Pith Number

pith:E5MRKVTJ

pith:2012:E5MRKVTJEM45KXJ5IDHPIL7ZTA

not attested not anchored not stored refs pending

Scale function vs Topological entropy

Anna Giordano Bruno, Dikran Dikranjan, Federico Berlai

arxiv:1210.1749 v2 · 2012-10-05 · math.GN · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E5MRKVTJEM45KXJ5IDHPIL7ZTA}

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	2026-05-18T03:21:43.543299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

27591556692339d55d3d40cef42ff9980f69025cae2d49d7c1a198100e39a6e6

Aliases

arxiv: 1210.1749 · arxiv_version: 1210.1749v2 · doi: 10.48550/arxiv.1210.1749 · pith_short_12: E5MRKVTJEM45 · pith_short_16: E5MRKVTJEM45KXJ5 · pith_short_8: E5MRKVTJ

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/E5MRKVTJEM45KXJ5IDHPIL7ZTA \
  | 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: 27591556692339d55d3d40cef42ff9980f69025cae2d49d7c1a198100e39a6e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b21507cfbf5c18bcb8a67ce9fb757245a970768bfe41a2bab4fc74028ae28770",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2012-10-05T13:19:46Z",
    "title_canon_sha256": "cb3ddcb4b4d20573e1b5380561d85a23b6c2175f79cd00c0d91e538c366ccf97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.1749",
    "kind": "arxiv",
    "version": 2
  }
}