Pith Number

pith:VRYUUX2Z

pith:2016:VRYUUX2ZX3KYOS45TVUL7QSVSS

not attested not anchored not stored refs pending

(Topological) modular forms with level structures: decompositions and duality

Lennart Meier

arxiv:1609.09264 v2 · 2016-09-29 · math.AT · 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{VRYUUX2ZX3KYOS45TVUL7QSVSS}

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	2026-05-18T00:50:29.109325Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac714a5f59bed5874b9d9d68bfc25594b31461d7341585d49c2254ad830be3f8

Aliases

arxiv: 1609.09264 · arxiv_version: 1609.09264v2 · doi: 10.48550/arxiv.1609.09264 · pith_short_12: VRYUUX2ZX3KY · pith_short_16: VRYUUX2ZX3KYOS45 · pith_short_8: VRYUUX2Z

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/VRYUUX2ZX3KYOS45TVUL7QSVSS \
  | 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: ac714a5f59bed5874b9d9d68bfc25594b31461d7341585d49c2254ad830be3f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b572d2f72d08a97d765428964bd61396aeb571b0b2ac6f16c3b26c42b320024",
    "cross_cats_sorted": [
      "math.AG",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-09-29T09:07:24Z",
    "title_canon_sha256": "7a8975ba9dbb4a9c210ff46463d1d6aeb0c6c24c8a8de3d6df71ba28e0e487c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.09264",
    "kind": "arxiv",
    "version": 2
  }
}