Pith Number

pith:VZROSZPM

pith:2022:VZROSZPML7G7765RLTGRQMLMF4

not attested not anchored not stored refs pending

Smooth numbers are orthogonal to nilsequences

Lilian Matthiesen, Mengdi Wang

arxiv:2211.16892 v2 · 2022-11-30 · 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{VZROSZPML7G7765RLTGRQMLMF4}

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	2026-07-05T12:07:34.805998Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae62e965ec5fcdfffbb15ccd18316c2f1c6540e80283085c7b19be69b7a9af43

Aliases

arxiv: 2211.16892 · arxiv_version: 2211.16892v2 · doi: 10.48550/arxiv.2211.16892 · pith_short_12: VZROSZPML7G7 · pith_short_16: VZROSZPML7G7765R · pith_short_8: VZROSZPM

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/VZROSZPML7G7765RLTGRQMLMF4 \
  | 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: ae62e965ec5fcdfffbb15ccd18316c2f1c6540e80283085c7b19be69b7a9af43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "668eee3fd306084aac3864dac0913dcda1b2c2ab7cb8a96783d2d65a7c36a942",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-11-30T10:45:17Z",
    "title_canon_sha256": "c32f931f855c858e2ba44092ccd0829e90644bb027842715e2e8566c85db8dc0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.16892",
    "kind": "arxiv",
    "version": 2
  }
}