Pith Number

pith:CX6QI2B5

pith:2018:CX6QI2B5UOXCHKAZ7LSSTX5AE2

not attested not anchored not stored refs pending

A refined combination theorem for hierarchically hyperbolic groups

Bruno Robbio, Federico Berlai

arxiv:1810.06476 v2 · 2018-10-15 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CX6QI2B5UOXCHKAZ7LSSTX5AE2}

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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.

Cited by

1 paper in Pith

Hierarchically hyperbolic groups and uniform exponential growth

Receipt and verification

First computed	2026-07-05T00:06:31.415147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15fd04683da3ae23a819fae529dfa02687b464f1c49bc672e1a5e09157a64628

Aliases

arxiv: 1810.06476 · arxiv_version: 1810.06476v2 · doi: 10.48550/arxiv.1810.06476 · pith_short_12: CX6QI2B5UOXC · pith_short_16: CX6QI2B5UOXCHKAZ · pith_short_8: CX6QI2B5

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/CX6QI2B5UOXCHKAZ7LSSTX5AE2 \
  | 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: 15fd04683da3ae23a819fae529dfa02687b464f1c49bc672e1a5e09157a64628

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d01f11c69e079a7b20e47ea28343c2e4d76ddf616505f61c34e487ad7c5d1fad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-10-15T15:47:36Z",
    "title_canon_sha256": "e4f28d93b94e5916bc5a281cb879524a2007e23925a51394d922cc28cb87225c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.06476",
    "kind": "arxiv",
    "version": 2
  }
}