Pith Number

pith:NNF3TR2R

pith:2026:NNF3TR2RDX7K2CHK74CTRGCN5K

not attested not anchored not stored refs pending

Distribution of Sandpile groups of random directed bipartite graphs

Deepesh Singhal

arxiv:2606.10214 v1 · 2026-06-08 · math.CO · 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{NNF3TR2RDX7K2CHK74CTRGCN5K}

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	2026-06-10T01:08:59.891893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b4bb9c7511dfead08eaff0538984deaac4919064b3aa591836bad959f59eee9

Aliases

arxiv: 2606.10214 · arxiv_version: 2606.10214v1 · doi: 10.48550/arxiv.2606.10214 · pith_short_12: NNF3TR2RDX7K · pith_short_16: NNF3TR2RDX7K2CHK · pith_short_8: NNF3TR2R

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/NNF3TR2RDX7K2CHK74CTRGCN5K \
  | 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: 6b4bb9c7511dfead08eaff0538984deaac4919064b3aa591836bad959f59eee9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f61317e78c0d21ef221e563de143896396061add510b7518cfa319554302a76",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-08T22:08:54Z",
    "title_canon_sha256": "5cc9ae519c7256c21358d025933d03a19c5d3b616ce79104fd013c45ba2349a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.10214",
    "kind": "arxiv",
    "version": 1
  }
}