Pith Number

pith:ULULMKRJ

pith:2011:ULULMKRJSGT3KVASQDZDF6B7YQ

not attested not anchored not stored refs pending

On the growth of Betti numbers of locally symmetric spaces

Ian Biringer, Iddo Samet, Jean Raimbault, Miklos Abert, Nicolas Bergeron, Nikolay Nikolov, Tsachik Gelander

arxiv:1104.5559 v1 · 2011-04-29 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ULULMKRJSGT3KVASQDZDF6B7YQ}

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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	2026-05-18T04:23:20.775994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2e8b62a2991a7b5541280f232f83fc427c35ebd4a88c97fcd6fdf8f513664e0

Aliases

arxiv: 1104.5559 · arxiv_version: 1104.5559v1 · doi: 10.48550/arxiv.1104.5559 · pith_short_12: ULULMKRJSGT3 · pith_short_16: ULULMKRJSGT3KVAS · pith_short_8: ULULMKRJ

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/ULULMKRJSGT3KVASQDZDF6B7YQ \
  | 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: a2e8b62a2991a7b5541280f232f83fc427c35ebd4a88c97fcd6fdf8f513664e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9235df15ba541caa7bcf6850502e0551c81a94271cb428dbb314a016f5a0676f",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-04-29T07:08:44Z",
    "title_canon_sha256": "fb33f7bb517179db0dcee94ef6a2f64e2b64fc3d3b907ee66b8ca7eae4b8bc2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.5559",
    "kind": "arxiv",
    "version": 1
  }
}