Pith Number

pith:P4PZ3E2K

pith:2006:P4PZ3E2KWR7OW32SQPZFW7QNGW

not attested not anchored not stored refs pending

Quark lepton complementarity and renormalization group effects

Alexei Yu. Smirnov, Michael A. Schmidt

arxiv:hep-ph/0607232 v2 · 2006-07-21 · 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{P4PZ3E2KWR7OW32SQPZFW7QNGW}

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	2026-07-04T15:17:07.779585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f1f9d934ab47eeb6f5283f25b7e0d35b99ed86cf6ca6a2dd2b8129d61783f97

Aliases

arxiv: hep-ph/0607232 · arxiv_version: hep-ph/0607232v2 · doi: 10.48550/arxiv.hep-ph/0607232 · pith_short_12: P4PZ3E2KWR7O · pith_short_16: P4PZ3E2KWR7OW32S · pith_short_8: P4PZ3E2K

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/P4PZ3E2KWR7OW32SQPZFW7QNGW \
  | 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: 7f1f9d934ab47eeb6f5283f25b7e0d35b99ed86cf6ca6a2dd2b8129d61783f97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae66b96d301d16b3dd454c9e32810909c2473354f433e677e4ef9630b9189e61",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2006-07-21T14:45:33Z",
    "title_canon_sha256": "60887dc45dabbd93d51fad2a4cb23a2fa3ad2ca83ba3a56c2fe919b93e0628dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0607232",
    "kind": "arxiv",
    "version": 2
  }
}