Pith Number

pith:4L2ARN5D

pith:2013:4L2ARN5DROPKIYYEA7G5AY22PM

not attested not anchored not stored refs pending

Strong approximation and descent

Dasheng Wei, Ulrich Derenthal

arxiv:1311.3914 v2 · 2013-11-15 · math.NT · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4L2ARN5DROPKIYYEA7G5AY22PM}

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	2026-05-18T02:31:30.127994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2f408b7a38b9ea4630407cdd0635a7b3e89befd6a4cf86ae8e009bcca561d1e

Aliases

arxiv: 1311.3914 · arxiv_version: 1311.3914v2 · doi: 10.48550/arxiv.1311.3914 · pith_short_12: 4L2ARN5DROPK · pith_short_16: 4L2ARN5DROPKIYYE · pith_short_8: 4L2ARN5D

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/4L2ARN5DROPKIYYEA7G5AY22PM \
  | 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: e2f408b7a38b9ea4630407cdd0635a7b3e89befd6a4cf86ae8e009bcca561d1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcf927bc7ac5a36e763c8e0a73529c9b84b26865bf4cca2523b61e7872293b05",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-15T16:36:17Z",
    "title_canon_sha256": "c79e50d34b077ab03b6c41ab8120360dfc2898275238e2b2d83cf101b50156cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.3914",
    "kind": "arxiv",
    "version": 2
  }
}