Pith Number

pith:6OLUPPEV

pith:2011:6OLUPPEVU5F6D4W5RXJAAPTHG5

not attested not anchored not stored refs pending

Elementary computation of the stable reduction of the Drinfeld modular curve $X(\pi^2)$

Takahiro Tsushima

arxiv:1109.4381 v1 · 2011-09-20 · 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{6OLUPPEVU5F6D4W5RXJAAPTHG5}

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	2026-05-18T04:12:43.385401Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f39747bc95a74be1f2dd8dd2003e67375ff0fff5ff69b79386245d9177dcfe50

Aliases

arxiv: 1109.4381 · arxiv_version: 1109.4381v1 · doi: 10.48550/arxiv.1109.4381 · pith_short_12: 6OLUPPEVU5F6 · pith_short_16: 6OLUPPEVU5F6D4W5 · pith_short_8: 6OLUPPEV

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/6OLUPPEVU5F6D4W5RXJAAPTHG5 \
  | 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: f39747bc95a74be1f2dd8dd2003e67375ff0fff5ff69b79386245d9177dcfe50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6dab67b0d79be81d75573e53df9f21e66b5d2492a41a6aa7d00faa9fdf8c0b75",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-09-20T18:10:05Z",
    "title_canon_sha256": "2ecc835948bb60f2bc4d9d0e37a58e7a56b6ea3d972aae3e3158b64944217bcf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4381",
    "kind": "arxiv",
    "version": 1
  }
}