Pith Number

pith:25VQ6CD2

pith:2015:25VQ6CD2FGBYWDWWMSVSV2SGAX

not attested not anchored not stored refs pending

Tree-Shifts: The entropy of tree-shifts of finite type

Chih-Hung Chang, Jung-Chao Ban

arxiv:1509.08325 v3 · 2015-09-28 · 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{25VQ6CD2FGBYWDWWMSVSV2SGAX}

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	2026-05-18T00:49:34.884718Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d76b0f087a29838b0ed664ab2aea4605c72db330f4b5fd9fb63707feedfc8920

Aliases

arxiv: 1509.08325 · arxiv_version: 1509.08325v3 · doi: 10.48550/arxiv.1509.08325 · pith_short_12: 25VQ6CD2FGBY · pith_short_16: 25VQ6CD2FGBYWDWW · pith_short_8: 25VQ6CD2

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/25VQ6CD2FGBYWDWWMSVSV2SGAX \
  | 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: d76b0f087a29838b0ed664ab2aea4605c72db330f4b5fd9fb63707feedfc8920

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc49b0fb4cf09674cfb5b8cec1e3d487ebde881dd35197d92f0529a72deff863",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-09-28T14:11:18Z",
    "title_canon_sha256": "e72fbb9821771c39da07dbbeba6167fd5bb978675829ba89fb2da1e3e19f5fd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08325",
    "kind": "arxiv",
    "version": 3
  }
}