Pith Number

pith:CTGGUKKP

pith:2020:CTGGUKKPY2YJBLE2BIU7LTA743

not attested not anchored not stored refs pending

Integral solutions to the one-loop renormalization-group equations for lepton flavor mixing parameters and the Jarlskog invariant

Di Zhang

arxiv:2007.12976 v2 · 2020-07-25 · hep-ph · hep-ex

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CTGGUKKPY2YJBLE2BIU7LTA743}

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

1 paper in Pith

Complete Two-loop Renormalization Group Equation of the Weinberg Operator

Receipt and verification

First computed	2026-07-05T02:11:56.903111Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14cc6a294fc6b090ac9a0a29f5cc1fe6f6e5138b68aa51ec0499d989697ba17b

Aliases

arxiv: 2007.12976 · arxiv_version: 2007.12976v2 · doi: 10.48550/arxiv.2007.12976 · pith_short_12: CTGGUKKPY2YJ · pith_short_16: CTGGUKKPY2YJBLE2 · pith_short_8: CTGGUKKP

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/CTGGUKKPY2YJBLE2BIU7LTA743 \
  | 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: 14cc6a294fc6b090ac9a0a29f5cc1fe6f6e5138b68aa51ec0499d989697ba17b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40d91b09992c47ed3c470a24c6b851d53d3745b84b14caf5556ad62852900de4",
    "cross_cats_sorted": [
      "hep-ex"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2020-07-25T17:00:58Z",
    "title_canon_sha256": "ed3d7b0b15f9285aae747cb58bbeacd08cda2e7b94c0873050c09f2458137701"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2007.12976",
    "kind": "arxiv",
    "version": 2
  }
}