Pith Number

pith:5S3BF4M6

pith:2012:5S3BF4M635HEGVSUXRHCOVYVBV

not attested not anchored not stored refs pending

Limit free computation of entropy

Anna Giordano Bruno, Dikran Dikranjan

arxiv:1205.5009 v1 · 2012-05-22 · math.DS · 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{5S3BF4M635HEGVSUXRHCOVYVBV}

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	2026-05-18T03:55:03.090456Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ecb612f19edf4e435654bc4e2757150d7a5b98914dfa28c799965effe37c80c5

Aliases

arxiv: 1205.5009 · arxiv_version: 1205.5009v1 · doi: 10.48550/arxiv.1205.5009 · pith_short_12: 5S3BF4M635HE · pith_short_16: 5S3BF4M635HEGVSU · pith_short_8: 5S3BF4M6

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/5S3BF4M635HEGVSUXRHCOVYVBV \
  | 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: ecb612f19edf4e435654bc4e2757150d7a5b98914dfa28c799965effe37c80c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "137f1e4d35b623dc12eaf2d125e5f3891ef29631947cd7e65450726ee4150974",
    "cross_cats_sorted": [
      "math.GN",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-05-22T19:12:08Z",
    "title_canon_sha256": "1640368e39c62ca6f7b3043b373b4c7efb9569083c99ac5e8b25aea636a4720b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.5009",
    "kind": "arxiv",
    "version": 1
  }
}