Pith Number

pith:QHHAOYBZ

pith:2011:QHHAOYBZUTS2ECJZWKARUT2ATP

not attested not anchored not stored refs pending

A characterization of the locally finite networks admitting non-constant harmonic functions of finite energy

Johannes Carmesin

arxiv:1105.2049 v1 · 2011-05-10 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QHHAOYBZUTS2ECJZWKARUT2ATP}

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	2026-05-18T04:22:21.589842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81ce076039a4e5a20939b2811a4f409bcd236193f3fa409972781ce8dc1b1f3d

Aliases

arxiv: 1105.2049 · arxiv_version: 1105.2049v1 · doi: 10.48550/arxiv.1105.2049 · pith_short_12: QHHAOYBZUTS2 · pith_short_16: QHHAOYBZUTS2ECJZ · pith_short_8: QHHAOYBZ

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/QHHAOYBZUTS2ECJZWKARUT2ATP \
  | 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: 81ce076039a4e5a20939b2811a4f409bcd236193f3fa409972781ce8dc1b1f3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b5d8e76a9e34aedcb72b0efa4755d0dfaeb40e2d8bede356171fadedeaf231c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-05-10T20:25:16Z",
    "title_canon_sha256": "1308b030e1e579ea1acb2aa69ab36b36e6b8927ba98ceb5b39cd308d65e72f40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2049",
    "kind": "arxiv",
    "version": 1
  }
}