Pith Number

pith:UPHDO2VW

pith:2016:UPHDO2VWAPO4RQSJAKR24KS2A7

not attested not anchored not stored refs pending

On the Law of Large Numbers for Discrete Fourier Transform

Na Zhang

arxiv:1602.07268 v1 · 2016-02-23 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UPHDO2VWAPO4RQSJAKR24KS2A7}

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	2026-05-18T01:20:06.793189Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3ce376ab603ddc8c24902a3ae2a5a07f2938ffdf872bd8b85842fa111f958c2

Aliases

arxiv: 1602.07268 · arxiv_version: 1602.07268v1 · doi: 10.48550/arxiv.1602.07268 · pith_short_12: UPHDO2VWAPO4 · pith_short_16: UPHDO2VWAPO4RQSJ · pith_short_8: UPHDO2VW

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/UPHDO2VWAPO4RQSJAKR24KS2A7 \
  | 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: a3ce376ab603ddc8c24902a3ae2a5a07f2938ffdf872bd8b85842fa111f958c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55bf1d9c5656af8667985b7ed072d133fa946896b0212df6d625d930ee080a4b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-02-23T19:15:12Z",
    "title_canon_sha256": "6147fcad9d480c9d6bf7b4b07b89a77d25dbb3068555a292a16daa3b5b2938f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.07268",
    "kind": "arxiv",
    "version": 1
  }
}