Pith Number

pith:3PD6GT5A

pith:2011:3PD6GT5APOBCWQB45YMERB4AL6

not attested not anchored not stored refs pending

On the symmetry of the Liouville function in almost all short intervals

Giovanni Coppola

arxiv:1103.4451 v2 · 2011-03-23 · 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{3PD6GT5APOBCWQB45YMERB4AL6}

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	2026-05-18T04:21:29.729985Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbc7e34fa07b822b403cee184887805f9b5176a7b94f5c0b33f45eb67d4e0b58

Aliases

arxiv: 1103.4451 · arxiv_version: 1103.4451v2 · doi: 10.48550/arxiv.1103.4451 · pith_short_12: 3PD6GT5APOBC · pith_short_16: 3PD6GT5APOBCWQB4 · pith_short_8: 3PD6GT5A

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/3PD6GT5APOBCWQB45YMERB4AL6 \
  | 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: dbc7e34fa07b822b403cee184887805f9b5176a7b94f5c0b33f45eb67d4e0b58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73529670621a14f7dc41f994fc922799e8b2faff24a6d54280f9a0a10eaf5157",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-03-23T06:11:14Z",
    "title_canon_sha256": "88add158368289dc35ce9c44b37f81bb4a5e852e83d7863e4b5f22390727eac6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4451",
    "kind": "arxiv",
    "version": 2
  }
}