Pith Number

pith:EJ4ILH3U

pith:2010:EJ4ILH3URKAXWSLZ7UM5GXCVKL

not attested not anchored not stored refs pending

Multiplicative zero-one laws and metric number theory

Alan Haynes, Sanju Velani, Victor Beresnevich

arxiv:1012.0675 v2 · 2010-12-03 · 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{EJ4ILH3URKAXWSLZ7UM5GXCVKL}

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	2026-05-18T03:13:43.847171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2278859f748a817b4979fd19d35c5552de9517eb825dc412c9a18bebd45c88d9

Aliases

arxiv: 1012.0675 · arxiv_version: 1012.0675v2 · doi: 10.48550/arxiv.1012.0675 · pith_short_12: EJ4ILH3URKAX · pith_short_16: EJ4ILH3URKAXWSLZ · pith_short_8: EJ4ILH3U

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/EJ4ILH3URKAXWSLZ7UM5GXCVKL \
  | 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: 2278859f748a817b4979fd19d35c5552de9517eb825dc412c9a18bebd45c88d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a14c8550c6f43b8a12954afcbeb290a7773c01697ee9ea1f62cf216c755ed116",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-12-03T09:34:15Z",
    "title_canon_sha256": "9b2a86010b2b5451f6da7fbd10e8a0d3b22c13a1346a94d7856b4acced4915e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0675",
    "kind": "arxiv",
    "version": 2
  }
}