Pith Number

pith:NDYLQXMP

pith:2015:NDYLQXMPVEWZFG5TIIOGIP5NLL

not attested not anchored not stored refs pending

Self-improvement of uniform fatness revisited

Antti V. V\"ah\"akangas, Heli Tuominen, Juha Lehrb\"ack

arxiv:1512.06514 v1 · 2015-12-21 · math.CA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NDYLQXMPVEWZFG5TIIOGIP5NLL}

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	2026-05-18T01:24:00.340378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68f0b85d8fa92d929bb3421c643fad5aebb46fd36634371e26593256d913a194

Aliases

arxiv: 1512.06514 · arxiv_version: 1512.06514v1 · doi: 10.48550/arxiv.1512.06514 · pith_short_12: NDYLQXMPVEWZ · pith_short_16: NDYLQXMPVEWZFG5T · pith_short_8: NDYLQXMP

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/NDYLQXMPVEWZFG5TIIOGIP5NLL \
  | 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: 68f0b85d8fa92d929bb3421c643fad5aebb46fd36634371e26593256d913a194

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c260782493e0a834b1f86e5d4993a3d580fac99161a2192790ec683f38c4bf77",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-12-21T08:17:33Z",
    "title_canon_sha256": "c62ca74c536bc0931bc468365cc8d07563a239d4173065b780cce366e638cef8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06514",
    "kind": "arxiv",
    "version": 1
  }
}