Pith Number

pith:5QXBX475

pith:2013:5QXBX475Q7BXUNBI2WMWDQIOTF

not attested not anchored not stored refs pending

Logarithmic Representability of Integers as k-Sums

Anant P. Godbole, Samuel Gutekunst, Vince Lyzinski, Yan Zhuang

arxiv:1302.1808 v1 · 2013-02-07 · 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{5QXBX475Q7BXUNBI2WMWDQIOTF}

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	2026-05-18T03:34:14.567832Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec2e1bf3fd87c37a3428d59961c10e994acf5f9cc2c394950f6b1ec95cbb02e9

Aliases

arxiv: 1302.1808 · arxiv_version: 1302.1808v1 · doi: 10.48550/arxiv.1302.1808 · pith_short_12: 5QXBX475Q7BX · pith_short_16: 5QXBX475Q7BXUNBI · pith_short_8: 5QXBX475

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/5QXBX475Q7BXUNBI2WMWDQIOTF \
  | 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: ec2e1bf3fd87c37a3428d59961c10e994acf5f9cc2c394950f6b1ec95cbb02e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de3bf4c0b28e340b911e425afbfd8b6b8ac80adbdc9803a71f95c7efa669d699",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-02-07T17:33:30Z",
    "title_canon_sha256": "a2c9ac86bd6f37455734cea4fed98406bada80e6af5729f7362c2368a84f786c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.1808",
    "kind": "arxiv",
    "version": 1
  }
}