Pith Number

pith:32SITMRN

pith:2021:32SITMRNPNEQJC23FICQ4SPAOH

not attested not anchored not stored refs pending

Random Permutations -- A geometric point of view

Jacopo Borga

arxiv:2107.09699 v1 · 2021-07-20 · 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{32SITMRNPNEQJC23FICQ4SPAOH}

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.

Cited by

1 paper in Pith

Complete pivoting growth of butterfly matrices and butterfly Hadamard matrices

Receipt and verification

First computed	2026-07-05T02:59:38.747817Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dea489b22d7b49048b5b2a050e49e071f6b7633e80a487eff66328cb5fc4b3be

Aliases

arxiv: 2107.09699 · arxiv_version: 2107.09699v1 · doi: 10.48550/arxiv.2107.09699 · pith_short_12: 32SITMRNPNEQ · pith_short_16: 32SITMRNPNEQJC23 · pith_short_8: 32SITMRN

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/32SITMRNPNEQJC23FICQ4SPAOH \
  | 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: dea489b22d7b49048b5b2a050e49e071f6b7633e80a487eff66328cb5fc4b3be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2aff1d171f927c01f724b6c8809aadc011f6b78bd77c888f4812f4176e4243d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2021-07-20T18:07:10Z",
    "title_canon_sha256": "89b0dc14ae585a0c9257d506ebba99c44ac82e85aa7fa458fba4e0b658960bf5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.09699",
    "kind": "arxiv",
    "version": 1
  }
}