Pith Number

pith:XC6LVEVX

pith:2011:XC6LVEVXH6NWZOXHFMORSLLVHD

not attested not anchored not stored refs pending

Polynomial Growth Harmonic Functions on Finitely Generated Abelian Groups

Bobo Hua, Juergen Jost, Xianqing Li-Jost

arxiv:1112.6284 v3 · 2011-12-29 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XC6LVEVXH6NWZOXHFMORSLLVHD}

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	2026-05-18T03:26:42.932871Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8bcba92b73f9b6cbae72b1d192d7538f9b605967f6c73896cc0fa9d03d23956

Aliases

arxiv: 1112.6284 · arxiv_version: 1112.6284v3 · doi: 10.48550/arxiv.1112.6284 · pith_short_12: XC6LVEVXH6NW · pith_short_16: XC6LVEVXH6NWZOXH · pith_short_8: XC6LVEVX

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/XC6LVEVXH6NWZOXHFMORSLLVHD \
  | 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: b8bcba92b73f9b6cbae72b1d192d7538f9b605967f6c73896cc0fa9d03d23956

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc7af503fda12acc4c03acd83799882e012b569b63101bee5e6e5185b8a33f1f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-12-29T11:46:03Z",
    "title_canon_sha256": "ddb454161e6d845562e11cfa9025377c76c0353b9185b17cc4a98d50fc50e6f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.6284",
    "kind": "arxiv",
    "version": 3
  }
}