Pith Number

pith:B64QSO4B

pith:2014:B64QSO4BJLVS5ZQ2STSV63A774

not attested not anchored not stored refs pending

Complexity and directional entropy in two dimensions

Bryna Kra, Ryan Broderick, Van Cyr

arxiv:1409.5056 v1 · 2014-09-17 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B64QSO4BJLVS5ZQ2STSV63A774}

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	2026-05-18T02:42:37.940605Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0fb9093b814aeb2ee61a94e55f6c1fff36b0dacdf96f1c61f2fa9a38d8c0e125

Aliases

arxiv: 1409.5056 · arxiv_version: 1409.5056v1 · doi: 10.48550/arxiv.1409.5056 · pith_short_12: B64QSO4BJLVS · pith_short_16: B64QSO4BJLVS5ZQ2 · pith_short_8: B64QSO4B

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/B64QSO4BJLVS5ZQ2STSV63A774 \
  | 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: 0fb9093b814aeb2ee61a94e55f6c1fff36b0dacdf96f1c61f2fa9a38d8c0e125

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f36d6ec7c04eec8f25c4579c74825478a11a41b733ae578e84c8194770b0ea47",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-09-17T16:26:15Z",
    "title_canon_sha256": "8f3bb4b53e458d32c92362e4a0363f54c5c5bdfe85dfaf6d0b2c49afc240bc02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.5056",
    "kind": "arxiv",
    "version": 1
  }
}