Pith Number

pith:6FM452K6

pith:2025:6FM452K6HJKAPMA7IMLI5JEGW5

not attested not anchored not stored refs pending

Generalized chip firing and critical groups of arithmetical structures on trees

Alexander Diaz-Lopez, Darren Glass, Joel Louwsma, Kassie Archer

arxiv:2505.05392 v2 · 2025-05-08 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6FM452K6HJKAPMA7IMLI5JEGW5}

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

Arithmetical Structures on Ladder Graphs

Receipt and verification

First computed	2026-07-05T11:31:27.946665Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f159cee95e3a5407b01f43168ea486b7731a0256dafb8e6a62a918325c82e163

Aliases

arxiv: 2505.05392 · arxiv_version: 2505.05392v2 · doi: 10.48550/arxiv.2505.05392 · pith_short_12: 6FM452K6HJKA · pith_short_16: 6FM452K6HJKAPMA7 · pith_short_8: 6FM452K6

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/6FM452K6HJKAPMA7IMLI5JEGW5 \
  | 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: f159cee95e3a5407b01f43168ea486b7731a0256dafb8e6a62a918325c82e163

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "303bb168de4dfe20c9b3a3ba783c815de0c5e7240e16a30abbc8d73222ecf826",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-05-08T16:27:32Z",
    "title_canon_sha256": "259cb34d4b844366cc3d10a92bd1b54c790eb4a051dba27b34d46565badc435c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.05392",
    "kind": "arxiv",
    "version": 2
  }
}