Pith Number

pith:DWX3MOMQ

pith:2016:DWX3MOMQVL7EI6V5GOJX2FXSH4

not attested not anchored not stored refs pending

Infinitely supported Liouville measures of Schreier graphs

Kate Juschenko, Tianyi Zheng

arxiv:1608.03554 v1 · 2016-08-11 · math.GR · 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{DWX3MOMQVL7EI6V5GOJX2FXSH4}

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	2026-05-18T01:09:28.742579Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1dafb63990aafe447abd33937d16f23f15583e5b627a41abb5efd3a62f875a36

Aliases

arxiv: 1608.03554 · arxiv_version: 1608.03554v1 · doi: 10.48550/arxiv.1608.03554 · pith_short_12: DWX3MOMQVL7E · pith_short_16: DWX3MOMQVL7EI6V5 · pith_short_8: DWX3MOMQ

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/DWX3MOMQVL7EI6V5GOJX2FXSH4 \
  | 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: 1dafb63990aafe447abd33937d16f23f15583e5b627a41abb5efd3a62f875a36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0c239d8fa736ead217aee729913652fd2e53a30baa56c52337f80e60f6eb0c9",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-08-11T17:59:01Z",
    "title_canon_sha256": "f57b7d647b5949f9d6ba8b666fd650b279e13e7d19a4be97cb5218309430e81a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.03554",
    "kind": "arxiv",
    "version": 1
  }
}