Pith Number

pith:MLL4FJMK

pith:2021:MLL4FJMKNK736B7JNBIHJFEEIU

not attested not anchored not stored refs pending

Common and Sidorenko equations in Abelian groups

Leo Versteegen

arxiv:2109.04445 v2 · 2021-09-09 · math.CO · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MLL4FJMKNK736B7JNBIHJFEEIU}

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	2026-07-05T03:13:06.389848Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62d7c2a58a6abfbf07e96850749484451d667d84cd08954ff92f8d8dd7b9c91a

Aliases

arxiv: 2109.04445 · arxiv_version: 2109.04445v2 · doi: 10.48550/arxiv.2109.04445 · pith_short_12: MLL4FJMKNK73 · pith_short_16: MLL4FJMKNK736B7J · pith_short_8: MLL4FJMK

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/MLL4FJMKNK736B7JNBIHJFEEIU \
  | 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: 62d7c2a58a6abfbf07e96850749484451d667d84cd08954ff92f8d8dd7b9c91a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33b092435e0e5fc36f52f5e4f238b4685ebde6d67deb26a0e0774f42b0b08f7c",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-09-09T17:43:41Z",
    "title_canon_sha256": "df94e3ba3930d0ea55818e26b54fe6de178885c2849d69c450aa8af10803aac8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.04445",
    "kind": "arxiv",
    "version": 2
  }
}