Pith Number

pith:TM3YWQKL

pith:2011:TM3YWQKLREF4O4OU5JMJ3LHOBQ

not attested not anchored not stored refs pending

Kinetic and mass mixing with three abelian groups

Julian Heeck, Werner Rodejohann

arxiv:1109.1508 v2 · 2011-09-07 · 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{TM3YWQKLREF4O4OU5JMJ3LHOBQ}

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

Renormalisation and invariants for two U(1)s

Receipt and verification

First computed	2026-05-18T04:09:56.015879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b378b414b890bc771d4ea589dacee0c1c12e3e13888f559fcceb39a5822c349

Aliases

arxiv: 1109.1508 · arxiv_version: 1109.1508v2 · doi: 10.48550/arxiv.1109.1508 · pith_short_12: TM3YWQKLREF4 · pith_short_16: TM3YWQKLREF4O4OU · pith_short_8: TM3YWQKL

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/TM3YWQKLREF4O4OU5JMJ3LHOBQ \
  | 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: 9b378b414b890bc771d4ea589dacee0c1c12e3e13888f559fcceb39a5822c349

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7549e6deba60699b65b6cf670781f4c00137805684ef9f08ed9b059a4efb2cb5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2011-09-07T16:37:33Z",
    "title_canon_sha256": "970637d59021c30a5c62dfa3455b3e025fa866575e3f1dd9b75911d48d38dcc4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1508",
    "kind": "arxiv",
    "version": 2
  }
}