Pith Number

pith:ZEFZYNPA

pith:2001:ZEFZYNPAL6JN3UJYRFXE6RBIEX

not attested not anchored not stored refs pending

On the modular invariance of mass eigenstates and CP violation

Thomas Dent (MCTP, University of Michigan)

arxiv:hep-th/0111024 v3 · 2001-11-02 · hep-th · 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{ZEFZYNPAL6JN3UJYRFXE6RBIEX}

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

Modular Invariant Models of Lepton Masses at Levels 4 and 5

Receipt and verification

First computed	2026-07-04T17:21:07.054324Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c90b9c35e05f92ddd138896e4f442825e1d9a845a79c0fd3ed323a8dc911fceb

Aliases

arxiv: hep-th/0111024 · arxiv_version: hep-th/0111024v3 · doi: 10.48550/arxiv.hep-th/0111024 · pith_short_12: ZEFZYNPAL6JN · pith_short_16: ZEFZYNPAL6JN3UJY · pith_short_8: ZEFZYNPA

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/ZEFZYNPAL6JN3UJYRFXE6RBIEX \
  | 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: c90b9c35e05f92ddd138896e4f442825e1d9a845a79c0fd3ed323a8dc911fceb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40fc5a76b4e9dcd2d279d317151e5675d63f431ce1538866d4a01f94cf46f007",
    "cross_cats_sorted": [
      "hep-ph"
    ],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "2001-11-02T20:58:10Z",
    "title_canon_sha256": "f386a4206bd23028451c18865861169f0ac900b139406a3c2c3dbdda7137d5bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/0111024",
    "kind": "arxiv",
    "version": 3
  }
}