Pith Number

pith:URLYE4DV

pith:2014:URLYE4DVIY6FOXJVWXWG6XWCMH

not attested not anchored not stored refs pending

Characterisations of algebraic properties of groups in terms of harmonic functions

Matthew Tointon

arxiv:1409.6326 v5 · 2014-09-22 · math.GR · math.CO · math.MG · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{URLYE4DVIY6FOXJVWXWG6XWCMH}

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	2026-05-18T01:04:09.621263Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a457827075463c575d35b5ec6f5ec261dd2bc6004a96cdbc7ddf78adf67f2833

Aliases

arxiv: 1409.6326 · arxiv_version: 1409.6326v5 · doi: 10.48550/arxiv.1409.6326 · pith_short_12: URLYE4DVIY6F · pith_short_16: URLYE4DVIY6FOXJV · pith_short_8: URLYE4DV

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/URLYE4DVIY6FOXJVWXWG6XWCMH \
  | 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: a457827075463c575d35b5ec6f5ec261dd2bc6004a96cdbc7ddf78adf67f2833

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c9f411bc1a6ee95b8554cdaacabb97012ba15bc9c1663d782aa83434d448ca0",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-09-22T20:02:36Z",
    "title_canon_sha256": "8fa0f31c4ee12d4fe57612e779c62befd01467f528840414d8fd07e30de1e26b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.6326",
    "kind": "arxiv",
    "version": 5
  }
}