Pith Number

pith:7E3HQNT3

pith:2015:7E3HQNT3GTKJIM65AJTTACD57Q

not attested not anchored not stored refs pending

The number of 1...d-avoiding permutations of length d+r for SYMBOLIC d but numeric r

Doron Zeilberger, Nathaniel Shar, Shalosh B. Ekhad

arxiv:1504.02513 v1 · 2015-04-09 · 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{7E3HQNT3GTKJIM65AJTTACD57Q}

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	2026-05-18T02:19:07.467898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f93678367b34d49433dd026730087dfc257dec6ff288a0938d6266df40745296

Aliases

arxiv: 1504.02513 · arxiv_version: 1504.02513v1 · doi: 10.48550/arxiv.1504.02513 · pith_short_12: 7E3HQNT3GTKJ · pith_short_16: 7E3HQNT3GTKJIM65 · pith_short_8: 7E3HQNT3

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/7E3HQNT3GTKJIM65AJTTACD57Q \
  | 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: f93678367b34d49433dd026730087dfc257dec6ff288a0938d6266df40745296

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f66ce54208e80593c6f6bd81b2d127063f3c84f5db116c0959daf648152c8436",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-04-09T22:37:55Z",
    "title_canon_sha256": "2697a178bcc5a01aa452b2f91456b55134f71c762dd592c5133e7913448acdd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.02513",
    "kind": "arxiv",
    "version": 1
  }
}