{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SKAJ7EU7CBLKWKAK5MR32LL7X3","short_pith_number":"pith:SKAJ7EU7","canonical_record":{"source":{"id":"2506.19009","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-06-23T18:05:10Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"09b1f9e981bdcab0577b5e65a9ce976113e636daf98ef09d957f144a84531a36","abstract_canon_sha256":"f49ac6196452937f64e049512195d313e51f2ca9a50cf1c1e2a8417fecb71840"},"schema_version":"1.0"},"canonical_sha256":"92809f929f1056ab280aeb23bd2d7fbee7842e603147c03a0b4ec334e78de68a","source":{"kind":"arxiv","id":"2506.19009","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.19009","created_at":"2026-07-05T11:26:07Z"},{"alias_kind":"arxiv_version","alias_value":"2506.19009v1","created_at":"2026-07-05T11:26:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.19009","created_at":"2026-07-05T11:26:07Z"},{"alias_kind":"pith_short_12","alias_value":"SKAJ7EU7CBLK","created_at":"2026-07-05T11:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"SKAJ7EU7CBLKWKAK","created_at":"2026-07-05T11:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"SKAJ7EU7","created_at":"2026-07-05T11:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SKAJ7EU7CBLKWKAK5MR32LL7X3","target":"record","payload":{"canonical_record":{"source":{"id":"2506.19009","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-06-23T18:05:10Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"09b1f9e981bdcab0577b5e65a9ce976113e636daf98ef09d957f144a84531a36","abstract_canon_sha256":"f49ac6196452937f64e049512195d313e51f2ca9a50cf1c1e2a8417fecb71840"},"schema_version":"1.0"},"canonical_sha256":"92809f929f1056ab280aeb23bd2d7fbee7842e603147c03a0b4ec334e78de68a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:26:07.913828Z","signature_b64":"rIBdbyBf7MYmlDI4h4qMkb1qsdpSGS8Eoio/Vrm7LZf713uRjXxEfEuSKhuxwGt4pg6n4sSE6KANMDLDaTTtBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92809f929f1056ab280aeb23bd2d7fbee7842e603147c03a0b4ec334e78de68a","last_reissued_at":"2026-07-05T11:26:07.913365Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:26:07.913365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.19009","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":"2026-07-05T11:26:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DJnDQ1PMRPfh0AO96L3hkZV1S0ZodnLlEDu5LKa6nM2uK+wztqpYlknw0SgWSXlFBZ1qegWrG5Mc5jiguVj3Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T23:11:58.100968Z"},"content_sha256":"4ccb9736d7129cce533fb0a0441ceda563cb9cdce4cb668b77f43d768759e07c","schema_version":"1.0","event_id":"sha256:4ccb9736d7129cce533fb0a0441ceda563cb9cdce4cb668b77f43d768759e07c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SKAJ7EU7CBLKWKAK5MR32LL7X3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orthogonal eigenvectors and singular vectors of tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.SP","authors_text":"Alvaro Ribot, Anna Seigal, Piotr Zwiernik","submitted_at":"2025-06-23T18:05:10Z","abstract_excerpt":"The spectral theorem says that a real symmetric matrix has an orthogonal basis of eigenvectors and that, for a matrix with distinct eigenvalues, the basis is unique (up to signs). In this paper, we study the symmetric tensors with an orthogonal basis of eigenvectors and show that, for a generic such tensor, the orthogonal basis is unique. This resolves a conjecture by Mesters and Zwiernik. We also study the non-symmetric setting. The singular value decomposition says that a real matrix has an orthogonal basis of singular vector pairs and that, for a matrix with distinct singular values, the ba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.19009","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/2506.19009/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":"2026-07-05T11:26:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3z/EphHJ02n/9BQ1wdYpSnbDWUvtnDBdKIknXVZ+yhkB6v4jMsEejpa0yKQQ07QtXgVKEoFc0oTo37EpmahtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T23:11:58.101467Z"},"content_sha256":"9d83c7b77bbbc5bae7e2c6c07cfb4505d764bfd902279517d16096d573fca4eb","schema_version":"1.0","event_id":"sha256:9d83c7b77bbbc5bae7e2c6c07cfb4505d764bfd902279517d16096d573fca4eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SKAJ7EU7CBLKWKAK5MR32LL7X3/bundle.json","state_url":"https://