Pith Number

pith:YZCNRHZJ

pith:2010:YZCNRHZJEO7L5BS6JWGGRUP3YK

not attested not anchored not stored refs pending

Statistics and compression of scl

Danny Calegari, Joseph Maher

arxiv:1008.4952 v4 · 2010-08-29 · math.GR · math.DS · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YZCNRHZJEO7L5BS6JWGGRUP3YK}

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	2026-05-17T23:53:36.906458Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c644d89f2923bebe865e4d8c68d1fbc2b912ef0158193c83d434651180bbe35d

Aliases

arxiv: 1008.4952 · arxiv_version: 1008.4952v4 · doi: 10.48550/arxiv.1008.4952 · pith_short_12: YZCNRHZJEO7L · pith_short_16: YZCNRHZJEO7L5BS6 · pith_short_8: YZCNRHZJ

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/YZCNRHZJEO7L5BS6JWGGRUP3YK \
  | 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: c644d89f2923bebe865e4d8c68d1fbc2b912ef0158193c83d434651180bbe35d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9af9df642281b5163a26528db56ccbf94f9627bed418893dc3a8ac5e12868a2f",
    "cross_cats_sorted": [
      "math.DS",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-08-29T20:16:48Z",
    "title_canon_sha256": "41e82977c7aadbb00b4c76bf019d5a827d60f3f65890915dc913ba220ae39fd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4952",
    "kind": "arxiv",
    "version": 4
  }
}