Pith Number

pith:ZIIKQLAX

pith:2016:ZIIKQLAXIT7CPPINSXIWTJFYZT

not attested not anchored not stored refs pending

Amenability and paradoxical decompositions for pseudogroups and for discrete metric spaces

Pierre de la Harpe, Rostislav I. Grigorchuk, Tullio Ceccherini-Silberstein

arxiv:1603.04212 v1 · 2016-03-14 · math.GR · math.DS · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZIIKQLAXIT7CPPINSXIWTJFYZT}

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	2026-05-18T01:19:09.082492Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca10a82c1744fe27bd0d95d169a4b8ccdb5868c11bdbe9d17486fc603677c670

Aliases

arxiv: 1603.04212 · arxiv_version: 1603.04212v1 · doi: 10.48550/arxiv.1603.04212 · pith_short_12: ZIIKQLAXIT7C · pith_short_16: ZIIKQLAXIT7CPPIN · pith_short_8: ZIIKQLAX

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/ZIIKQLAXIT7CPPINSXIWTJFYZT \
  | 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: ca10a82c1744fe27bd0d95d169a4b8ccdb5868c11bdbe9d17486fc603677c670

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9941af2900e49f306414d9b280fbb1d87b09fdab3faca432c5811d53201cc48e",
    "cross_cats_sorted": [
      "math.DS",
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-03-14T11:26:13Z",
    "title_canon_sha256": "ddbf58c062fd710550fa013851c13b2564454c2c6285ec42574fb6c7f362e3e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.04212",
    "kind": "arxiv",
    "version": 1
  }
}