Pith Number

pith:M3BC3EA7

pith:2010:M3BC3EA7RUJZWECWEDDP4ZLIPS

not attested not anchored not stored refs pending

The number of permutations with k inversions

G\'abor Heged\"us

arxiv:1002.2054 v1 · 2010-02-10 · math.CO · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M3BC3EA7RUJZWECWEDDP4ZLIPS}

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	2026-05-18T01:02:59.679437Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66c22d901f8d139b105620c6fe65687c9b93cdd6c3d6e2ccfb05f206e97c0eac

Aliases

arxiv: 1002.2054 · arxiv_version: 1002.2054v1 · doi: 10.48550/arxiv.1002.2054 · pith_short_12: M3BC3EA7RUJZ · pith_short_16: M3BC3EA7RUJZWECW · pith_short_8: M3BC3EA7

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/M3BC3EA7RUJZWECWEDDP4ZLIPS \
  | 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: 66c22d901f8d139b105620c6fe65687c9b93cdd6c3d6e2ccfb05f206e97c0eac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89d2b1143c02f661b70a7e44b519dcffa219b73d9f2eca72abca867f46881ef1",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-02-10T10:05:18Z",
    "title_canon_sha256": "f87ff3d34450250eec51ca2216e10161680614cd3778e181976193876736645a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.2054",
    "kind": "arxiv",
    "version": 1
  }
}