Pith Number

pith:3RPUT4C5

pith:2016:3RPUT4C54K4LJI7BQMQBPQBHPV

not attested not anchored not stored refs pending

Permutation Polynomials of the form ${\tt X}^r(a+{\tt X}^{2(q-1)})$ --- A Nonexistence Result

Xiang-dong Hou

arxiv:1609.03662 v1 · 2016-09-13 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3RPUT4C54K4LJI7BQMQBPQBHPV}

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	2026-05-18T01:04:42.735585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc5f49f05de2b8b4a3e1832017c0277d44322a11aa50b79983ef227e2a75835e

Aliases

arxiv: 1609.03662 · arxiv_version: 1609.03662v1 · doi: 10.48550/arxiv.1609.03662 · pith_short_12: 3RPUT4C54K4L · pith_short_16: 3RPUT4C54K4LJI7B · pith_short_8: 3RPUT4C5

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/3RPUT4C54K4LJI7BQMQBPQBHPV \
  | 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: dc5f49f05de2b8b4a3e1832017c0277d44322a11aa50b79983ef227e2a75835e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d439c5807b4cd75ade9e8944aaf2ee2586355d160383aed4ed5eca7972a9ae5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-09-13T02:51:35Z",
    "title_canon_sha256": "ffec426b7390224007c161220bd30847e279dc592e04647329aa539eb4507cf6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.03662",
    "kind": "arxiv",
    "version": 1
  }
}