Pith Number

pith:MHDA7GNB

pith:2016:MHDA7GNB5ZQGGALFPH5C3OSFI5

not attested not anchored not stored refs pending

Minimal growth harmonic functions on lamplighter groups

Ariel Yadin, Gady Kozma, Hugo Duminil-Copin, Itai Benjamini

arxiv:1607.00753 v1 · 2016-07-04 · math.PR · 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{MHDA7GNB5ZQGGALFPH5C3OSFI5}

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	2026-05-18T01:11:34.340548Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61c60f99a1ee6063016579fa2dba4547748504e1699e33e559789b1e2099cf52

Aliases

arxiv: 1607.00753 · arxiv_version: 1607.00753v1 · doi: 10.48550/arxiv.1607.00753 · pith_short_12: MHDA7GNB5ZQG · pith_short_16: MHDA7GNB5ZQGGALF · pith_short_8: MHDA7GNB

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/MHDA7GNB5ZQGGALFPH5C3OSFI5 \
  | 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: 61c60f99a1ee6063016579fa2dba4547748504e1699e33e559789b1e2099cf52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5efcda2b2e13bd7fec890d61f0f011f9966bf5edafc3cfcc242644cccbc02931",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-07-04T07:16:10Z",
    "title_canon_sha256": "0b2aed8b9092c3ceeb92d3e6bdcc54a8e78c54b7350569cdc5990724a8995fde"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.00753",
    "kind": "arxiv",
    "version": 1
  }
}