Pith Number

pith:ZOWOOVW7

pith:2026:ZOWOOVW76COIIR2JSPTIJAC4FM

not attested not anchored not stored refs pending

Group-invariant moments under tomographic projections

Amnon Balanov, Dan Edidin, Tamir Bendory

The d-th moments of random tomographic projections determine the full d-th order rotation-invariant moments of the original object whenever d is at most the projection dimension.

arxiv:2604.08330 v2 · 2026-04-09 · eess.SP · cs.IT · math.IT

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Claims

C1strongest claim

We prove that, whenever d≤m, the d-th order moment of the projected data determines the full d-th order Haar-orbit moment of f, independently of the ambient dimension n. We further provide an explicit algorithmic procedure for recovering the latter from the former.

C2weakest assumption

The observations are of the form Y = P(R·f) where R is Haar-uniform in SO(n) and P projects onto an m-dimensional subspace; the determination holds only for d ≤ m and may fail if rotations are not uniform or if d exceeds m.

C3one line summary

d-th order moments of m-dimensional projections determine the d-th order Haar-invariant moments of the n-dimensional object for d ≤ m, independently of n.

Cited by

2 papers in Pith

The generalized method of moments is (almost) statistically efficient in low-SNR Gaussian latent-variable models

Beyond Frequency Marching: Orbit Recovery in Dihedral and Projected Multireference Alignment

Receipt and verification

First computed	2026-06-26T01:15:51.418338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbace756dff09c84474993e684805c2b1f5415e4bfb337b1570a71790c74ab47

Aliases

arxiv: 2604.08330 · arxiv_version: 2604.08330v2 · doi: 10.48550/arxiv.2604.08330 · pith_short_12: ZOWOOVW76COI · pith_short_16: ZOWOOVW76COIIR2J · pith_short_8: ZOWOOVW7

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZOWOOVW76COIIR2JSPTIJAC4FM \
  | 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: cbace756dff09c84474993e684805c2b1f5415e4bfb337b1570a71790c74ab47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08872c57ba897382f7a161b6437ab66bf1a100df1af5a5e4b8ce7cd3d0e9f75b",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "eess.SP",
    "submitted_at": "2026-04-09T15:03:34Z",
    "title_canon_sha256": "78dc6a50eed35e096f3bcbcfa006927ff99aae321906b262ad4ac430fbffffdc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.08330",
    "kind": "arxiv",
    "version": 2
  }
}