Pith Number

pith:TIFXVEU5

pith:2020:TIFXVEU57SMIYZ2EZNY2A5L3S3

not attested not anchored not stored refs pending

The peak and descent statistics over ballot permutations

David G.L. Wang, T. Zhao

arxiv:2009.05973 v2 · 2020-09-13 · 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{TIFXVEU57SMIYZ2EZNY2A5L3S3}

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	2026-07-05T01:35:38.451681Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a0b7a929dfc988c6744cb71a0757b96d9b4fdc5d1c7cd70335055ec543d86ca

Aliases

arxiv: 2009.05973 · arxiv_version: 2009.05973v2 · doi: 10.48550/arxiv.2009.05973 · pith_short_12: TIFXVEU57SMI · pith_short_16: TIFXVEU57SMIYZ2E · pith_short_8: TIFXVEU5

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/TIFXVEU57SMIYZ2EZNY2A5L3S3 \
  | 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: 9a0b7a929dfc988c6744cb71a0757b96d9b4fdc5d1c7cd70335055ec543d86ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40e2a4cd357efbae44ea2fc18c0b25d26beea4c176c1fa0060b64edbe5aa88f0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-09-13T10:22:39Z",
    "title_canon_sha256": "72933083beceaf5ec23e6b1706e5497f298791ed4742bbf950fa5f5fd841ed36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2009.05973",
    "kind": "arxiv",
    "version": 2
  }
}