Pith Number

pith:7MUQG5HV

pith:2026:7MUQG5HVM3B3MGFPVSFUSFIIG4

not attested not anchored not stored refs pending

Sandpile groups of random bipartite graphs and families of distributions with the same moments

Deepesh Singhal, Jason Fulman, Nathan Kaplan, S. Ole Warnaar

arxiv:2607.08607 v1 · 2026-07-09 · math.CO · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7MUQG5HVM3B3MGFPVSFUSFIIG4}

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	2026-07-10T01:19:55.245940Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb290374f566c3b618afac8b4915083723f1a7bf5359c88bcf13d99244a7213e

Aliases

arxiv: 2607.08607 · arxiv_version: 2607.08607v1 · doi: 10.48550/arxiv.2607.08607 · pith_short_12: 7MUQG5HVM3B3 · pith_short_16: 7MUQG5HVM3B3MGFP · pith_short_8: 7MUQG5HV

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/7MUQG5HVM3B3MGFPVSFUSFIIG4 \
  | 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: fb290374f566c3b618afac8b4915083723f1a7bf5359c88bcf13d99244a7213e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e01237ec61de8bbc1f70a647caf47c72a46ddf209697e7a592bb4bf3793fb7c",
    "cross_cats_sorted": [
      "math.NT",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-09T15:36:05Z",
    "title_canon_sha256": "97e18143fa929ad37acf5f20e30b84b6d9cf4729792b1f25e0245d7307e354e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08607",
    "kind": "arxiv",
    "version": 1
  }
}