Pith Number

pith:2BFID3KM

pith:2015:2BFID3KMUJSBZGNSHDHAU2YKRV

not attested not anchored not stored refs pending

Generalized CP and $\Delta (3n^2)$ Family Symmetry for Semi-Direct Predictions of the PMNS Matrix

Gui-Jun Ding, Stephen F. King

arxiv:1510.03188 v1 · 2015-10-12 · 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{2BFID3KMUJSBZGNSHDHAU2YKRV}

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	2026-05-18T01:21:52.358638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d04a81ed4ca2641c99b238ce0a6b0a8d67130b882baa9f76778974f5232ae2c6

Aliases

arxiv: 1510.03188 · arxiv_version: 1510.03188v1 · doi: 10.48550/arxiv.1510.03188 · pith_short_12: 2BFID3KMUJSB · pith_short_16: 2BFID3KMUJSBZGNS · pith_short_8: 2BFID3KM

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/2BFID3KMUJSBZGNSHDHAU2YKRV \
  | 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: d04a81ed4ca2641c99b238ce0a6b0a8d67130b882baa9f76778974f5232ae2c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "744db33e30783de622947a62090d3633d60dc50cedc239b1d2718683ccde5732",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2015-10-12T09:02:37Z",
    "title_canon_sha256": "b925247407ff10d6f5b57d705b2f648a97333eb316ab6bbdc6d5eab9bdc395a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03188",
    "kind": "arxiv",
    "version": 1
  }
}