Pith Number

pith:MK6O3OGP

pith:2016:MK6O3OGPIJUKS63K5AMXJZ4FUG

not attested not anchored not stored refs pending

Stallings folds for CAT(0) cube complexes and quasiconvex subgroups

Benjamin Beeker, Nir Lazarovich

arxiv:1605.02758 v2 · 2016-05-09 · 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{MK6O3OGPIJUKS63K5AMXJZ4FUG}

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	2026-05-18T00:36:19.649472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62bcedb8cf4268a97b6ae81974e785a19c87a68c4d1a5aa647a281e1f22ac4a2

Aliases

arxiv: 1605.02758 · arxiv_version: 1605.02758v2 · doi: 10.48550/arxiv.1605.02758 · pith_short_12: MK6O3OGPIJUK · pith_short_16: MK6O3OGPIJUKS63K · pith_short_8: MK6O3OGP

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/MK6O3OGPIJUKS63K5AMXJZ4FUG \
  | 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: 62bcedb8cf4268a97b6ae81974e785a19c87a68c4d1a5aa647a281e1f22ac4a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64ff9a718db72dfa43e8dea3fee10755a1a48e39c084f2bf77e3d9edcea0404e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-05-09T20:18:20Z",
    "title_canon_sha256": "895fc3dde34f698b62ae76afb2325ef182737d4af5d163f3ba15b7b535687a5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.02758",
    "kind": "arxiv",
    "version": 2
  }
}