Pith Number

pith:HGLY3RIF

pith:2011:HGLY3RIFED4VTDQ2WEHAY72J3N

not attested not anchored not stored refs pending

$Z^n$-free groups are CAT(0)

Inna Bumagin, Olga Kharlampovich

arxiv:1103.2784 v2 · 2011-03-14 · 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{HGLY3RIFED4VTDQ2WEHAY72J3N}

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	2026-05-18T02:58:01.125576Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39978dc50520f9598e1ab10e0c7f49db73771305dd184c35cd89b8535c5ec08e

Aliases

arxiv: 1103.2784 · arxiv_version: 1103.2784v2 · doi: 10.48550/arxiv.1103.2784 · pith_short_12: HGLY3RIFED4V · pith_short_16: HGLY3RIFED4VTDQ2 · pith_short_8: HGLY3RIF

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/HGLY3RIFED4VTDQ2WEHAY72J3N \
  | 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: 39978dc50520f9598e1ab10e0c7f49db73771305dd184c35cd89b8535c5ec08e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f98a86874a6e2ce65864203c2119a26dad81900a94f39e4a8559f4fb51aa5d91",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-03-14T20:50:16Z",
    "title_canon_sha256": "0071b52cda8eec394719e52183c54896ebc8e9b792e619bcb0a1f5abeb639d29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2784",
    "kind": "arxiv",
    "version": 2
  }
}