Pith Number

pith:ZWLKU4WY

pith:2012:ZWLKU4WYCZVSDATWASUOQ4DWXM

not attested not anchored not stored refs pending

A Systematic Martingale Construction with Applications to Permutation Inequalities

J. Michael Steele, Vladimir Pozdnyakov

arxiv:1210.7503 v1 · 2012-10-28 · 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{ZWLKU4WYCZVSDATWASUOQ4DWXM}

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	2026-05-18T03:42:09.758240Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd96aa72d8166b21827604a8e87076bb3442de0a2a204261270458159d1d3195

Aliases

arxiv: 1210.7503 · arxiv_version: 1210.7503v1 · doi: 10.48550/arxiv.1210.7503 · pith_short_12: ZWLKU4WYCZVS · pith_short_16: ZWLKU4WYCZVSDATW · pith_short_8: ZWLKU4WY

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/ZWLKU4WYCZVSDATWASUOQ4DWXM \
  | 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: cd96aa72d8166b21827604a8e87076bb3442de0a2a204261270458159d1d3195

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f4d10d429e9630735d24dc4ae76eb8d0df07e4c257fd9ec55a2ed7700c604e2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-10-28T20:02:04Z",
    "title_canon_sha256": "369d94ad05cbd831cc38ba1e066e59577277905f129504161f573b671b795672"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.7503",
    "kind": "arxiv",
    "version": 1
  }
}