Pith Number

pith:2PUCNZE5

pith:2012:2PUCNZE56L7STY4GJTO4ZILF7Z

not attested not anchored not stored refs pending

Jointly maximal products in weighted growth spaces

Janne Gr\"ohn, Jos\'e \'Angel Pel\'aez, Jouni R\"atty\"a

arxiv:1210.3318 v2 · 2012-10-11 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2PUCNZE56L7STY4GJTO4ZILF7Z}

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	2026-05-18T03:37:18.750566Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3e826e49df2ff29e3864cddcca165fe7619594d22691be37eadef058d620100

Aliases

arxiv: 1210.3318 · arxiv_version: 1210.3318v2 · doi: 10.48550/arxiv.1210.3318 · pith_short_12: 2PUCNZE56L7S · pith_short_16: 2PUCNZE56L7STY4G · pith_short_8: 2PUCNZE5

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/2PUCNZE56L7STY4GJTO4ZILF7Z \
  | 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: d3e826e49df2ff29e3864cddcca165fe7619594d22691be37eadef058d620100

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b873c9f90e1440b6a2421e2876ec530eb23ce65f64f4e8a3b59cbe2b342e366",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2012-10-11T18:48:26Z",
    "title_canon_sha256": "ed236db5a3828951035c10111201302bedac731915220298c5cf11dd45abadd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.3318",
    "kind": "arxiv",
    "version": 2
  }
}