Pith Number

pith:P57PIVEZ

pith:2011:P57PIVEZWYPQNBPJNYLENCKFXG

not attested not anchored not stored refs pending

On (not) computing the Mobius function using bounded depth circuits

Ben Green

arxiv:1103.4991 v4 · 2011-03-25 · 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{P57PIVEZWYPQNBPJNYLENCKFXG}

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	2026-05-18T03:54:27.790387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f7ef45499b61f0685e96e16468945b980ef4b28ebf600c94634373b77070531

Aliases

arxiv: 1103.4991 · arxiv_version: 1103.4991v4 · doi: 10.48550/arxiv.1103.4991 · pith_short_12: P57PIVEZWYPQ · pith_short_16: P57PIVEZWYPQNBPJ · pith_short_8: P57PIVEZ

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/P57PIVEZWYPQNBPJNYLENCKFXG \
  | 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: 7f7ef45499b61f0685e96e16468945b980ef4b28ebf600c94634373b77070531

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad791fb79a6af93d6c425983a39f9f7c83fc49d7e3b2d42ce7e1cc78e08f2906",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-03-25T15:12:17Z",
    "title_canon_sha256": "e62db250d077b0dbbf588e2c903d76ca6fbbd77f84886842486798e6fd00dc5d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4991",
    "kind": "arxiv",
    "version": 4
  }
}