Pith Number

pith:GTNAKDWX

pith:2006:GTNAKDWXVFC3XSW5CCCU2ZWYVJ

not attested not anchored not stored refs pending

A4 family symmetry and quark-lepton unification

Michal Malinsky, Stephen F. King

arxiv:hep-ph/0610250 v2 · 2006-10-19 · 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{GTNAKDWXVFC3XSW5CCCU2ZWYVJ}

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.

Cited by

1 paper in Pith

Fermion Masses and Mixing in Pati-Salam Unification with $S_3$ Modular Symmetry

Receipt and verification

First computed	2026-07-04T17:25:23.999424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34da050ed7a945bbcadd10854d66d8aa7e826a3d4bacee769a7b201ab5210b19

Aliases

arxiv: hep-ph/0610250 · arxiv_version: hep-ph/0610250v2 · doi: 10.48550/arxiv.hep-ph/0610250 · pith_short_12: GTNAKDWXVFC3 · pith_short_16: GTNAKDWXVFC3XSW5 · pith_short_8: GTNAKDWX

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/GTNAKDWXVFC3XSW5CCCU2ZWYVJ \
  | 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: 34da050ed7a945bbcadd10854d66d8aa7e826a3d4bacee769a7b201ab5210b19

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32be5954e37807fa7f78caeb1376094b78c403f64754050655c1331e759f0f5b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2006-10-19T16:19:45Z",
    "title_canon_sha256": "8f42f99f6b0b2414db7425797041a62bf6368bd8b6a01dd0e851c2ae5b23e0ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0610250",
    "kind": "arxiv",
    "version": 2
  }
}