Pith Number

pith:7MVDPSY2

pith:2020:7MVDPSY2D7DRT3BKTJFKY75FFP

not attested not anchored not stored refs pending

Explicit Kronecker-Weyl theorems and applications to prime number races

Alexandre Bailleul

arxiv:2007.05763 v3 · 2020-07-11 · 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{7MVDPSY2D7DRT3BKTJFKY75FFP}

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	2026-07-05T04:35:54.848971Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb2a37cb1a1fc719ec2a9a4aac7fa52bfdf3ddde0612c301bc75a71017777d2d

Aliases

arxiv: 2007.05763 · arxiv_version: 2007.05763v3 · doi: 10.48550/arxiv.2007.05763 · pith_short_12: 7MVDPSY2D7DR · pith_short_16: 7MVDPSY2D7DRT3BK · pith_short_8: 7MVDPSY2

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/7MVDPSY2D7DRT3BKTJFKY75FFP \
  | 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: fb2a37cb1a1fc719ec2a9a4aac7fa52bfdf3ddde0612c301bc75a71017777d2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4f078d4e2df10f1a010ad1dd4d7fe883c962dfbe25486ce60e826d0701b4831",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2020-07-11T12:57:49Z",
    "title_canon_sha256": "28f0199071e477c8a822cd0360056d275bd19b7b2b092692b8809e17c3d442e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2007.05763",
    "kind": "arxiv",
    "version": 3
  }
}