Pith Number

pith:PZO6ZLNM

pith:2012:PZO6ZLNMAC6PCCOJAHVNNRYM3U

not attested not anchored not stored refs pending

The variational principle of topological pressure for actions of sofic groupoids

Ercai Chen, Xiaoyao Zhou

arxiv:1212.6604 v1 · 2012-12-29 · 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{PZO6ZLNMAC6PCCOJAHVNNRYM3U}

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	2026-05-18T03:37:31.419969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e5decadac00bcf109c901ead6c70cdd1d6af63fa955acc4afcb9c58161eaeed

Aliases

arxiv: 1212.6604 · arxiv_version: 1212.6604v1 · doi: 10.48550/arxiv.1212.6604 · pith_short_12: PZO6ZLNMAC6P · pith_short_16: PZO6ZLNMAC6PCCOJ · pith_short_8: PZO6ZLNM

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/PZO6ZLNMAC6PCCOJAHVNNRYM3U \
  | 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: 7e5decadac00bcf109c901ead6c70cdd1d6af63fa955acc4afcb9c58161eaeed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1444768873111955ebb512ec67fd953a3e936e504348d4d4e27eb80623d7575d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-12-29T10:05:59Z",
    "title_canon_sha256": "be8a3d2798d5b0119df537b507f02b0f8be11bb697fb979a7437775425faf743"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6604",
    "kind": "arxiv",
    "version": 1
  }
}