Pith Number

pith:6Q7MQDPD

pith:2012:6Q7MQDPDPKFVZMQ3WFU2EAV22M

not attested not anchored not stored refs pending

Cram\'er transform and t-entropy

Krzysztof Zajkowski, Urszula Ostaszewska

arxiv:1211.3285 v2 · 2012-11-14 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6Q7MQDPDPKFVZMQ3WFU2EAV22M}

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	2026-05-18T02:50:13.618801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f43ec80de37a8b5cb21bb169a202bad32ece40c843087c4fcacc0aa436d96349

Aliases

arxiv: 1211.3285 · arxiv_version: 1211.3285v2 · doi: 10.48550/arxiv.1211.3285 · pith_short_12: 6Q7MQDPDPKFV · pith_short_16: 6Q7MQDPDPKFVZMQ3 · pith_short_8: 6Q7MQDPD

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/6Q7MQDPDPKFVZMQ3WFU2EAV22M \
  | 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: f43ec80de37a8b5cb21bb169a202bad32ece40c843087c4fcacc0aa436d96349

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3a798ffc6e995c4efa5c5dd79c9b7ab5be92464af56ace89fa4187036113be1",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-11-14T12:06:25Z",
    "title_canon_sha256": "80c81d315a704aa7f7c48bbb75e36add089cacb06ab7912aa9e2a29195c4ba4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3285",
    "kind": "arxiv",
    "version": 2
  }
}