Pith Number

pith:5XVTNP3V

pith:2013:5XVTNP3V4L6QGJDOIKOAZWH45W

not attested not anchored not stored refs pending

Square-summable variation and absolutely continuous spectrum

Milivoje Lukic

arxiv:1303.4161 v2 · 2013-03-18 · math.SP · 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{5XVTNP3V4L6QGJDOIKOAZWH45W}

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.

Receipt and verification

First computed	2026-05-18T03:18:42.325090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

edeb36bf75e2fd03246e429c0cd8fced94a99cc3a9577523369916a7b2d24ef4

Aliases

arxiv: 1303.4161 · arxiv_version: 1303.4161v2 · doi: 10.48550/arxiv.1303.4161 · pith_short_12: 5XVTNP3V4L6Q · pith_short_16: 5XVTNP3V4L6QGJDO · pith_short_8: 5XVTNP3V

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/5XVTNP3V4L6QGJDOIKOAZWH45W \
  | 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: edeb36bf75e2fd03246e429c0cd8fced94a99cc3a9577523369916a7b2d24ef4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ba6a80d0bf317b05f6e53375c0e2055b8e25f2ec60f9e2c8b6f023a6ee6e753",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-03-18T05:54:31Z",
    "title_canon_sha256": "3d2f41447c7131862e97b40374e52c6be744cf0f51635e7761e77bbb92d76422"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.4161",
    "kind": "arxiv",
    "version": 2
  }
}