Pith Number

pith:4SPZTV2Z

pith:2011:4SPZTV2Z3REC6GZ5LQJV3R5YMR

not attested not anchored not stored refs pending

The variational principle of local pressure for actions of sofic group

Ercai Chen, Xiaoyao Zhou

arxiv:1112.5260 v2 · 2011-12-22 · 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{4SPZTV2Z3REC6GZ5LQJV3R5YMR}

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	2026-05-18T04:05:04.995578Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e49f99d759dc482f1b3d5c135dc7b86453f470b27a910eed4140447b3ebf3fe5

Aliases

arxiv: 1112.5260 · arxiv_version: 1112.5260v2 · doi: 10.48550/arxiv.1112.5260 · pith_short_12: 4SPZTV2Z3REC · pith_short_16: 4SPZTV2Z3REC6GZ5 · pith_short_8: 4SPZTV2Z

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/4SPZTV2Z3REC6GZ5LQJV3R5YMR \
  | 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: e49f99d759dc482f1b3d5c135dc7b86453f470b27a910eed4140447b3ebf3fe5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b4cd74895a713d7377103335af50cd5ade32bcedd1ec87c5a5bc4a6571e6aba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-12-22T10:16:01Z",
    "title_canon_sha256": "57f455f8c26e5e8c990aa10816fe44ac00ce49d69a1c6c9ebf35f503af6c88d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5260",
    "kind": "arxiv",
    "version": 2
  }
}