Pith Number

pith:X5D6EELE

pith:2011:X5D6EELE3GLR5R4JJZWIDJ4EAF

not attested not anchored not stored refs pending

On malnormal peripheral subgroups in fundamental groups of 3-manifolds

Claude Weber, Pierre de la Harpe

arxiv:1104.3062 v1 · 2011-04-15 · 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{X5D6EELE3GLR5R4JJZWIDJ4EAF}

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	2026-05-18T04:24:06.643975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf47e21164d9971ec7894e6c81a784014e42f8dcc0e5ac875772764523d11220

Aliases

arxiv: 1104.3062 · arxiv_version: 1104.3062v1 · doi: 10.48550/arxiv.1104.3062 · pith_short_12: X5D6EELE3GLR · pith_short_16: X5D6EELE3GLR5R4J · pith_short_8: X5D6EELE

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/X5D6EELE3GLR5R4JJZWIDJ4EAF \
  | 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: bf47e21164d9971ec7894e6c81a784014e42f8dcc0e5ac875772764523d11220

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30dc6da2293f6530f6c0cce175ba8e8ba8bfeacc30e736847bfc75f13066011c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-04-15T14:06:10Z",
    "title_canon_sha256": "bec153c1b5c8f5e529ae38e865418485402d4b6ffd53f13d1d1b24bccd5896b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.3062",
    "kind": "arxiv",
    "version": 1
  }
}