Pith Number

pith:ESBHFJNU

pith:2007:ESBHFJNURRMA3EZ7V7R3X2HEDS

not attested not anchored not stored refs pending

On Some Subgroup Chains Related to Kneser's Theorem

Gilles Zemor, Oriol Serra, Yahya Ould Hamidoune

arxiv:0704.0382 v1 · 2007-04-03 · 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{ESBHFJNURRMA3EZ7V7R3X2HEDS}

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	2026-07-04T15:15:13.105073Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

248272a5b48c580d933fafe3bbe8e41cba3798a9d2a28af53b768d8788972969

Aliases

arxiv: 0704.0382 · arxiv_version: 0704.0382v1 · doi: 10.48550/arxiv.0704.0382 · pith_short_12: ESBHFJNURRMA · pith_short_16: ESBHFJNURRMA3EZ7 · pith_short_8: ESBHFJNU

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/ESBHFJNURRMA3EZ7V7R3X2HEDS \
  | 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: 248272a5b48c580d933fafe3bbe8e41cba3798a9d2a28af53b768d8788972969

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4290ca92dffc12652b4ab3cf21955159126c0372bc729260a7b3606eb78d6b07",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-04-03T13:06:16Z",
    "title_canon_sha256": "62c6bbb7a63b40e13b48d57bce54a3c62edc4734b9c0be50178a0ec5c46a963a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0704.0382",
    "kind": "arxiv",
    "version": 1
  }
}