Pith Number

pith:WG5RLNXU

pith:2023:WG5RLNXUS2XNBHGTN2YLADJOQ5

not attested not anchored not stored refs pending

Typical sofic entropy and local limits for free group shift systems

Christopher Shriver

arxiv:2308.08041 v1 · 2023-08-15 · math.PR · 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{WG5RLNXUS2XNBHGTN2YLADJOQ5}

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.

Cited by

1 paper in Pith

Characterizing the limiting critical Potts measures on locally regular-tree-like expander graphs

Receipt and verification

First computed	2026-07-05T06:41:53.442301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1bb15b6f496aed09cd36eb0b00d2e87404d696d416330fcb7e0c0f882938006

Aliases

arxiv: 2308.08041 · arxiv_version: 2308.08041v1 · doi: 10.48550/arxiv.2308.08041 · pith_short_12: WG5RLNXUS2XN · pith_short_16: WG5RLNXUS2XNBHGT · pith_short_8: WG5RLNXU

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/WG5RLNXUS2XNBHGTN2YLADJOQ5 \
  | 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: b1bb15b6f496aed09cd36eb0b00d2e87404d696d416330fcb7e0c0f882938006

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe7c25b9434d796039e9fb9a8a8beaf92f3b7f844994d13ff1fed1ecc56b192c",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2023-08-15T21:06:04Z",
    "title_canon_sha256": "030bcdb88da55609289134c162962a51f4127d1a7f594cfcab195db8365c8fbb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2308.08041",
    "kind": "arxiv",
    "version": 1
  }
}