Pith Number

pith:LZCHRCYM

pith:2017:LZCHRCYMDMEK5ZT3KFFSFEKPGK

not attested not anchored not stored refs pending

Sandpile Groups of Random Bipartite Graphs

Shaked Koplewitz

arxiv:1705.07519 v1 · 2017-05-21 · 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{LZCHRCYMDMEK5ZT3KFFSFEKPGK}

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

Chip-Firing Games and Critical Groups

Receipt and verification

First computed	2026-05-18T00:44:05.318823Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e44788b0c1b08aee67b514b22914f32a654ac90b4d48e3a7c56bfe28b7c2b9a

Aliases

arxiv: 1705.07519 · arxiv_version: 1705.07519v1 · doi: 10.48550/arxiv.1705.07519 · pith_short_12: LZCHRCYMDMEK · pith_short_16: LZCHRCYMDMEK5ZT3 · pith_short_8: LZCHRCYM

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/LZCHRCYMDMEK5ZT3KFFSFEKPGK \
  | 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: 5e44788b0c1b08aee67b514b22914f32a654ac90b4d48e3a7c56bfe28b7c2b9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62c23d2420a6a56c4903fe4ca70157882c818f865806e0bf32bbe185d3a0e4f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-05-21T22:45:52Z",
    "title_canon_sha256": "c81b04b34f848428d50aef02a5052ec87fda49f20375efb175280fb9d4e9d7a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.07519",
    "kind": "arxiv",
    "version": 1
  }
}