Pith Number

pith:EO4Y3O7G

pith:2018:EO4Y3O7GK57TGZGGOME3ZP7SXV

not attested not anchored not stored refs pending

Equidistribution of expanding translates of curves and Diophantine approximation on matrices

Pengyu Yang

arxiv:1809.08515 v3 · 2018-09-23 · math.DS · 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{EO4Y3O7GK57TGZGGOME3ZP7SXV}

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	2026-05-17T23:52:15.538773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23b98dbbe6577f3364c67309bcbff2bd65c0f7cfce333446be7b097f945dc9d6

Aliases

arxiv: 1809.08515 · arxiv_version: 1809.08515v3 · doi: 10.48550/arxiv.1809.08515 · pith_short_12: EO4Y3O7GK57T · pith_short_16: EO4Y3O7GK57TGZGG · pith_short_8: EO4Y3O7G

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/EO4Y3O7GK57TGZGGOME3ZP7SXV \
  | 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: 23b98dbbe6577f3364c67309bcbff2bd65c0f7cfce333446be7b097f945dc9d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fafc1412f2ad71d4f3622b91d509eb79c4d28d2d9d383aeec21b652d5fbfe0d",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-09-23T02:25:44Z",
    "title_canon_sha256": "6f14d7e20909200556db39e73c96805a1c90528697a74e4de6cb3ea638c3ee83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.08515",
    "kind": "arxiv",
    "version": 3
  }
}