Pith Number

pith:DNIWTQZ4

pith:2006:DNIWTQZ4JB4LJJCBQPH4NSNY3U

not attested not anchored not stored refs pending

On uniform exponential growth for solvable groups

Emmanuel Breuillard

arxiv:math/0602076 v2 · 2006-02-04 · 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{DNIWTQZ4JB4LJJCBQPH4NSNY3U}

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.

Cited by

1 paper in Pith

A uniform Tits alternative for endomorphisms of the projective line

Receipt and verification

First computed	2026-07-04T14:58:29.621368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b5169c33c4878b4a44183cfc6c9b8dd1587a370959326a89eed2836671afb77

Aliases

arxiv: math/0602076 · arxiv_version: math/0602076v2 · doi: 10.48550/arxiv.math/0602076 · pith_short_12: DNIWTQZ4JB4L · pith_short_16: DNIWTQZ4JB4LJJCB · pith_short_8: DNIWTQZ4

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/DNIWTQZ4JB4LJJCBQPH4NSNY3U \
  | 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: 1b5169c33c4878b4a44183cfc6c9b8dd1587a370959326a89eed2836671afb77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed83a7cd714e514a329a3d29642d107bf61e0a20e80388f94f79529779a869d4",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2006-02-04T23:53:05Z",
    "title_canon_sha256": "f288c1aa85b8fa863bd0b6c2f91cd51f35f8754769a8eb3d277b213c3a793797"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0602076",
    "kind": "arxiv",
    "version": 2
  }
}