Pith Number

pith:2QQN3KK4

pith:2012:2QQN3KK4KT2TVE4HL4IDVWQBUU

not attested not anchored not stored refs pending

On Fourier analytic properties of graphs

Jonathan M. Fraser, Tuomas Orponen, Tuomas Sahlsten

arxiv:1211.4803 v2 · 2012-11-20 · math.CA · 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{2QQN3KK4KT2TVE4HL4IDVWQBUU}

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	2026-05-18T02:41:10.356414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d420dda95c54f53a93875f103ada01a53e7959719e54e5c544771bac3382237e

Aliases

arxiv: 1211.4803 · arxiv_version: 1211.4803v2 · doi: 10.48550/arxiv.1211.4803 · pith_short_12: 2QQN3KK4KT2T · pith_short_16: 2QQN3KK4KT2TVE4H · pith_short_8: 2QQN3KK4

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/2QQN3KK4KT2TVE4HL4IDVWQBUU \
  | 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: d420dda95c54f53a93875f103ada01a53e7959719e54e5c544771bac3382237e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0f7568d0c76ef6103b8bdeb1fc20f4bb8ade54a31e8bab3318875b74783f717",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-11-20T17:05:21Z",
    "title_canon_sha256": "c9d500a899763d8ce771201d26530f53d3a481a8a5715337de298f9e9b510544"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4803",
    "kind": "arxiv",
    "version": 2
  }
}