Pith Number

pith:4LCEMZUG

pith:1998:4LCEMZUGIGQUMOVZKXL3JBWOMR

not attested not anchored not stored refs pending

A Brief Review of Three-Family Grand Unification in String Theory

Zurab Kakushadze

arxiv:hep-th/9807240 v1 · 1998-07-31 · hep-th · hep-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4LCEMZUGIGQUMOVZKXL3JBWOMR}

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	2026-05-18T02:52:24.016487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2c446668641a1463ab955d7b486ce646fcbfc5b06f428b35de7f950411f50c6

Aliases

arxiv: hep-th/9807240 · arxiv_version: hep-th/9807240v1 · doi: 10.48550/arxiv.hep-th/9807240 · pith_short_12: 4LCEMZUGIGQU · pith_short_16: 4LCEMZUGIGQUMOVZ · pith_short_8: 4LCEMZUG

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/4LCEMZUGIGQUMOVZKXL3JBWOMR \
  | 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: e2c446668641a1463ab955d7b486ce646fcbfc5b06f428b35de7f950411f50c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "531928cd5284565e9835882e830ab856d0a7cc08532f2a24ccaa9de13909f347",
    "cross_cats_sorted": [
      "hep-ph"
    ],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "1998-07-31T12:27:11Z",
    "title_canon_sha256": "6584e7d87e0bf1095408f56ed8e18c4910d2f81a157eb04a8d7a4b6b0bc24ca7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/9807240",
    "kind": "arxiv",
    "version": 1
  }
}