Pith Number

pith:NC622SJU

pith:2013:NC622SJUBGMP2LQUV5CICJZ6VQ

not attested not anchored not stored refs pending

On free-group algorithms that sandwich a subgroup between free-product factors

Warren Dicks

arxiv:1306.3880 v1 · 2013-06-17 · 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{NC622SJUBGMP2LQUV5CICJZ6VQ}

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	2026-05-18T02:16:21.489515Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68bdad49340998fd2e14af4481273eac15be1193fed83afc44a25c2ba64b692f

Aliases

arxiv: 1306.3880 · arxiv_version: 1306.3880v1 · doi: 10.48550/arxiv.1306.3880 · pith_short_12: NC622SJUBGMP · pith_short_16: NC622SJUBGMP2LQU · pith_short_8: NC622SJU

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/NC622SJUBGMP2LQUV5CICJZ6VQ \
  | 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: 68bdad49340998fd2e14af4481273eac15be1193fed83afc44a25c2ba64b692f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36490aea390b4ef1d6e3373e997b7b2a596dbf3ff51c36e90dd285b4a50b88c1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-06-17T14:48:16Z",
    "title_canon_sha256": "b6790ce468a51a25f351554fee08fc90ec5f00d1a9a6c254a316aae1b56443f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3880",
    "kind": "arxiv",
    "version": 1
  }
}