Pith Number

pith:DUURB4TT

pith:2011:DUURB4TTTITY6FX3JCPEYF27HI

not attested not anchored not stored refs pending

On the correlation of the Moebius function with random rank-one systems

Jean Bourgain

arxiv:1112.1032 v1 · 2011-12-05 · 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{DUURB4TTTITY6FX3JCPEYF27HI}

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	2026-05-18T04:06:57.178346Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d2910f2739a278f16fb489e4c175f3a249c6e23ea355b259d8c1a5230236407

Aliases

arxiv: 1112.1032 · arxiv_version: 1112.1032v1 · doi: 10.48550/arxiv.1112.1032 · pith_short_12: DUURB4TTTITY · pith_short_16: DUURB4TTTITY6FX3 · pith_short_8: DUURB4TT

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/DUURB4TTTITY6FX3JCPEYF27HI \
  | 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: 1d2910f2739a278f16fb489e4c175f3a249c6e23ea355b259d8c1a5230236407

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4b7b68747fce8197573f9fab0c1a2a8e19a987497a8beb0374e1466cd8f634e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-12-05T19:36:07Z",
    "title_canon_sha256": "da905ae9f797d8edc5f2135ba11fb93c04aeb164fa9438ec314d98a20cc0c584"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1032",
    "kind": "arxiv",
    "version": 1
  }
}