Pith Number

pith:PZZ6SM2T

pith:2016:PZZ6SM2TOXAB5YQEUZSWBVCPWF

not attested not anchored not stored refs pending

A note on multiplicative functions on progressions to large moduli

Ben Green

arxiv:1604.04481 v4 · 2016-04-15 · 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{PZZ6SM2TOXAB5YQEUZSWBVCPWF}

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	2026-05-18T00:17:55.387574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e73e9335375c01ee204a66560d44fb1623e3cee2d412a4d7a0e2b57e07e2ac3

Aliases

arxiv: 1604.04481 · arxiv_version: 1604.04481v4 · doi: 10.48550/arxiv.1604.04481 · pith_short_12: PZZ6SM2TOXAB · pith_short_16: PZZ6SM2TOXAB5YQE · pith_short_8: PZZ6SM2T

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/PZZ6SM2TOXAB5YQEUZSWBVCPWF \
  | 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: 7e73e9335375c01ee204a66560d44fb1623e3cee2d412a4d7a0e2b57e07e2ac3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c99743e2555039dbbaa6f3544cdce45d6a75f5d4405971a554e17f09bb8f971",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-04-15T13:04:27Z",
    "title_canon_sha256": "a13d622bee1a473bd47503828d650deec981bc8a5b33ae33529832885e16a68d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.04481",
    "kind": "arxiv",
    "version": 4
  }
}