Pith Number

pith:VKVFEZNI

pith:2015:VKVFEZNIZAFZP5S73SOBC7SWSI

not attested not anchored not stored refs pending

From self-similar groups to self-similar sets and spectra

Rostislav Grigorchuk, Volodymyr Nekrashevych, Zoran Sunic

arxiv:1503.06887 v1 · 2015-03-24 · math.GR · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VKVFEZNIZAFZP5S73SOBC7SWSI}

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	2026-05-18T02:20:29.852683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaaa5265a8c80b97f65fdc9c117e569204ea74347cec4b75710bc297c6dce977

Aliases

arxiv: 1503.06887 · arxiv_version: 1503.06887v1 · doi: 10.48550/arxiv.1503.06887 · pith_short_12: VKVFEZNIZAFZ · pith_short_16: VKVFEZNIZAFZP5S7 · pith_short_8: VKVFEZNI

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/VKVFEZNIZAFZP5S73SOBC7SWSI \
  | 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: aaaa5265a8c80b97f65fdc9c117e569204ea74347cec4b75710bc297c6dce977

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa8b18a07ce479b211dbcf41e78145aa7472ec6ba472cfdfb9669e297b584a88",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-03-24T01:30:38Z",
    "title_canon_sha256": "23fa8ee73a9b65462afc2ec8265ce6cf2c77bde579661fa8e94f748cec9cd637"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.06887",
    "kind": "arxiv",
    "version": 1
  }
}