Pith Number

pith:TLV44SE5

pith:2016:TLV44SE5NQ2MLLMQDVEUIJWB2Y

not attested not anchored not stored refs pending

Inequalities for critical exponents in $d$-dimensional sandpiles

Antal A. J\'arai, Jack Hanson, Sandeep Bhupatiraju

arxiv:1602.06475 v2 · 2016-02-20 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TLV44SE5NQ2MLLMQDVEUIJWB2Y}

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	2026-05-18T00:34:10.520836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9aebce489d6c34c5ad901d494426c1d6243d31761e469394e54ca7c66e9a4829

Aliases

arxiv: 1602.06475 · arxiv_version: 1602.06475v2 · doi: 10.48550/arxiv.1602.06475 · pith_short_12: TLV44SE5NQ2M · pith_short_16: TLV44SE5NQ2MLLMQ · pith_short_8: TLV44SE5

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/TLV44SE5NQ2MLLMQDVEUIJWB2Y \
  | 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: 9aebce489d6c34c5ad901d494426c1d6243d31761e469394e54ca7c66e9a4829

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcd75df33f8758f63e222a781171921604f4a1e8ac74873276b56e3349dfbadf",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-02-20T23:44:14Z",
    "title_canon_sha256": "eb41100f1c576c93d75ae906534df50175537213f475d1213c4731296a1d420c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.06475",
    "kind": "arxiv",
    "version": 2
  }
}