Pith Number

pith:XU5M36MR

pith:2015:XU5M36MRR5QLIIGCMW3UHUPKHF

not attested not anchored not stored refs pending

Invariance principle on the slice

Elchanan Mossel, Guy Kindler, Karl Wimmer, Yuval Filmus

arxiv:1504.01689 v3 · 2015-04-07 · 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{XU5M36MRR5QLIIGCMW3UHUPKHF}

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	2026-05-18T01:20:17.256263Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd3acdf9918f60b420c265b743d1ea3955fd3d60effa65b036566e1207c0fbcf

Aliases

arxiv: 1504.01689 · arxiv_version: 1504.01689v3 · doi: 10.48550/arxiv.1504.01689 · pith_short_12: XU5M36MRR5QL · pith_short_16: XU5M36MRR5QLIIGC · pith_short_8: XU5M36MR

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/XU5M36MRR5QLIIGCMW3UHUPKHF \
  | 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: bd3acdf9918f60b420c265b743d1ea3955fd3d60effa65b036566e1207c0fbcf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bef788573b62ceb59dc37b00d2760beb1a1c88d3ec3f2c0489c39a52ae333b21",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-04-07T18:01:23Z",
    "title_canon_sha256": "ea5a79ef45ef8fee90ebadca18092555f7a630e9e8b3700dee1f344b847e1fd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.01689",
    "kind": "arxiv",
    "version": 3
  }
}