Pith Number

pith:QCKGCCGH

pith:2017:QCKGCCGHUTUEDQ5QDNF3FQVRR6

not attested not anchored not stored refs pending

Average Length of Cycles in Rectangular Lattice

Ryuhei Mori

arxiv:1706.05184 v1 · 2017-06-16 · cond-mat.stat-mech · 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{QCKGCCGHUTUEDQ5QDNF3FQVRR6}

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	2026-05-18T00:42:14.515030Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80946108c7a4e841c3b01b4bb2c2b18f92381c5684febb153e18544fbfcd84a7

Aliases

arxiv: 1706.05184 · arxiv_version: 1706.05184v1 · doi: 10.48550/arxiv.1706.05184 · pith_short_12: QCKGCCGHUTUE · pith_short_16: QCKGCCGHUTUEDQ5Q · pith_short_8: QCKGCCGH

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/QCKGCCGHUTUEDQ5QDNF3FQVRR6 \
  | 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: 80946108c7a4e841c3b01b4bb2c2b18f92381c5684febb153e18544fbfcd84a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f1e8c163f57de4dac0d741565b6833aea9b3d0fa60e3fe7522446b3a0aa8ff8",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2017-06-16T08:51:38Z",
    "title_canon_sha256": "c33c82ea408c6a3462fbacbb1c02581dafb62694a48bc24d2188c8f678cbdc64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.05184",
    "kind": "arxiv",
    "version": 1
  }
}