Pith Number

pith:X3AOIKM4

pith:2016:X3AOIKM4OPTLYLLVPV4L67CCN5

not attested not anchored not stored refs pending

Complexity volumes of splittable groups

Mihalis Sykiotis

arxiv:1604.02725 v2 · 2016-04-10 · 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{X3AOIKM4OPTLYLLVPV4L67CCN5}

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	2026-05-18T00:22:53.074500Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bec0e4299c73e6bc2d757d78bf7c426f7271f01d4b6d6f6030f843d18babc699

Aliases

arxiv: 1604.02725 · arxiv_version: 1604.02725v2 · doi: 10.48550/arxiv.1604.02725 · pith_short_12: X3AOIKM4OPTL · pith_short_16: X3AOIKM4OPTLYLLV · pith_short_8: X3AOIKM4

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/X3AOIKM4OPTLYLLVPV4L67CCN5 \
  | 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: bec0e4299c73e6bc2d757d78bf7c426f7271f01d4b6d6f6030f843d18babc699

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf182f0eaafe38fd70fe76ee5e40bf2b1a9752ce6fe684cf1b15dbec9e818dc1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-04-10T19:40:09Z",
    "title_canon_sha256": "483dd10717c7c80fb0f62213053b38d8c0b8a629b05668c7a3e039341c7ee6ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.02725",
    "kind": "arxiv",
    "version": 2
  }
}