Pith Number

pith:4HNKX2RA

pith:2003:4HNKX2RAU55YSZQB7UDOOLIPEZ

not attested not anchored not stored refs pending

Dense Dirac combs in Euclidean space with pure point diffraction

Christoph Richard

arxiv:math-ph/0302049 v2 · 2003-02-21 · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4HNKX2RAU55YSZQB7UDOOLIPEZ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Cited by

1 paper in Pith

On almost periodicity in crystalline measures

Receipt and verification

First computed	2026-07-04T15:13:53.611069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1daabea20a77b896601fd06e72d0f2673a54cce584777806703cf2c0228b82f

Aliases

arxiv: math-ph/0302049 · arxiv_version: math-ph/0302049v2 · doi: 10.48550/arxiv.math-ph/0302049 · pith_short_12: 4HNKX2RAU55Y · pith_short_16: 4HNKX2RAU55YSZQB · pith_short_8: 4HNKX2RA

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/4HNKX2RAU55YSZQB7UDOOLIPEZ \
  | 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: e1daabea20a77b896601fd06e72d0f2673a54cce584777806703cf2c0228b82f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9905add9e3d8bceb7423ba3ccdee5e0ba1c8a5eef3224e50045943eaac8e1bb0",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2003-02-21T09:55:49Z",
    "title_canon_sha256": "67932fb5e597bcd88a655f79312da0c367beadca752d050e5f20fb674008205d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0302049",
    "kind": "arxiv",
    "version": 2
  }
}