Pith Number

pith:XXKBJC2R

pith:2011:XXKBJC2RH45O6QMUYDRO3C6L6R

not attested not anchored not stored refs pending

Dirac Lepton Angle Matrix v.s. Majorana Lepton Angle Matrix and Their Renormalization Group Running Behaviours

Shu Luo

arxiv:1109.4260 v2 · 2011-09-20 · 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{XXKBJC2RH45O6QMUYDRO3C6L6R}

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	2026-05-18T02:00:28.818484Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdd4148b513f3aef4194c0e2ed8bcbf454587bb7533ac4d795d3eae9bf055887

Aliases

arxiv: 1109.4260 · arxiv_version: 1109.4260v2 · doi: 10.48550/arxiv.1109.4260 · pith_short_12: XXKBJC2RH45O · pith_short_16: XXKBJC2RH45O6QMU · pith_short_8: XXKBJC2R

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/XXKBJC2RH45O6QMUYDRO3C6L6R \
  | 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: bdd4148b513f3aef4194c0e2ed8bcbf454587bb7533ac4d795d3eae9bf055887

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "944dad4de2e81cda2cc2646c3f5b3442129abdbd5ca66d8d1e09532c08fb9877",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2011-09-20T10:38:37Z",
    "title_canon_sha256": "b19770b9fbaed9dee6d3a329c2063fde35e5686eb036aa5da0ec7f14d7bb7d24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4260",
    "kind": "arxiv",
    "version": 2
  }
}