Pith Number

pith:VYYVPXH2

pith:2018:VYYVPXH2B67MPSU6XUD4NXQQ5Q

not attested not anchored not stored refs pending

On the joint spectral radius for isometries of non-positively curved spaces and uniform growth

Emmanuel Breuillard, Koji Fujiwara

arxiv:1804.00748 v1 · 2018-04-02 · 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{VYYVPXH2B67MPSU6XUD4NXQQ5Q}

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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	2026-05-18T00:19:32.293345Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae3157dcfa0fbec7ca9ebd07c6de10ec398a4618c99a048cb9007fb0798693a6

Aliases

arxiv: 1804.00748 · arxiv_version: 1804.00748v1 · doi: 10.48550/arxiv.1804.00748 · pith_short_12: VYYVPXH2B67M · pith_short_16: VYYVPXH2B67MPSU6 · pith_short_8: VYYVPXH2

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/VYYVPXH2B67MPSU6XUD4NXQQ5Q \
  | 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: ae3157dcfa0fbec7ca9ebd07c6de10ec398a4618c99a048cb9007fb0798693a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62f9ab30898cefefa94408ac7d2fca50d7a8d35f14ad5478b4bcd0909283e7cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-04-02T22:09:51Z",
    "title_canon_sha256": "dbc94b0e25d755a843c641723b677e90428d789564d4f17c5e837c1ca1177968"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.00748",
    "kind": "arxiv",
    "version": 1
  }
}