Pith Number

pith:WTQC52EF

pith:2013:WTQC52EF2HQQDTJZAB4PPZFBYN

not attested not anchored not stored refs pending

Trait substitution trees on two time scales analysis

Anton Bovier, Shi-dong Wang

arxiv:1304.4640 v1 · 2013-04-16 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WTQC52EF2HQQDTJZAB4PPZFBYN}

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	2026-05-18T03:27:44.093779Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4e02ee885d1e101cd390078f7e4a1c374ffbeeaddcbd5b52646712fbcd1a229

Aliases

arxiv: 1304.4640 · arxiv_version: 1304.4640v1 · doi: 10.48550/arxiv.1304.4640 · pith_short_12: WTQC52EF2HQQ · pith_short_16: WTQC52EF2HQQDTJZ · pith_short_8: WTQC52EF

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/WTQC52EF2HQQDTJZAB4PPZFBYN \
  | 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: b4e02ee885d1e101cd390078f7e4a1c374ffbeeaddcbd5b52646712fbcd1a229

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23378ea95ff1433af8f2345c897d76c70378fc4c43108d3f1bb3929f36753eca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-04-16T22:48:19Z",
    "title_canon_sha256": "2f3a24fdc396e24ecc6cfaba12037f89377e158365234918698f1067de00d154"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.4640",
    "kind": "arxiv",
    "version": 1
  }
}