Pith Number

pith:COBM3MBL

pith:2010:COBM3MBLEJTG3UJ7FQ3CXA52ZS

not attested not anchored not stored refs pending

All finitely presentable groups from link complements and Kleinian groups

Iain R. Aitchison

arxiv:1008.1311 v1 · 2010-08-07 · math.GT · 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{COBM3MBLEJTG3UJ7FQ3CXA52ZS}

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	2026-05-18T04:42:33.352418Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1382cdb02b22666dd13f2c362b83bacca5bfeb48ff8085e0ba07d943f3c68334

Aliases

arxiv: 1008.1311 · arxiv_version: 1008.1311v1 · doi: 10.48550/arxiv.1008.1311 · pith_short_12: COBM3MBLEJTG · pith_short_16: COBM3MBLEJTG3UJ7 · pith_short_8: COBM3MBL

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/COBM3MBLEJTG3UJ7FQ3CXA52ZS \
  | 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: 1382cdb02b22666dd13f2c362b83bacca5bfeb48ff8085e0ba07d943f3c68334

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "266dfae1ca16bead4a5d3766b297e8544f96d99532ad8b74cb031433441d47a6",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-08-07T07:26:21Z",
    "title_canon_sha256": "4b09c4d8549489ef1e3304b0c10453f25483183d0a1121d41a43a81ebfa82e4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.1311",
    "kind": "arxiv",
    "version": 1
  }
}