Pith Number

pith:ZUGXMDH7

pith:2013:ZUGXMDH7UKFK654KK2VDH4ZDEP

not attested not anchored not stored refs pending

$\Phi$-Harmonic Functions on Discrete Groups and First $\ell^\Phi$-Cohomology

Roman Panenko, Yaroslav Kopylov

arxiv:1311.2246 v3 · 2013-11-10 · 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{ZUGXMDH7UKFK654KK2VDH4ZDEP}

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	2026-05-18T01:23:45.534449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd0d760cffa28aaf778a56aa33f32323ca4fb843c16ab71f208ea4069ced37a6

Aliases

arxiv: 1311.2246 · arxiv_version: 1311.2246v3 · doi: 10.48550/arxiv.1311.2246 · pith_short_12: ZUGXMDH7UKFK · pith_short_16: ZUGXMDH7UKFK654K · pith_short_8: ZUGXMDH7

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/ZUGXMDH7UKFK654KK2VDH4ZDEP \
  | 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: cd0d760cffa28aaf778a56aa33f32323ca4fb843c16ab71f208ea4069ced37a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b104d1be4aa487e8035ca5884d6b1d5bba39b8ec021c524c3b7e15dfc51658d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-11-10T07:09:44Z",
    "title_canon_sha256": "66ced60821ce720f42cacf3ea1e43659c324d5b9f963efd514f8bf9e6783bf98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.2246",
    "kind": "arxiv",
    "version": 3
  }
}