Pith Number

pith:MXY4JCZT

pith:2009:MXY4JCZTYOM76SHRNDYZLUWZGQ

not attested not anchored not stored refs pending

Multiplicative mimicry and improvements of the Polya-Vinogradov inequality

Leo Goldmakher

arxiv:0911.5547 v2 · 2009-11-30 · 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{MXY4JCZTYOM76SHRNDYZLUWZGQ}

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	2026-05-18T04:38:58.237870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65f1c48b33c399ff48f168f195d2d934368caf1be5da7370772d9af67dd70235

Aliases

arxiv: 0911.5547 · arxiv_version: 0911.5547v2 · doi: 10.48550/arxiv.0911.5547 · pith_short_12: MXY4JCZTYOM7 · pith_short_16: MXY4JCZTYOM76SHR · pith_short_8: MXY4JCZT

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/MXY4JCZTYOM76SHRNDYZLUWZGQ \
  | 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: 65f1c48b33c399ff48f168f195d2d934368caf1be5da7370772d9af67dd70235

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b4aea91a3e196a3d9d9d2cda3bc65ce45efe5b6d728cc206f4a3f471b1bd452",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-11-30T05:49:57Z",
    "title_canon_sha256": "f63a8a083a49ea103e7fd5741459e1f12933e1e7f063f133512dcea4ac66501a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.5547",
    "kind": "arxiv",
    "version": 2
  }
}