Pith Number

pith:CCKREJV4

pith:2022:CCKREJV4R7EKD3NF3HQOMIQTJ2

not attested not anchored not stored refs pending

Paucity phenomena for polynomial products

Max Wenqiang Xu, Victor Y. Wang

arxiv:2211.02908 v2 · 2022-11-05 · math.NT · 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{CCKREJV4R7EKD3NF3HQOMIQTJ2}

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	2026-07-05T08:56:01.645632Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10951226bc8fc8a1eda5d9e0e622134e923879bd6d491a7148930e992641ab90

Aliases

arxiv: 2211.02908 · arxiv_version: 2211.02908v2 · doi: 10.48550/arxiv.2211.02908 · pith_short_12: CCKREJV4R7EK · pith_short_16: CCKREJV4R7EKD3NF · pith_short_8: CCKREJV4

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/CCKREJV4R7EKD3NF3HQOMIQTJ2 \
  | 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: 10951226bc8fc8a1eda5d9e0e622134e923879bd6d491a7148930e992641ab90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6e7f35983e5e801db7489f5d9e746ec9079fe35584951dc27c5e480f79f58c2",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-11-05T13:46:54Z",
    "title_canon_sha256": "a1b2be9034cb8bb44a54aab955ef31cd56c61daa64b40e482f0714194e38bfb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.02908",
    "kind": "arxiv",
    "version": 2
  }
}