Pith Number

pith:KZXQMBQG

pith:2009:KZXQMBQGYPVNN5TJR4PWZVGWH4

not attested not anchored not stored refs pending

Asymptotic growth and least common multiples in groups

D. B. McReynolds, K. Bou-Rabee

arxiv:0907.3681 v2 · 2009-07-21 · 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{KZXQMBQGYPVNN5TJR4PWZVGWH4}

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	2026-05-18T00:00:41.744545Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

566f060606c3ead6f6698f1f6cd4d63f34a88b13b3876c652eff08eca37ceaf0

Aliases

arxiv: 0907.3681 · arxiv_version: 0907.3681v2 · doi: 10.48550/arxiv.0907.3681 · pith_short_12: KZXQMBQGYPVN · pith_short_16: KZXQMBQGYPVNN5TJ · pith_short_8: KZXQMBQG

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/KZXQMBQGYPVNN5TJR4PWZVGWH4 \
  | 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: 566f060606c3ead6f6698f1f6cd4d63f34a88b13b3876c652eff08eca37ceaf0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "046202d76fa8b15f6ac0198b77c6432d8406ac7e323a2099a727bd9470bbc1ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-07-21T15:27:39Z",
    "title_canon_sha256": "93e58e81dc2ceec88bfe525884f56a87053e9dbc8c4cee01b5de9470d9a04279"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.3681",
    "kind": "arxiv",
    "version": 2
  }
}