Pith Number

pith:ZA2S4GPE

pith:2012:ZA2S4GPEZTG722FSZSJWC2I2FG

not attested not anchored not stored refs pending

On CM values of Borcherds products and harmonic weak Maass forms of weight one

Stephan Ehlen

arxiv:1208.2386 v1 · 2012-08-11 · 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{ZA2S4GPEZTG722FSZSJWC2I2FG}

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	2026-05-18T03:48:58.016754Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8352e19e4cccdfd68b2cc9361691a2990abc689fe260032cbac40e9d98c2240

Aliases

arxiv: 1208.2386 · arxiv_version: 1208.2386v1 · doi: 10.48550/arxiv.1208.2386 · pith_short_12: ZA2S4GPEZTG7 · pith_short_16: ZA2S4GPEZTG722FS · pith_short_8: ZA2S4GPE

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/ZA2S4GPEZTG722FSZSJWC2I2FG \
  | 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: c8352e19e4cccdfd68b2cc9361691a2990abc689fe260032cbac40e9d98c2240

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d84b76226f92cf8801d1e80e1999e126e9a95f27a968ae3f6af32cd19eae0c6e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-08-11T21:50:35Z",
    "title_canon_sha256": "4ad9f674e4610bc0ff1e6b6bd063d9e094081904ab3e346d7ea01e439a2e6fa9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.2386",
    "kind": "arxiv",
    "version": 1
  }
}