Pith Number

pith:RQ43A5BN

pith:2012:RQ43A5BNBAR5VHUKDJI6E43QGO

not attested not anchored not stored refs pending

An Abramov formula for stationary spaces of discrete groups

Omer Tamuz, Yair Hartman, Yuri Lima

arxiv:1204.5414 v1 · 2012-04-24 · math.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RQ43A5BNBAR5VHUKDJI6E43QGO}

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	2026-05-17T23:53:36.209613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c39b0742d0823da9e8a1a51e273703384421e572a6c167d00b29d80e01d655e

Aliases

arxiv: 1204.5414 · arxiv_version: 1204.5414v1 · doi: 10.48550/arxiv.1204.5414 · pith_short_12: RQ43A5BNBAR5 · pith_short_16: RQ43A5BNBAR5VHUK · pith_short_8: RQ43A5BN

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/RQ43A5BNBAR5VHUKDJI6E43QGO \
  | 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: 8c39b0742d0823da9e8a1a51e273703384421e572a6c167d00b29d80e01d655e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68d7ebff779f93dcad204defc05c94acb2219dde01ed691292c4d30a9205f201",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-04-24T15:39:29Z",
    "title_canon_sha256": "e080fd337ff32ab3fc32e9bbffb5b80840cd760169aa16134545dc9b4b63496b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.5414",
    "kind": "arxiv",
    "version": 1
  }
}