Pith Number

pith:MRUCOMJ4

pith:2015:MRUCOMJ4GC3YA5D7ASKGARXHPT

not attested not anchored not stored refs pending

Density dichotomy in random words

Danny Rorabaugh, Joshua Cooper

arxiv:1504.04424 v2 · 2015-04-17 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MRUCOMJ4GC3YA5D7ASKGARXHPT}

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	2026-05-18T01:02:13.972302Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

646827313c30b780747f04946046e77cdefc74227e613ab032672a63e0d6b5c4

Aliases

arxiv: 1504.04424 · arxiv_version: 1504.04424v2 · doi: 10.48550/arxiv.1504.04424 · pith_short_12: MRUCOMJ4GC3Y · pith_short_16: MRUCOMJ4GC3YA5D7 · pith_short_8: MRUCOMJ4

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/MRUCOMJ4GC3YA5D7ASKGARXHPT \
  | 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: 646827313c30b780747f04946046e77cdefc74227e613ab032672a63e0d6b5c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf5fdcbe8b255092a78f2b0cecee57995c1769e3e4a8106f379b505a10ad9082",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-04-17T02:16:42Z",
    "title_canon_sha256": "b071ef7b82e5dda8ee47911fd7593e6c56d2773ca8697e7837598b05a9a49003"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.04424",
    "kind": "arxiv",
    "version": 2
  }
}