{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_72955291e2d2cd4385ab023ff7fd0c75d7fa3f6fca02d0348a89cd27b475a87b","bitcoin_anchor":{"bitcoin_attestations":["bitcoin_block_949451"],"calendar_attestations":["https://finney.calendar.eternitywall.com","https://btc.calendar.catallaxy.com","https://alice.btc.calendar.opentimestamps.org","https://bob.btc.calendar.opentimestamps.org"],"ots_url":"/registry/data/substrate/anchors/77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3.ots","stamped_at":"2026-05-15T03:00:03Z","status":"bitcoin"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_72955291e2d2cd4385ab023ff7fd0c75d7fa3f6fca02d0348a89cd27b475a87b","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"45eac8ba97c1bbbb490a32321e18e2af3e3d22ca574577c6c54fb95552bf04d1","published":"Thu, 07 May 2026 00:00:00 -0400","receipt_hash":"45eac8ba97c1bbbb490a32321e18e2af3e3d22ca574577c6c54fb95552bf04d1","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"45eac8ba97c1bbbb490a32321e18e2af3e3d22ca574577c6c54fb95552bf04d1","observed_at":"2026-05-07T04:43:30.601849Z","parent_run_hash":"b20b3beeadde500bb99eda3b869d50b00c5259b2c78c650d83e786ac81b85801","published":"Thu, 07 May 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2605.03283v1 Announce Type: cross \nAbstract: We provide a unified theoretical analysis of Linear Discriminant Analysis with simultaneous multilabel scatter matrix formulations and Stiefel orthogonality constraints. Our contributions span both algebraic structure and statistical guarantees. On the algebraic side, we characterize the rank of the multilabel between-class scatter matrix, showing that the effective discriminant dimensionality can strictly exceed the classical single-label bound of $C-1$; we establish a multilabel partition of variance and prove that all four Fisher objectives are equivalent under the $W^\\top S_t^{ML} W = I_r$ constraint while characterizing their divergence under the Stiefel constraint; and we prove a two-sided label-distance preservation bound relating projected distances to Hamming distances in label space. On the statistical side, we establish a finite-sample $O(k_{\\max}\\sqrt{d\\log d/n}/gap_r)$ bound on the subspace estimation error under sub-Gauss","title":"On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants","url":"https://arxiv.org/abs/2605.03283","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.03283v1 Announce Type: cross \nAbstract: We provide a unified theoretical analysis of Linear Discriminant Analysis with simultaneous multilabel scatter matrix formulations and Stiefel orthogonality constraints. Our contributions span both algebraic structure and statistical guarantees. On the algebraic side, we characterize the rank of the multilabel between-class scatter matrix, showing that the effective discriminant dimensionality can strictly exceed the classical single-label bound of $C-1$; we establish a multilabel partition of variance and prove that all four Fisher objectives are equivalent under the $W^\\top S_t^{ML} W = I_r$ constraint while characterizing their divergence under the Stiefel constraint; and we prove a two-sided label-distance preservation bound relating projected distances to Hamming distances in label space. On the statistical side, we establish a finite-sample $O(k_{\\max}\\sqrt{d\\log d/n}/gap_r)$ bound on the subspace estimation error under sub-Gauss","title":"On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-07T04:43:30Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.03283"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:0d6cb754d80de9a468fa53b80f77896ce93b6c356370f71c5849620453aabc6a66d16be80e1d363c6ea60753fd3e0a340d80290d89447b58eb8e67170a41920d","signer":"crovia.substrate","subject":{"observed_at":"2026-05-07T04:43:30Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.03283"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"28d94169a3f25eaa696b6f1ab7153c8a27dad24645d85f444735c7792345070f","leaf_index":118268,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"af8f499c4c5b203d992bca803970343d0fc128b3ca3a821f99bd6f53d7622842","side":"right"},{"sibling":"730d86671faf0c2edd43c43016415b0cbbb2a7e0387ad4eae7f3c302f124cda1","side":"right"},{"sibling":"a384f56bc45ba5ff785e761514114cea84e42dd91b035a117ad7731a94073e93","side":"left"},{"sibling":"203154e6ed4ad460bcfd467b1d5aa91ce37d23a01d17767e7e2dd1390794f3f1","side":"left"},{"sibling":"068ed2eeac6074c0ecb706625c280809640e9e948cc090e343cdf256238f3354","side":"left"},{"sibling":"f1ce40097c7b14a0d22084f542808967c45441bde11e15fd0e39b5936adf6130","side":"left"},{"sibling":"1b5d9d099a141dbd9b65685d9424ef07b508b27c0e01ef2b925d1dd5d95de03a","side":"left"},{"sibling":"c25c853cb3dd8c7f1b99fc80fd602c044932de34c1b34bd69ab1d5b8c94e42b1","side":"left"},{"sibling":"3d3124224341dac361f0e93f24f70795342ba216dc1c0065e7fa7592d943b488","side":"left"},{"sibling":"438bef084db8613e8143527769e3c677e12a59f8a6e2dea114f88afab0446a43","side":"right"},{"sibling":"8e758a4477dfc0838d2e8ea2bdbd583bc3192683e75fd9cde217ee6a3b2f3ac8","side":"left"},{"sibling":"4219f746e463e594ccd6447debdf736a57e77319b12bcb74d8ece2b5860064c6","side":"left"},{"sibling":"05f89b32c00462e60adf95c1fe4579cdc2791b36e8b17573d8f3b5fd5da95a0b","side":"right"},{"sibling":"8ccd9937a2c0d5c04044d07d1557791b7d07bb31eac41a39a675608d44b38f23","side":"right"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_72955291e2d2cd4385ab023ff7fd0c75d7fa3f6fca02d0348a89cd27b475a87b"}}