Pith Number

pith:WLSBIBV7

pith:2010:WLSBIBV7N34YWZNFEDJWOATQOV

not attested not anchored not stored refs pending

On the Sandpile group of the cone of a graph

Carlos A. Alfaro, Carlos E. Valencia

arxiv:1004.3321 v4 · 2010-04-19 · 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{WLSBIBV7N34YWZNFEDJWOATQOV}

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	2026-05-18T04:01:13.435830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2e41406bf6ef98b65a520d36702707554cdf7792de00f5f4e2cd727949a481d

Aliases

arxiv: 1004.3321 · arxiv_version: 1004.3321v4 · doi: 10.48550/arxiv.1004.3321 · pith_short_12: WLSBIBV7N34Y · pith_short_16: WLSBIBV7N34YWZNF · pith_short_8: WLSBIBV7

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/WLSBIBV7N34YWZNFEDJWOATQOV \
  | 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: b2e41406bf6ef98b65a520d36702707554cdf7792de00f5f4e2cd727949a481d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eebfda1dbcbd8815ec454c408b667cdb3fbc3f0f7304b4adaa2eab238a72200d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-04-19T22:52:25Z",
    "title_canon_sha256": "af435ab37de08259b6adea25161d33d6651588ed43d8395ca9aa2fc76a63d4d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.3321",
    "kind": "arxiv",
    "version": 4
  }
}