Pith Number

pith:AE7RFJLQ

pith:2026:AE7RFJLQIEAMQQ55UBVR5P7PLL

not attested not anchored not stored refs pending

Avalanche homology of digraphs via sandpile dynamics

Henri Riihim\"aki, Jason P. Smith

arxiv:2606.26786 v1 · 2026-06-25 · math.AT · 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{AE7RFJLQIEAMQQ55UBVR5P7PLL}

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	2026-06-26T01:15:59.641221Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

013f12a5704100c843bda06b1ebfef5ac3583fe6cbc3e88a77e8563aa0570cf4

Aliases

arxiv: 2606.26786 · arxiv_version: 2606.26786v1 · doi: 10.48550/arxiv.2606.26786 · pith_short_12: AE7RFJLQIEAM · pith_short_16: AE7RFJLQIEAMQQ55 · pith_short_8: AE7RFJLQ

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/AE7RFJLQIEAMQQ55UBVR5P7PLL \
  | 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: 013f12a5704100c843bda06b1ebfef5ac3583fe6cbc3e88a77e8563aa0570cf4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6748ed19261959bc9d3157f145da7da0ab2cc33ea83e53bd73506b8c023ca1ae",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-06-25T09:21:42Z",
    "title_canon_sha256": "7459e250985c1bc1db4c7f7876dd78631221a8cb8e48e94f2b4af2ef0ead9cff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.26786",
    "kind": "arxiv",
    "version": 1
  }
}