Pith Number

pith:PTU4T3F3

pith:2021:PTU4T3F3EG7ECFGSIRKXIGWPXM

not attested not anchored not stored refs pending

Zee model in a modular $A_4$ symmetry

Hiroshi Okada, Takaaki Nomura, Yong-Hui Qi

arxiv:2111.10944 v3 · 2021-11-22 · 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{PTU4T3F3EG7ECFGSIRKXIGWPXM}

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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	2026-07-05T10:08:09.346380Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ce9c9ecbb21be4114d24455741acfbb232ec81fe2bf508f3c93569195964053

Aliases

arxiv: 2111.10944 · arxiv_version: 2111.10944v3 · doi: 10.48550/arxiv.2111.10944 · pith_short_12: PTU4T3F3EG7E · pith_short_16: PTU4T3F3EG7ECFGS · pith_short_8: PTU4T3F3

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/PTU4T3F3EG7ECFGSIRKXIGWPXM \
  | 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: 7ce9c9ecbb21be4114d24455741acfbb232ec81fe2bf508f3c93569195964053

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a388dadc8c36e9ca0b32b4ba9a6b1c49f54959e480b0be9902d1a7950fb51b9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2021-11-22T01:58:50Z",
    "title_canon_sha256": "578b8b6790d9c7455d2f9e09094ba81ce574d0468d3ee7c9e7ffcd10ad116112"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.10944",
    "kind": "arxiv",
    "version": 3
  }
}