Pith Number

pith:ZXNRFRKP

pith:2011:ZXNRFRKPROKNKU6ASNK6NTJQPP

not attested not anchored not stored refs pending

On the Fourier-Walsh Spectrum on the Moebius Function

Jean Bourgain

arxiv:1112.1423 v1 · 2011-12-06 · 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{ZXNRFRKPROKNKU6ASNK6NTJQPP}

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	2026-05-18T04:06:54.550737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cddb12c54f8b94d553c09355e6cd307bc73ab117ea3f84e7c3d7e6512e5f8ace

Aliases

arxiv: 1112.1423 · arxiv_version: 1112.1423v1 · doi: 10.48550/arxiv.1112.1423 · pith_short_12: ZXNRFRKPROKN · pith_short_16: ZXNRFRKPROKNKU6A · pith_short_8: ZXNRFRKP

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/ZXNRFRKPROKNKU6ASNK6NTJQPP \
  | 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: cddb12c54f8b94d553c09355e6cd307bc73ab117ea3f84e7c3d7e6512e5f8ace

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c75d0b2202fa31902bf2133191729dd3f950a21c5228c0f59e00d22ab4751ce",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-12-06T21:18:16Z",
    "title_canon_sha256": "4dd38a8ef38e59cb94940fab1a3d0d573ce4560b83d5ea8a1c527d30b10b75b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1423",
    "kind": "arxiv",
    "version": 1
  }
}