Pith Number

pith:7DCDE2D3

pith:2010:7DCDE2D3QFYU2MZ22U535WA47A

not attested not anchored not stored refs pending

A fixed point theorem for L^1 spaces

Nicolas Monod, Tsachik Gelander, Uri Bader

arxiv:1012.1488 v2 · 2010-12-07 · math.FA · math.GR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7DCDE2D3QFYU2MZ22U535WA47A}

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	2026-05-18T03:51:36.062523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8c432687b81714d333ad53bbed81cf80e2610a8980a4e3f7663a900b441285c

Aliases

arxiv: 1012.1488 · arxiv_version: 1012.1488v2 · doi: 10.48550/arxiv.1012.1488 · pith_short_12: 7DCDE2D3QFYU · pith_short_16: 7DCDE2D3QFYU2MZ2 · pith_short_8: 7DCDE2D3

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/7DCDE2D3QFYU2MZ22U535WA47A \
  | 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: f8c432687b81714d333ad53bbed81cf80e2610a8980a4e3f7663a900b441285c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d90635f3b9ad1ed58b5c74b772bfc3221754d3b9133e2c26e9f069114915409f",
    "cross_cats_sorted": [
      "math.GR",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-12-07T12:39:41Z",
    "title_canon_sha256": "8845646da59e09c60a882b5bfa99feb6689e6b7125d60f42ed15521f722c34af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1488",
    "kind": "arxiv",
    "version": 2
  }
}