Pith Number

pith:YTBXVPHB

pith:2016:YTBXVPHBS6X6FTCTIQRDVATHU6

not attested not anchored not stored refs pending

Efficient Finite Groups Arising in the Study of Relative Asphericity

Gerald Williams, William A. Bogley

arxiv:1607.01951 v1 · 2016-07-07 · 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{YTBXVPHBS6X6FTCTIQRDVATHU6}

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	2026-05-18T01:11:22.944828Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4c37abce197afe2cc5344223a8267a7b946f6be4a5014af02a5848b55bf712f

Aliases

arxiv: 1607.01951 · arxiv_version: 1607.01951v1 · doi: 10.48550/arxiv.1607.01951 · pith_short_12: YTBXVPHBS6X6 · pith_short_16: YTBXVPHBS6X6FTCT · pith_short_8: YTBXVPHB

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/YTBXVPHBS6X6FTCTIQRDVATHU6 \
  | 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: c4c37abce197afe2cc5344223a8267a7b946f6be4a5014af02a5848b55bf712f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea09b81fb457231049f69045ff4952fe817d1d4a5b21042608864869c5b0aa75",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-07-07T10:30:10Z",
    "title_canon_sha256": "5cb2c86f5f892d90b854ef62a8644083a82eef519b927e42425c4aa2d4f195c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.01951",
    "kind": "arxiv",
    "version": 1
  }
}