Pith Number

pith:PX572WLA

pith:2018:PX572WLA4AO73CCFLR23C2RXLG

not attested not anchored not stored refs pending

The isoperimetric spectrum of finitely presented groups

Mark Sapir

arxiv:1808.05840 v1 · 2018-08-17 · 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{PX572WLA4AO73CCFLR23C2RXLG}

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	2026-05-18T00:07:51.943412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7dfbfd5960e01dfd88455c75b16a37599a06ff7f81ffc70d2f9d813897113515

Aliases

arxiv: 1808.05840 · arxiv_version: 1808.05840v1 · doi: 10.48550/arxiv.1808.05840 · pith_short_12: PX572WLA4AO7 · pith_short_16: PX572WLA4AO73CCF · pith_short_8: PX572WLA

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/PX572WLA4AO73CCFLR23C2RXLG \
  | 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: 7dfbfd5960e01dfd88455c75b16a37599a06ff7f81ffc70d2f9d813897113515

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ff7fd28a30b8698f2097e5f48645fbdd1cf93c76303b86cde9a11765e269523",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-08-17T12:39:44Z",
    "title_canon_sha256": "5f735c7fbfdde61675554fbfea8d7e191252e14c20f22bf6b3ce16cc8c42b6cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.05840",
    "kind": "arxiv",
    "version": 1
  }
}