Pith Number

pith:GCAAZJ2K

pith:2013:GCAAZJ2KCMHCNFYYVQQHW2TU27

not attested not anchored not stored refs pending

Limit sets for modules over groups on CAT(0) spaces -- from the Euclidean to the hyperbolic

Robert Bieri, Ross Geoghegan

arxiv:1306.3403 v4 · 2013-06-14 · 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{GCAAZJ2KCMHCNFYYVQQHW2TU27}

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	2026-05-18T01:00:54.292215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30800ca74a130e269718ac207b6a74d7c43864dbeb7457843cd53a30b6cbc9c6

Aliases

arxiv: 1306.3403 · arxiv_version: 1306.3403v4 · doi: 10.48550/arxiv.1306.3403 · pith_short_12: GCAAZJ2KCMHC · pith_short_16: GCAAZJ2KCMHCNFYY · pith_short_8: GCAAZJ2K

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/GCAAZJ2KCMHCNFYYVQQHW2TU27 \
  | 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: 30800ca74a130e269718ac207b6a74d7c43864dbeb7457843cd53a30b6cbc9c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3f86d00f9b005d96d76879d2d35da3cf3a67e65f3e54d8cc3d3843352bdb883",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-06-14T14:11:01Z",
    "title_canon_sha256": "d9af5a20911f0c2da5d628efcce93b3d1f366cc51e8d362d0625e3fd999d8dde"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3403",
    "kind": "arxiv",
    "version": 4
  }
}