Pith Number

pith:Y7FD6GV6

pith:2016:Y7FD6GV6EXQ5BALP3ZAX42SXSU

not attested not anchored not stored refs pending

Entropy along expanding foliations

Jiagang Yang

arxiv:1601.05504 v2 · 2016-01-21 · 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{Y7FD6GV6EXQ5BALP3ZAX42SXSU}

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	2026-05-17T23:58:31.419247Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7ca3f1abe25e1d0816fde417e6a579520ed9a3fcef13076f0ecb72dbcce58cb

Aliases

arxiv: 1601.05504 · arxiv_version: 1601.05504v2 · doi: 10.48550/arxiv.1601.05504 · pith_short_12: Y7FD6GV6EXQ5 · pith_short_16: Y7FD6GV6EXQ5BALP · pith_short_8: Y7FD6GV6

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/Y7FD6GV6EXQ5BALP3ZAX42SXSU \
  | 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: c7ca3f1abe25e1d0816fde417e6a579520ed9a3fcef13076f0ecb72dbcce58cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68f081e0abc765d62ed7592143968ed7bcc339e0cae20bd10cfa643db47e0186",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-01-21T03:58:34Z",
    "title_canon_sha256": "c8cb4ecf902f2481ee986ba27418f498b8cf15ca65e7f7d8083dd0dd991191f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.05504",
    "kind": "arxiv",
    "version": 2
  }
}