Pith Number

pith:GLKIPPSJ

pith:2011:GLKIPPSJOZD2J2FMPYUXNMVHV5

not attested not anchored not stored refs pending

Fixed points for actions of Aut(Fn) on CAT(0) spaces

Olga Varghese

arxiv:1112.5014 v4 · 2011-12-21 · math.GR · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GLKIPPSJOZD2J2FMPYUXNMVHV5}

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	2026-05-18T01:19:42.766594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32d487be497647a4e8ac7e2976b2a7af639c30da49e379cdb12bd503630d7175

Aliases

arxiv: 1112.5014 · arxiv_version: 1112.5014v4 · doi: 10.48550/arxiv.1112.5014 · pith_short_12: GLKIPPSJOZD2 · pith_short_16: GLKIPPSJOZD2J2FM · pith_short_8: GLKIPPSJ

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/GLKIPPSJOZD2J2FMPYUXNMVHV5 \
  | 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: 32d487be497647a4e8ac7e2976b2a7af639c30da49e379cdb12bd503630d7175

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7211ba711b2dc6b883b109f62e61709e358c5d81d702d620cf1a98db1ecda28",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-12-21T13:08:36Z",
    "title_canon_sha256": "d4fc87fd185fe1f6947d27880394f609a865fc500f0861e38dc14ce976c5073d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5014",
    "kind": "arxiv",
    "version": 4
  }
}