra, correspond to  fixed points of self-maps of a projective space. We determine the number of eigenvectors and eigenvalues of a generic tensor, and we show that the number of normalized eigenvalues of a symmetric tensor is always finite. We also examine the characteristic polynomial and how its coefficients are related to discriminants and resultants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4953","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":"2026-05-18T00:13:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tjr1eqKBRqHqFRtZSV+XtWQgJkCMM5ZQv+xbX0Pu59VFmFnxUEJCVzrq5NSdICUE5TmdNo4dhjmMNfRGnex6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T09:25:45.984452Z"},"content_sha256":"7b04893615e9dfbe3d9d6e6dc5885289bd6fbe198e2286c7be719e49755421ce","schema_version":"1.0","event_id":"sha256:7b04893615e9dfbe3d9d6e6dc5885289bd6fbe198e2286c7be719e49755421ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZHCTSSOAYIDHBHVGOTYOLZ3MAV/bundle.json","state_url":"https://pith.science/pith/ZHCTSSOAYIDHBHVGOTYOLZ3MAV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZHCTSSOAYIDHBHVGOTYOLZ3MAV/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":"2026-08-03T09:25:45Z","links":{"resolver":"https://pith.science/pith/ZHCTSSOAYIDHBHVGOTYOLZ3MAV","bundle":"https://pith.science/pith/ZHCTSSOAYIDHBHVGOTYOLZ3MAV/bundle.json","state":"https://pith.science/pith/ZHCTSSOAYIDHBHVGOTYOLZ3MAV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZHCTSSOAYIDHBHVGOTYOLZ3MAV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZHCTSSOAYIDHBHVGOTYOLZ3MAV","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":"f86aedcce2110889d93e87b8efd97cd9266e65fbe81289921c86e1cb22e7662d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-04-28T05:02:31Z","title_canon_sha256":"7a03fbd162fbb82eb50f56f1335e68871aeba1be81ffa6e683b857ed33e61cee"},"schema_version":"1.0","source":{"id":"1004.4953","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.4953","created_at":"2026-05-18T00:13:14Z"},{"alias_kind":"arxiv_version","alias_value":"1004.4953v2","created_at":"2026-05-18T00:13:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4953","created_at":"2026-05-18T00:13:14Z"},{"alias_kind":"pith_short_12","alias_value":"ZHCTSSOAYIDH","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZHCTSSOAYIDHBHVG","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZHCTSSOA","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:7b04893615e9dfbe3d9d6e6dc5885289bd6fbe198e2286c7be719e49755421ce","target":"graph","created_at":"2026-05-18T00:13:14Z","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":"Eigenvectors of tensors, as studied recently in numerical multilinear algebra, correspond to  fixed points of self-maps of a projective space. We determine the number of eigenvectors and eigenvalues of a generic tensor, and we show that the number of normalized eigenvalues of a symmetric tensor is always finite. We also examine the characteristic polynomial and how its coefficients are related to discriminants and resultants.","authors_text":"Bernd Sturmfels, Dustin Cartwright","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-04-28T05:02:31Z","title":"The Number of Eigenvalues of a Tensor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4953","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":"sha256:539d2f5b6169f3cb0fc76bd6dadca5d7eb947d307d623bd1f774ad2395da303b","target":"record","created_at":"2026-05-18T00:13:14Z","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":"f86aedcce2110889d93e87b8efd97cd9266e65fbe81289921c86e1cb22e7662d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-04-28T05:02:31Z","title_canon_sha256":"7a03fbd162fbb82eb50f56f1335e68871aeba1be81ffa6e683b857ed33e61cee"},"schema_version":"1.0","source":{"id":"1004.4953","kind":"arxiv","version":2}},"canonical_sha256":"c9c53949c0c206709ea674f0e5e76c055d73fcb8561df4e3263c4cd9ef00151d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9c53949c0c206709ea674f0e5e76c055d73fcb8561df4e3263c4cd9ef00151d","first_computed_at":"2026-05-18T00:13:14.251569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:14.251569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"31Byt4ASbvd0TGPFwesTNIPwEWzAf9ra5XtQP6ZIHqhiKze29Nt75SDHdEyILHlBIvlve3CEbQTUcuEl9fqjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:14.252180Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.4953","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:539d2f5b6169f3cb0fc76bd6dadca5d7eb947d307d623bd1f774ad2395da303b","sha256:7b04893615e9dfbe3d9d6e6dc5885289bd6fbe198e2286c7be719e49755421ce"],"state_sha256":"a7b9fad24acf51b78b2a4120e3d57e10d589e57310dbd9e2049e0eff02d0a193"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LChbKcI7/YUup/WCeXhaqoxkP2HNWTtQR7pOZXrNdT3rQzLlBcoiMNfkS9YbAsU+XlSAS4elTqhD4CuhjBKLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T09:25:45.987577Z","bundle_sha256":"a532c730cda2f60c3bdc6b09dfe0f10eb67af47e909de130d72f1b360b63955d"}}