Pith Number

pith:M2CX4JQO

pith:2019:M2CX4JQOSXZZJY7Q66SQ7EZ33V

not attested not anchored not stored refs pending

Towards unification of quark and lepton flavors in $A_4$ modular invariance

Hiroshi Okada, Morimitsu Tanimoto

arxiv:1905.13421 v6 · 2019-05-31 · 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{M2CX4JQOSXZZJY7Q66SQ7EZ33V}

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

Zee models with a non-invertible $Z_M$ symmetry

Receipt and verification

First computed	2026-07-05T03:00:26.389821Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66857e260e95f394e3f0f7a50f933bdd50fdf62b746938670f86a31b2470719b

Aliases

arxiv: 1905.13421 · arxiv_version: 1905.13421v6 · doi: 10.48550/arxiv.1905.13421 · pith_short_12: M2CX4JQOSXZZ · pith_short_16: M2CX4JQOSXZZJY7Q · pith_short_8: M2CX4JQO

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/M2CX4JQOSXZZJY7Q66SQ7EZ33V \
  | 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: 66857e260e95f394e3f0f7a50f933bdd50fdf62b746938670f86a31b2470719b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "043450ff2e1aa186850fae3faeb14ea1d2877eada97478852e248c4b07bb4568",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2019-05-31T05:32:28Z",
    "title_canon_sha256": "0bf699782a0fab971f8c10152f33e23b1b090fff75c81529d8d0f9d753d351c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.13421",
    "kind": "arxiv",
    "version": 6
  }
}