Pith Number

pith:JIFM6GTK

pith:2012:JIFM6GTKHS55WOUQJELLKLBTYU

not attested not anchored not stored refs pending

On trivial words in finitely presented groups

A. Rechnitzer, E. J. Janse van Rensburg, M. Elder, T. Wong

arxiv:1210.3425 v3 · 2012-10-12 · math.GR · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JIFM6GTKHS55WOUQJELLKLBTYU}

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	2026-05-18T03:04:13.979396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a0acf1a6a3cbbdb3a904916b52c33c512deb06f09666f809c708760d6deb8ab

Aliases

arxiv: 1210.3425 · arxiv_version: 1210.3425v3 · doi: 10.48550/arxiv.1210.3425 · pith_short_12: JIFM6GTKHS55 · pith_short_16: JIFM6GTKHS55WOUQ · pith_short_8: JIFM6GTK

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/JIFM6GTKHS55WOUQJELLKLBTYU \
  | 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: 4a0acf1a6a3cbbdb3a904916b52c33c512deb06f09666f809c708760d6deb8ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "483be8addf2762ccdf0b37ce0a5c1ec88007508f3f9b2f01f936fdfaf8afcb95",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-10-12T04:01:32Z",
    "title_canon_sha256": "1fa60e1f3f969b9999b8e7b1c6798ac7a693994ad1c029d1135d996a0f6c5f3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.3425",
    "kind": "arxiv",
    "version": 3
  }
}