Pith Number

pith:W2BAXAJB

pith:2011:W2BAXAJBAVY2ZW5Z7ESS2QDVAX

not attested not anchored not stored refs pending

Spiegelungssatz: a combinatorial proof for the 4-rank

Emmanuel Royer, Laurent Habsieger (ICJ)

arxiv:1102.2971 v2 · 2011-02-15 · 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{W2BAXAJBAVY2ZW5Z7ESS2QDVAX}

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	2026-05-18T04:23:22.008680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6820b81210571acdbb9f9252d407505da426a5dca6783807efbca46625e5873

Aliases

arxiv: 1102.2971 · arxiv_version: 1102.2971v2 · doi: 10.48550/arxiv.1102.2971 · pith_short_12: W2BAXAJBAVY2 · pith_short_16: W2BAXAJBAVY2ZW5Z · pith_short_8: W2BAXAJB

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/W2BAXAJBAVY2ZW5Z7ESS2QDVAX \
  | 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: b6820b81210571acdbb9f9252d407505da426a5dca6783807efbca46625e5873

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d91985f832ea1b07be807b7720bcf3345635e376c5cad22db9fe2016adf3ada",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-02-15T05:49:49Z",
    "title_canon_sha256": "657c96554faca3f4ee895e40ef2b93bc325bc3fa17cb7400f4c483e19b5e59c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.2971",
    "kind": "arxiv",
    "version": 2
  }
}