Pith Number

pith:5CMVDZOF

pith:2010:5CMVDZOFTR5BVURLXW3ZNGP5QH

not attested not anchored not stored refs pending

Variational principles for topological entropies of subsets

De-Jun Feng, Wen Huang

arxiv:1012.1103 v1 · 2010-12-06 · math.DS · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5CMVDZOFTR5BVURLXW3ZNGP5QH}

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	2026-05-18T04:34:01.815175Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e89951e5c59c7a1ad22bbdb79699fd81f7dc7c938534569f9c7e744c4d2ecde9

Aliases

arxiv: 1012.1103 · arxiv_version: 1012.1103v1 · doi: 10.48550/arxiv.1012.1103 · pith_short_12: 5CMVDZOFTR5B · pith_short_16: 5CMVDZOFTR5BVURL · pith_short_8: 5CMVDZOF

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/5CMVDZOFTR5BVURLXW3ZNGP5QH \
  | 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: e89951e5c59c7a1ad22bbdb79699fd81f7dc7c938534569f9c7e744c4d2ecde9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "933f9188738aaf6b2a32c7bce045c6218738f9582871af610f2023be420b2c7d",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-12-06T09:38:54Z",
    "title_canon_sha256": "66416e8276d88eddd15bc46c69459a5b41482833ad81bf0cc0223b60360faff2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1103",
    "kind": "arxiv",
    "version": 1
  }
}