Pith Number

pith:DFHD6OBT

pith:2026:DFHD6OBTHB2OM4DOVC65LR5INP

not attested not anchored not stored refs pending

Algebraic Diversity: Group-Theoretic Spectral Estimation from Single Observations

Mitchell A. Thornton

Group averaging applied to a single observation can match the subspace estimation of traditional multi-observation covariance methods.

arxiv:2604.03634 v5 · 2026-04-04 · cs.LG · cs.IT · eess.SP · math.IT

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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

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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

A General Replacement Theorem proves that a group-averaged estimator from one snapshot achieves equivalent subspace decomposition to multi-snapshot covariance estimation.

C2weakest assumption

That the data object possesses representation-theoretic symmetry under a chosen group G such that the group action preserves the relevant subspace structure without requiring prior knowledge of that symmetry.

C3one line summary

Group-averaged estimators from one observation achieve equivalent subspace decomposition to multi-observation covariance methods, with variance scaling by group order and unifying DFT, DCT, and KLT as special cases.

Formal links

2 machine-checked theorem links

Cited by

6 papers in Pith

Algebraic Diversity: Principles of a Group-Theoretic Approach to Signal Processing

Unification of Signal Transform Theory

Polynomial-Time Optimal Group Selection via the Double-Commutator Eigenvalue Problem

Unification of Signal Transform Theory

Algebraic Diversity: Principles of a Group-Theoretic Approach to Signal Processing

Receipt and verification

First computed	2026-06-05T01:14:37.922742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

194e3f38333874e6706ea8bdd5c7a86bcb811ff087d3f165537c913274c597d5

Aliases

arxiv: 2604.03634 · arxiv_version: 2604.03634v5 · doi: 10.48550/arxiv.2604.03634 · pith_short_12: DFHD6OBTHB2O · pith_short_16: DFHD6OBTHB2OM4DO · pith_short_8: DFHD6OBT

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DFHD6OBTHB2OM4DOVC65LR5INP \
  | 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: 194e3f38333874e6706ea8bdd5c7a86bcb811ff087d3f165537c913274c597d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51343877ee3516b64fbad2860ca50dfd3f7cc45c6fb0914cb13536946cd89aad",
    "cross_cats_sorted": [
      "cs.IT",
      "eess.SP",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-04-04T08:08:34Z",
    "title_canon_sha256": "b0e70f31da9c5aa45e90f411858e765dbda248f7dad0de173ef81d38a6bcc22d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.03634",
    "kind": "arxiv",
    "version": 5
  }
}