Pith Number

pith:S76ZDM4K

pith:2010:S76ZDM4KNFXDS64KG4SDWY3FVQ

not attested not anchored not stored refs pending

Pattern closure of groups of tree automorphisms

Zoran Sunic

arxiv:1012.1688 v2 · 2010-12-08 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S76ZDM4KNFXDS64KG4SDWY3FVQ}

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	2026-05-18T04:33:49.475917Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97fd91b38a696e397b8a37243b6365ac271866c031d9901cd636cff80ada641c

Aliases

arxiv: 1012.1688 · arxiv_version: 1012.1688v2 · doi: 10.48550/arxiv.1012.1688 · pith_short_12: S76ZDM4KNFXD · pith_short_16: S76ZDM4KNFXDS64K · pith_short_8: S76ZDM4K

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/S76ZDM4KNFXDS64KG4SDWY3FVQ \
  | 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: 97fd91b38a696e397b8a37243b6365ac271866c031d9901cd636cff80ada641c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55758aa2988648a0adfe2478ff55355a685b5aa5e446aebbed2c8b5b4f6c7be6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-12-08T05:47:24Z",
    "title_canon_sha256": "b4c796ddfa99e4aa2c2eca0ec0b06a07388040ecdaef2be02b6a56307b097fba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1688",
    "kind": "arxiv",
    "version": 2
  }
}