Pith Number

pith:LP74F7PG

pith:2015:LP74F7PGYMPGE5PC3WQVHJIWPS

not attested not anchored not stored refs pending

The Picard groups of the stacks $Y_0(2)$ and $Y_0(3)$

Andrew Niles

arxiv:1504.07913 v1 · 2015-04-29 · math.AG · 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{LP74F7PGYMPGE5PC3WQVHJIWPS}

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	2026-05-18T02:17:31.917613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bffc2fde6c31e6275e2dda153a5167cbc45e6e2f6fd54ab0446e718a43391cf

Aliases

arxiv: 1504.07913 · arxiv_version: 1504.07913v1 · doi: 10.48550/arxiv.1504.07913 · pith_short_12: LP74F7PGYMPG · pith_short_16: LP74F7PGYMPGE5PC · pith_short_8: LP74F7PG

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/LP74F7PGYMPGE5PC3WQVHJIWPS \
  | 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: 5bffc2fde6c31e6275e2dda153a5167cbc45e6e2f6fd54ab0446e718a43391cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ec075062085ad668eee38bb8091dbeb4a38281488978e8d6ddfd17a91f4a90a",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-04-29T16:09:08Z",
    "title_canon_sha256": "31deab2df4f8dbc0b0650bcc4d8b9aa50cce6afe13d42c5e90595c3f2de7856f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.07913",
    "kind": "arxiv",
    "version": 1
  }
}