Pith Number

pith:4BOLW5HM

pith:2017:4BOLW5HM5UUPM2Z6IJLUGQH2AT

not attested not anchored not stored refs pending

The Sandpile Group of a Thick Cycle Graph

Ashley K. Wheeler, Diane Christine Alar, Jonathan Celaya, Luis David Garc\'ia Puente, Micah Henson

arxiv:1710.06006 v1 · 2017-10-16 · 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{4BOLW5HM5UUPM2Z6IJLUGQH2AT}

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.

Cited by

1 paper in Pith

The sandpile group of a polygon flower

Receipt and verification

First computed	2026-05-18T00:32:38.054863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e05cbb74eced28f66b3e42574340fa04f282ac962756a624eaecd96062157dd1

Aliases

arxiv: 1710.06006 · arxiv_version: 1710.06006v1 · doi: 10.48550/arxiv.1710.06006 · pith_short_12: 4BOLW5HM5UUP · pith_short_16: 4BOLW5HM5UUPM2Z6 · pith_short_8: 4BOLW5HM

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/4BOLW5HM5UUPM2Z6IJLUGQH2AT \
  | 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: e05cbb74eced28f66b3e42574340fa04f282ac962756a624eaecd96062157dd1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e7bdf5da21a8126f46438ca4656b68e1af58411b6f439799683b05bf242777c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-10-16T22:00:42Z",
    "title_canon_sha256": "e6c7e968895813edb51a6ef838cf0a01f063e2317dbd14f6f8e66d34d2d7dc11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.06006",
    "kind": "arxiv",
    "version": 1
  }
}