Pith Number

pith:VBGX4BQY

pith:2000:VBGX4BQYRA44PK52Q6OZ7ULJXW

not attested not anchored not stored refs pending

Analytic properties of zeta functions and subgroup growth

Fritz Grunewald, Marcus du Sautoy

arxiv:math/0011267 v1 · 2000-11-01 · 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{VBGX4BQYRA44PK52Q6OZ7ULJXW}

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	2026-07-04T14:34:57.309407Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a84d7e06188839c7abba879d9fd169bdb24fef1cb69e7f7b4c64737275a221af

Aliases

arxiv: math/0011267 · arxiv_version: math/0011267v1 · doi: 10.48550/arxiv.math/0011267 · pith_short_12: VBGX4BQYRA44 · pith_short_16: VBGX4BQYRA44PK52 · pith_short_8: VBGX4BQY

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/VBGX4BQYRA44PK52Q6OZ7ULJXW \
  | 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: a84d7e06188839c7abba879d9fd169bdb24fef1cb69e7f7b4c64737275a221af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ee884be5fd4a9f766adb539bb01aabf6bfe546229cb6155070cc1e49134c87b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2000-11-01T00:00:00Z",
    "title_canon_sha256": "4a81b8d69038c11bee1563a49d4c1759c418c3cf2f70c7a3d60deddca99ef5e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0011267",
    "kind": "arxiv",
    "version": 1
  }
}