Pith Number

pith:VEARIZUG

pith:2015:VEARIZUG6SJ6ZO3FECIUVYJXZ2

not attested not anchored not stored refs pending

Phase Uniqueness for the Mallows Measure on Permutations

Meg Walters, Shannon Starr

arxiv:1502.03727 v5 · 2015-02-12 · 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{VEARIZUG6SJ6ZO3FECIUVYJXZ2}

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	2026-05-18T00:15:05.861503Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a901146686f493ecbb6520914ae137cead390bb95a8263477da1ab9e744f72eb

Aliases

arxiv: 1502.03727 · arxiv_version: 1502.03727v5 · doi: 10.48550/arxiv.1502.03727 · pith_short_12: VEARIZUG6SJ6 · pith_short_16: VEARIZUG6SJ6ZO3F · pith_short_8: VEARIZUG

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/VEARIZUG6SJ6ZO3FECIUVYJXZ2 \
  | 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: a901146686f493ecbb6520914ae137cead390bb95a8263477da1ab9e744f72eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6432eed7c37b6e0a3b70d5223c2283b12562d1502d2eb5cd2f764c60168f31bb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-02-12T16:50:52Z",
    "title_canon_sha256": "17daab66966a50ac019bc7f6faf319ff5219cc3c556ac98832ffac4b6bc431b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.03727",
    "kind": "arxiv",
    "version": 5
  }
}