Pith Number

pith:UMQWNWX4

pith:2020:UMQWNWX4KTVWBAL5TJLTINUBGO

not attested not anchored not stored refs pending

Fermion Mass Hierarchies from Modular Symmetry

Simon J.D. King, Stephen F. King

arxiv:2002.00969 v2 · 2020-02-03 · 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{UMQWNWX4KTVWBAL5TJLTINUBGO}

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

Non-holomorphic $S^{\prime}_{4}$ modular symmetry for leptons and leptogenesis

Receipt and verification

First computed	2026-07-05T01:38:16.826868Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a32166dafc54eb60817d9a573436813381c2a7ead1297b3fd0c61fa7b98401ee

Aliases

arxiv: 2002.00969 · arxiv_version: 2002.00969v2 · doi: 10.48550/arxiv.2002.00969 · pith_short_12: UMQWNWX4KTVW · pith_short_16: UMQWNWX4KTVWBAL5 · pith_short_8: UMQWNWX4

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/UMQWNWX4KTVWBAL5TJLTINUBGO \
  | 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: a32166dafc54eb60817d9a573436813381c2a7ead1297b3fd0c61fa7b98401ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9da7906d9e36490a775514e113b5444d4e06620111815e71c20ed7e5ebfa8dc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2020-02-03T19:00:04Z",
    "title_canon_sha256": "973ae546ae8cd802fb17153f395b2ab4ed3e206980535c353c87c6a7d5807f02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2002.00969",
    "kind": "arxiv",
    "version": 2
  }
}