Pith Number

pith:G4T5W3GJ

pith:2019:G4T5W3GJ4HX2OFWIGML4AQ2NPS

not attested not anchored not stored refs pending

Trimaximal TM$_1$ mixing with two modular $S_4$ groups

Stephen F. King, Ye-Ling Zhou

arxiv:1908.02770 v3 · 2019-08-07 · 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{G4T5W3GJ4HX2OFWIGML4AQ2NPS}

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

4 papers in Pith

Lepton mixing from the $\Delta(96)$ Modular Littlest Seesaw

The Future of Lepton Flavor

Rephasing invariant CP phases and sum rules in TM$_{1,2}$ mixing

Two-loop neutrino mass model with modular $S_4$ symmetry

Receipt and verification

First computed	2026-07-05T00:29:39.351598Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3727db6cc9e1efa716c83317c0434d7c9c10a1bf1fe2c98672c676284e13c6bb

Aliases

arxiv: 1908.02770 · arxiv_version: 1908.02770v3 · doi: 10.48550/arxiv.1908.02770 · pith_short_12: G4T5W3GJ4HX2 · pith_short_16: G4T5W3GJ4HX2OFWI · pith_short_8: G4T5W3GJ

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/G4T5W3GJ4HX2OFWIGML4AQ2NPS \
  | 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: 3727db6cc9e1efa716c83317c0434d7c9c10a1bf1fe2c98672c676284e13c6bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89659023bd248639133be4cb8f2da8d49aa38e7b02e38c354f698278fc1d7d91",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2019-08-07T18:00:08Z",
    "title_canon_sha256": "dd8a9b225caba400bda4f8951a3c56bac457251bb3ae09ee34e2edfe3385d427"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.02770",
    "kind": "arxiv",
    "version": 3
  }
}