Pith Number

pith:4T6YLAD7

pith:2004:4T6YLAD7M25P5F7MAGXOM7UO5W

not attested not anchored not stored refs pending

L_delta groups are almost convex and have a sub-cubic Dehn function

Murray Elder

arxiv:math/0402205 v1 · 2004-02-12 · math.GR · 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{4T6YLAD7M25P5F7MAGXOM7UO5W}

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	2026-05-18T03:55:35.931768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4fd85807f66bafe97ec01aee67e8eed9703108450133eb14af7a96351890fee

Aliases

arxiv: math/0402205 · arxiv_version: math/0402205v1 · doi: 10.48550/arxiv.math/0402205 · pith_short_12: 4T6YLAD7M25P · pith_short_16: 4T6YLAD7M25P5F7M · pith_short_8: 4T6YLAD7

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/4T6YLAD7M25P5F7MAGXOM7UO5W \
  | 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: e4fd85807f66bafe97ec01aee67e8eed9703108450133eb14af7a96351890fee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "548e8d180a7da86640f7547c050717f8d75725001b13dba24b01b038e45229f9",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2004-02-12T16:04:03Z",
    "title_canon_sha256": "8d37a4f021e85dc57375ea67a1c807fa8c09d1591e8d7dbbb18c3ab50da612c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0402205",
    "kind": "arxiv",
    "version": 1
  }
}