Pith Number

pith:H5J7VBHR

pith:2003:H5J7VBHRRTM4LFA76OKYGUZ522

not attested not anchored not stored refs pending

Non-hopfian relatively free groups

A.M. Storozhev, S.V. Ivanov

arxiv:math/0312491 v1 · 2003-12-29 · 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{H5J7VBHRRTM4LFA76OKYGUZ522}

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	2026-07-04T14:38:07.660495Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f53fa84f18cd9c5941ff39583533dd6b348278180203182b33bd30018f2ca1d

Aliases

arxiv: math/0312491 · arxiv_version: math/0312491v1 · doi: 10.48550/arxiv.math/0312491 · pith_short_12: H5J7VBHRRTM4 · pith_short_16: H5J7VBHRRTM4LFA7 · pith_short_8: H5J7VBHR

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/H5J7VBHRRTM4LFA76OKYGUZ522 \
  | 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: 3f53fa84f18cd9c5941ff39583533dd6b348278180203182b33bd30018f2ca1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4b0fc423b1cede418b48a3cc25bab2ae6da5245b6a8ecca47dfdf550c12cd36",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2003-12-29T21:05:23Z",
    "title_canon_sha256": "a082de665f7c76d6e240c8afdcc8cc54e3ff6e69e2838c54817713a1d9f79dfd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0312491",
    "kind": "arxiv",
    "version": 1
  }
}