Pith Number

pith:W3AY7J6F

pith:2018:W3AY7J6FBOAOVPWMBWAOTVMCC7

not attested not anchored not stored refs pending

Modular $A_4$ invariance and neutrino mixing

Kenta Takagi, Morimitsu Tanimoto, Naoya Omoto, Takuya H. Tatsuishi, Tatsuo Kobayashi, Yusuke Shimizu

arxiv:1808.03012 v2 · 2018-08-09 · 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{W3AY7J6FBOAOVPWMBWAOTVMCC7}

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

2 papers in Pith

Massive modes on magnetized blow-up manifold of $T^2/\mathbb{Z}_N$

Lepton masses and mixing in non-holomorphic modular $A_4$ with universal couplings

Receipt and verification

First computed	2026-05-17T23:57:40.503834Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6c18fa7c50b80eabecc0d80e9d58217ce39cc68892afa5c462f152430881ef0

Aliases

arxiv: 1808.03012 · arxiv_version: 1808.03012v2 · doi: 10.48550/arxiv.1808.03012 · pith_short_12: W3AY7J6FBOAO · pith_short_16: W3AY7J6FBOAOVPWM · pith_short_8: W3AY7J6F

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/W3AY7J6FBOAOVPWMBWAOTVMCC7 \
  | 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: b6c18fa7c50b80eabecc0d80e9d58217ce39cc68892afa5c462f152430881ef0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "639b1c564c72fdb7fffd1f01da495eefedecc91235a2e72d57dd4ced76ee4908",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2018-08-09T03:57:54Z",
    "title_canon_sha256": "979db571825c17a060af1aa98eed13d366fcaab94010a437e083b60f3e611838"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.03012",
    "kind": "arxiv",
    "version": 2
  }
}