Pith Number

pith:IZBSX3OF

pith:2011:IZBSX3OF62H3ZEP7LD7GZNMSCZ

not attested not anchored not stored refs pending

Topological pressure and the variational principle for actions of sofic groups

Nhan-Phu Chung

arxiv:1110.0699 v3 · 2011-10-04 · 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{IZBSX3OF62H3ZEP7LD7GZNMSCZ}

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	2026-05-18T03:54:47.853392Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46432bedc5f68fbc91ff58fe6cb59216644615ad66060d4c56c64c868d024c33

Aliases

arxiv: 1110.0699 · arxiv_version: 1110.0699v3 · doi: 10.48550/arxiv.1110.0699 · pith_short_12: IZBSX3OF62H3 · pith_short_16: IZBSX3OF62H3ZEP7 · pith_short_8: IZBSX3OF

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/IZBSX3OF62H3ZEP7LD7GZNMSCZ \
  | 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: 46432bedc5f68fbc91ff58fe6cb59216644615ad66060d4c56c64c868d024c33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1f97b4ced3c848d1665f3202689305bc0320ddb574fe80e5af0994434c84aa3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-10-04T14:24:51Z",
    "title_canon_sha256": "b1f491c7677c61525eedcdae037df83741acf765a26ea343bc293346c5d0309d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.0699",
    "kind": "arxiv",
    "version": 3
  }
}