Pith Number

pith:3QAENFU3

pith:2010:3QAENFU3MFHBQLFDBZNGGFMA2O

not attested not anchored not stored refs pending

Entropy in a category

Anna Giordano Bruno, Dikran Dikranjan

arxiv:1006.5122 v2 · 2010-06-26 · math.GR · math.CT · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3QAENFU3MFHBQLFDBZNGGFMA2O}

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	2026-05-18T04:27:47.596411Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc0046969b614e182ca30e5a631580d3802f324039a62d746ee1c12fb885c98b

Aliases

arxiv: 1006.5122 · arxiv_version: 1006.5122v2 · doi: 10.48550/arxiv.1006.5122 · pith_short_12: 3QAENFU3MFHB · pith_short_16: 3QAENFU3MFHBQLFD · pith_short_8: 3QAENFU3

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/3QAENFU3MFHBQLFDBZNGGFMA2O \
  | 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: dc0046969b614e182ca30e5a631580d3802f324039a62d746ee1c12fb885c98b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f2b5fd72bbae84b1ca8a485d5cc96bdf0ddd8c85421ec61a6ceca143c9ff22e",
    "cross_cats_sorted": [
      "math.CT",
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-06-26T08:35:46Z",
    "title_canon_sha256": "b03bb8f571a29f9e35d4e467611461e11cae5c8912e65c4d5a4e077cbdee98c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.5122",
    "kind": "arxiv",
    "version": 2
  }
}