Pith Number

pith:4WHJLDVB

pith:2009:4WHJLDVBNCWXCB7PWFL2FA5R6I

not attested not anchored not stored refs pending

Yukawa Couplings in Heterotic Compactification

Andre Lukas, Dan Grayson, James Gray, Lara B. Anderson, Yang-Hui He

arxiv:0904.2186 v1 · 2009-04-15 · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4WHJLDVBNCWXCB7PWFL2FA5R6I}

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	2026-07-04T17:29:38.276290Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e58e958ea168ad7107efb157a283b1f21059466b11b0678967d35df7b71b44d3

Aliases

arxiv: 0904.2186 · arxiv_version: 0904.2186v1 · doi: 10.48550/arxiv.0904.2186 · pith_short_12: 4WHJLDVBNCWX · pith_short_16: 4WHJLDVBNCWXCB7P · pith_short_8: 4WHJLDVB

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/4WHJLDVBNCWXCB7PWFL2FA5R6I \
  | 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: e58e958ea168ad7107efb157a283b1f21059466b11b0678967d35df7b71b44d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61c06bda753222d9119c235a2830e3c308acd913dccd3149999db0e92a91c2c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2009-04-15T12:59:36Z",
    "title_canon_sha256": "3d0b5f31f01b9fc30cf7d958c7e53d966aa3004d4af84af00f53ece967069a97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.2186",
    "kind": "arxiv",
    "version": 1
  }
}