Pith Number

pith:3AAMLCDF

pith:2014:3AAMLCDFNBEQ3T3CWAMKNQ2ZOS

not attested not anchored not stored refs pending

Relative expanders

Goulnara Arzhantseva, Romain Tessera

arxiv:1402.1481 v3 · 2014-02-06 · math.GR · math.FA · 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{3AAMLCDFNBEQ3T3CWAMKNQ2ZOS}

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	2026-05-18T01:15:53.528986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d800c5886568490dcf62b018a6c35974ac55ec6e4e9a988033f7e57fa906a26c

Aliases

arxiv: 1402.1481 · arxiv_version: 1402.1481v3 · doi: 10.48550/arxiv.1402.1481 · pith_short_12: 3AAMLCDFNBEQ · pith_short_16: 3AAMLCDFNBEQ3T3C · pith_short_8: 3AAMLCDF

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/3AAMLCDFNBEQ3T3CWAMKNQ2ZOS \
  | 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: d800c5886568490dcf62b018a6c35974ac55ec6e4e9a988033f7e57fa906a26c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ff10678774e39cd902c85de3dea9f666c4fb1874bc94e15fe832f3b55277001",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-02-06T20:46:54Z",
    "title_canon_sha256": "36897fbdfb3f3a2e65921a5d45c807a8e0e5599441470a6e4056dea587569d11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.1481",
    "kind": "arxiv",
    "version": 3
  }
}