Pith Number

pith:DO5WUDAL

pith:2025:DO5WUDALQ6ZDR4CZP6ANFZVNYM

not attested not anchored not stored refs pending

Criticality of the abelian sandpile in dimension 1

Adrien Rezzouk

arxiv:2509.03697 v1 · 2025-09-03 · 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{DO5WUDALQ6ZDR4CZP6ANFZVNYM}

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	2026-07-05T12:04:44.491967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1bbb6a0c0b87b238f0597f80d2e6adc333e6eef4cb88f75e9a84c38eafcf2cfd

Aliases

arxiv: 2509.03697 · arxiv_version: 2509.03697v1 · doi: 10.48550/arxiv.2509.03697 · pith_short_12: DO5WUDALQ6ZD · pith_short_16: DO5WUDALQ6ZDR4CZ · pith_short_8: DO5WUDAL

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/DO5WUDALQ6ZDR4CZP6ANFZVNYM \
  | 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: 1bbb6a0c0b87b238f0597f80d2e6adc333e6eef4cb88f75e9a84c38eafcf2cfd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "011b9f18ab99fe460bf0f3695ff1b212bd2d32a426ae975a9819e7dca8a045f1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-09-03T20:28:07Z",
    "title_canon_sha256": "c0e44862c6273b348c6c2b80de83a807a7b68f512fc0a8aa223a325c72907818"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.03697",
    "kind": "arxiv",
    "version": 1
  }
}