Pith Number

pith:TY7DQM5Q

pith:2020:TY7DQM5QHI34OFS2MRDDCBSFGE

not attested not anchored not stored refs pending

Spontaneous CP violation by modulus $\tau$ in $A_4$ model of lepton flavors

Hiroshi Okada, Morimitsu Tanimoto

arxiv:2012.01688 v2 · 2020-12-03 · 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{TY7DQM5QHI34OFS2MRDDCBSFGE}

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.

Receipt and verification

First computed	2026-07-05T02:23:20.312649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e3e3833b03a37c7165a6446310645311038a2467ec4ad502a6f29896964288a

Aliases

arxiv: 2012.01688 · arxiv_version: 2012.01688v2 · doi: 10.48550/arxiv.2012.01688 · pith_short_12: TY7DQM5QHI34 · pith_short_16: TY7DQM5QHI34OFS2 · pith_short_8: TY7DQM5Q

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/TY7DQM5QHI34OFS2MRDDCBSFGE \
  | 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: 9e3e3833b03a37c7165a6446310645311038a2467ec4ad502a6f29896964288a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90fdd5a78795c5cb4d1016a6f58e634437444e7ca10fb8adb76f2a9e0577d47f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2020-12-03T03:50:20Z",
    "title_canon_sha256": "3eea4bde29359738faf62d1c7910c70b3b173c12a0d19001979502f259077126"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.01688",
    "kind": "arxiv",
    "version": 2
  }
}