Pith Number

pith:562KPEX3

pith:2020:562KPEX3H4HKABTBQVETYNUHJA

not attested not anchored not stored refs pending

Improved Lower Bounds for Permutation Arrays Using Permutation Rational Functions

Brian Malouf, I. Hal Sudborough, Linda Morales, Sergey Bereg, Thomas Stanley

arxiv:2003.10072 v2 · 2020-03-23 · math.CO · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{562KPEX3H4HKABTBQVETYNUHJA}

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	2026-07-05T02:26:11.600095Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efb4a792fb3f0ea0066185493c368748074eb509bcc992a029d3d8fc771e6e2c

Aliases

arxiv: 2003.10072 · arxiv_version: 2003.10072v2 · doi: 10.48550/arxiv.2003.10072 · pith_short_12: 562KPEX3H4HK · pith_short_16: 562KPEX3H4HKABTB · pith_short_8: 562KPEX3

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/562KPEX3H4HKABTBQVETYNUHJA \
  | 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: efb4a792fb3f0ea0066185493c368748074eb509bcc992a029d3d8fc771e6e2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24a965a99b921f54b53e784c67b8595a96b9bce8f130a41d7bffe17dbdc6bdeb",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-03-23T04:07:07Z",
    "title_canon_sha256": "fa2f80f0019d81d25fc0602d036cf8f9c8ee8b52315988def888b16f9f071449"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2003.10072",
    "kind": "arxiv",
    "version": 2
  }
}