Pith Number

pith:GG3I2S7K

pith:2012:GG3I2S7KO6BSMRVCHIRH7AYX4B

not attested not anchored not stored refs pending

Bounded-size rules: The barely subcritical regime

Amarjit Budhiraja, Shankar Bhamidi, Xuan Wang

arxiv:1212.5480 v1 · 2012-12-21 · math.PR · 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{GG3I2S7KO6BSMRVCHIRH7AYX4B}

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	2026-05-17T23:53:18.154011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31b68d4bea77832646a23a227f8317e042488e333a8dae6e7be063068854d0f8

Aliases

arxiv: 1212.5480 · arxiv_version: 1212.5480v1 · doi: 10.48550/arxiv.1212.5480 · pith_short_12: GG3I2S7KO6BS · pith_short_16: GG3I2S7KO6BSMRVC · pith_short_8: GG3I2S7K

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/GG3I2S7KO6BSMRVCHIRH7AYX4B \
  | 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: 31b68d4bea77832646a23a227f8317e042488e333a8dae6e7be063068854d0f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12eecd42d772c70ed52d8d6ab75a35f7f6658ff9b9d112b8162eb1cd29679534",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-12-21T15:12:51Z",
    "title_canon_sha256": "35038a2e4ecc636f0a828d7550e85248227f2543b7c3e0378647e96e327fe9fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5480",
    "kind": "arxiv",
    "version": 1
  }
}