Pith Number

pith:SOSPONMQ

pith:2017:SOSPONMQ4KZZKS2LIJRDYAJDXJ

not attested not anchored not stored refs pending

A graph-theoretic proof for Whitehead's second free-group algorithm

Warren Dicks

arxiv:1706.09679 v1 · 2017-06-29 · 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{SOSPONMQ4KZZKS2LIJRDYAJDXJ}

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	2026-05-18T00:41:14.187214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93a4f73590e2b3954b4b42623c0123ba422e1aa816e97ab681b469fc3c0b2b73

Aliases

arxiv: 1706.09679 · arxiv_version: 1706.09679v1 · doi: 10.48550/arxiv.1706.09679 · pith_short_12: SOSPONMQ4KZZ · pith_short_16: SOSPONMQ4KZZKS2L · pith_short_8: SOSPONMQ

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/SOSPONMQ4KZZKS2LIJRDYAJDXJ \
  | 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: 93a4f73590e2b3954b4b42623c0123ba422e1aa816e97ab681b469fc3c0b2b73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1c671671479aaa88f64477bbe8817065fcb48b0ad1d3e658d4e2454d4d4cc13",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-06-29T11:20:28Z",
    "title_canon_sha256": "0c8da333feabdb18145949f4214e87b43673376be227526e9dc1794b0488b289"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.09679",
    "kind": "arxiv",
    "version": 1
  }
}