Pith Number

pith:4OPM7UNG

pith:2011:4OPM7UNGOSBUZH6LPXV4EWEESZ

not attested not anchored not stored refs pending

Growth behaviors in the range $e^{r^\alpha}$

J\'er\'emie Brieussel

arxiv:1107.1632 v2 · 2011-07-08 · 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{4OPM7UNGOSBUZH6LPXV4EWEESZ}

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	2026-05-18T03:14:07.102994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e39ecfd1a674834c9fcb7debc25884964573e27f3fab3a6a42d8079907b3475a

Aliases

arxiv: 1107.1632 · arxiv_version: 1107.1632v2 · doi: 10.48550/arxiv.1107.1632 · pith_short_12: 4OPM7UNGOSBU · pith_short_16: 4OPM7UNGOSBUZH6L · pith_short_8: 4OPM7UNG

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/4OPM7UNGOSBUZH6LPXV4EWEESZ \
  | 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: e39ecfd1a674834c9fcb7debc25884964573e27f3fab3a6a42d8079907b3475a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "836c0342c350cd86966ac80550666fb5601be5ba23750315513b7dff1eeb19e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-07-08T13:47:03Z",
    "title_canon_sha256": "cf5e8f2ad22a9864e01a6d5bb22b18df05b3aac274e9f8838374e0e01a3b1939"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.1632",
    "kind": "arxiv",
    "version": 2
  }
}