Pith Number

pith:42VCRE37

pith:2025:42VCRE37TLEJ2KNUT4W4MSAHLF

not attested not anchored not stored refs pending

On the existence of weakly malnormal quasiconvex subgroups of hyperbolic groups

Pranab Sardar, Rakesh Halder

arxiv:2506.20161 v1 · 2025-06-25 · math.GR · math.GT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{42VCRE37TLEJ2KNUT4W4MSAHLF}

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	2026-07-05T11:27:01.265976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6aa28937f9ac89d29b49f2dc64807595792658c6de3eef2f321f2ed6908be07

Aliases

arxiv: 2506.20161 · arxiv_version: 2506.20161v1 · doi: 10.48550/arxiv.2506.20161 · pith_short_12: 42VCRE37TLEJ · pith_short_16: 42VCRE37TLEJ2KNU · pith_short_8: 42VCRE37

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/42VCRE37TLEJ2KNUT4W4MSAHLF \
  | 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: e6aa28937f9ac89d29b49f2dc64807595792658c6de3eef2f321f2ed6908be07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80b9b90f8c53610b31a02578ce9fadf528411d67c5d7864412740a70cbacbee5",
    "cross_cats_sorted": [
      "math.GT",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-06-25T06:29:57Z",
    "title_canon_sha256": "051bdd5f14b4dc40b00778cfb4e2026fca5a9c01d767ce35fe1242aefe3499b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.20161",
    "kind": "arxiv",
    "version": 1
  }
}