Pith Number

pith:SPKHH23Z

pith:2021:SPKHH23Z474XPIXW5HKOCVGUQ3

not attested not anchored not stored refs pending

Down-set thresholds

Benjamin Gunby, Bhargav Narayanan, Xiaoyu He

arxiv:2112.08525 v2 · 2021-12-15 · math.CO · 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{SPKHH23Z474XPIXW5HKOCVGUQ3}

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	2026-07-05T05:38:20.649688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93d473eb79e7f977a2f6e9d4e154d486c713ff24dec896d7dcb2f8a7b5018f4e

Aliases

arxiv: 2112.08525 · arxiv_version: 2112.08525v2 · doi: 10.48550/arxiv.2112.08525 · pith_short_12: SPKHH23Z474X · pith_short_16: SPKHH23Z474XPIXW · pith_short_8: SPKHH23Z

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/SPKHH23Z474XPIXW5HKOCVGUQ3 \
  | 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: 93d473eb79e7f977a2f6e9d4e154d486c713ff24dec896d7dcb2f8a7b5018f4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42be7e42fa9c16d85ae868d7614ff10f0c2631b064765c78e3c87a7e7fa5b903",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-12-15T23:18:36Z",
    "title_canon_sha256": "ebb4cac5326c522b73f773b65bc2cbd53441d70d28d78af06265cb2b96c3437e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.08525",
    "kind": "arxiv",
    "version": 2
  }
}