Pith Number

pith:OFQPHSRR

pith:2008:OFQPHSRRF64OIQRGUXMFRBE25M

not attested not anchored not stored refs pending

Combable functions, quasimorphisms, and the central limit theorem

Danny Calegari, Koji Fujiwara

arxiv:0805.1755 v3 · 2008-05-13 · math.GR · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OFQPHSRRF64OIQRGUXMFRBE25M}

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	2026-05-18T04:41:05.354357Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7160f3ca312fb8e44226a5d858849aeb151ef615ceeed49b5c4353cb43185768

Aliases

arxiv: 0805.1755 · arxiv_version: 0805.1755v3 · doi: 10.48550/arxiv.0805.1755 · pith_short_12: OFQPHSRRF64O · pith_short_16: OFQPHSRRF64OIQRG · pith_short_8: OFQPHSRR

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/OFQPHSRRF64OIQRGUXMFRBE25M \
  | 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: 7160f3ca312fb8e44226a5d858849aeb151ef615ceeed49b5c4353cb43185768

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cffd275f7dd9feece3197cb69a4e4c44b9459b9132410e62d80cdcc9cb98e5e2",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-05-13T15:55:38Z",
    "title_canon_sha256": "933258e94767ce93e2900dc0f1f5d2d7adfa4ff52e8b2e24e7d023d4b3a5a5a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0805.1755",
    "kind": "arxiv",
    "version": 3
  }
}