Pith Number

pith:Z76NZ7S3

pith:2026:Z76NZ7S3NNZYXRE57NB66ZTSIM

not attested not anchored not stored refs pending

On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants

Brian Keith-Norambuena, Juan Bekios-Calfa

All four multilabel Fisher objectives become equivalent under the total scatter constraint W^T S_t^{ML} W = I_r.

arxiv:2605.03283 v2 · 2026-05-05 · stat.ML · cs.AI · cs.LG

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\usepackage{pith}
\pithnumber{Z76NZ7S3NNZYXRE57NB66ZTSIM}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

All four Fisher objectives are equivalent under the W^T S_t^{ML} W = I_r constraint while the subspace estimation error admits a finite-sample O(k_max sqrt(d log d / n) / gap_r) bound with a matching Omega(sigma^2 d / (n gap_r)) minimax lower bound.

C2weakest assumption

The data are generated from a linear label-effect model with sub-Gaussian noise; numerical checks use only synthetic data and serve as sanity verification rather than real-world validation.

C3one line summary

Multilabel Fisher discriminants exhibit objective equivalence under total scatter normalization, with near-minimax optimal finite-sample subspace estimation rates under sub-Gaussian noise.

Receipt and verification

First computed	2026-06-30T01:18:18.596993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cffcdcfe5b6b738bc49dfb43ef66724315bdccf073eaff5ae651617faea0faa9

Aliases

arxiv: 2605.03283 · arxiv_version: 2605.03283v2 · doi: 10.48550/arxiv.2605.03283 · pith_short_12: Z76NZ7S3NNZY · pith_short_16: Z76NZ7S3NNZYXRE5 · pith_short_8: Z76NZ7S3

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Z76NZ7S3NNZYXRE57NB66ZTSIM \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: cffcdcfe5b6b738bc49dfb43ef66724315bdccf073eaff5ae651617faea0faa9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "668762e9d149920598c29603ae3f945d4c402f88ef298fd2dc51d798fb60ec7d",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-05T02:14:33Z",
    "title_canon_sha256": "abd03bd0917a4c09bc85425e09fa0b9ddc28f18399a058ee25665df6afbae77e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03283",
    "kind": "arxiv",
    "version": 2
  }
}