pith.science/pith/SKAJ7EU7CBLKWKAK5MR32LL7X3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SKAJ7EU7CBLKWKAK5MR32LL7X3/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":"2026-08-20T23:11:58Z","links":{"resolver":"https://pith.science/pith/SKAJ7EU7CBLKWKAK5MR32LL7X3","bundle":"https://pith.science/pith/SKAJ7EU7CBLKWKAK5MR32LL7X3/bundle.json","state":"https://pith.science/pith/SKAJ7EU7CBLKWKAK5MR32LL7X3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SKAJ7EU7CBLKWKAK5MR32LL7X3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SKAJ7EU7CBLKWKAK5MR32LL7X3","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":"f49ac6196452937f64e049512195d313e51f2ca9a50cf1c1e2a8417fecb71840","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-06-23T18:05:10Z","title_canon_sha256":"09b1f9e981bdcab0577b5e65a9ce976113e636daf98ef09d957f144a84531a36"},"schema_version":"1.0","source":{"id":"2506.19009","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.19009","created_at":"2026-07-05T11:26:07Z"},{"alias_kind":"arxiv_version","alias_value":"2506.19009v1","created_at":"2026-07-05T11:26:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.19009","created_at":"2026-07-05T11:26:07Z"},{"alias_kind":"pith_short_12","alias_value":"SKAJ7EU7CBLK","created_at":"2026-07-05T11:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"SKAJ7EU7CBLKWKAK","created_at":"2026-07-05T11:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"SKAJ7EU7","created_at":"2026-07-05T11:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:9d83c7b77bbbc5bae7e2c6c07cfb4505d764bfd902279517d16096d573fca4eb","target":"graph","created_at":"2026-07-05T11:26:07Z","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/2506.19009/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The spectral theorem says that a real symmetric matrix has an orthogonal basis of eigenvectors and that, for a matrix with distinct eigenvalues, the basis is unique (up to signs). In this paper, we study the symmetric tensors with an orthogonal basis of eigenvectors and show that, for a generic such tensor, the orthogonal basis is unique. This resolves a conjecture by Mesters and Zwiernik. We also study the non-symmetric setting. The singular value decomposition says that a real matrix has an orthogonal basis of singular vector pairs and that, for a matrix with distinct singular values, the ba","authors_text":"Alvaro Ribot, Anna Seigal, Piotr Zwiernik","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-06-23T18:05:10Z","title":"Orthogonal eigenvectors and singular vectors of tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.19009","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":"sha256:4ccb9736d7129cce533fb0a0441ceda563cb9cdce4cb668b77f43d768759e07c","target":"record","created_at":"2026-07-05T11:26:07Z","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":"f49ac6196452937f64e049512195d313e51f2ca9a50cf1c1e2a8417fecb71840","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-06-23T18:05:10Z","title_canon_sha256":"09b1f9e981bdcab0577b5e65a9ce976113e636daf98ef09d957f144a84531a36"},"schema_version":"1.0","source":{"id":"2506.19009","kind":"arxiv","version":1}},"canonical_sha256":"92809f929f1056ab280aeb23bd2d7fbee7842e603147c03a0b4ec334e78de68a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92809f929f1056ab280aeb23bd2d7fbee7842e603147c03a0b4ec334e78de68a","first_computed_at":"2026-07-05T11:26:07.913365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:26:07.913365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rIBdbyBf7MYmlDI4h4qMkb1qsdpSGS8Eoio/Vrm7LZf713uRjXxEfEuSKhuxwGt4pg6n4sSE6KANMDLDaTTtBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:26:07.913828Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.19009","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ccb9736d7129cce533fb0a0441ceda563cb9cdce4cb668b77f43d768759e07c","sha256:9d83c7b77bbbc5bae7e2c6c07cfb4505d764bfd902279517d16096d573fca4eb"],"state_sha256":"5cd6cd78cf59eb088d1476e7148b44701a2f2b75de036fc96512843e68888c07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vm5YsiGoRoo+VQ7jOklyPQE2xxRtUHg2iBxqp+sJLRI3mKrGfsbk4EEsV/yOeHr6EXihdEQMZ3SV7LswC+WcBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T23:11:58.105279Z","bundle_sha256":"36e8422171529861195593aa43a0a8c15fb58f7e29f9447f3300a42e873f19b4"}}