Pith Number

pith:M2X2FUF4

pith:2005:M2X2FUF4TYFS6MJOGMXJYBAKOO

not attested not anchored not stored refs pending

Neutrino mass matrices, texture zeros, and family symmetries

Walter Grimus

arxiv:hep-ph/0511078 v1 · 2005-11-07 · 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{M2X2FUF4TYFS6MJOGMXJYBAKOO}

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	2026-07-04T14:51:35.058445Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66afa2d0bc9e0b2f312e332e9c040a73be581dc6341935583be1e2ab95cae1da

Aliases

arxiv: hep-ph/0511078 · arxiv_version: hep-ph/0511078v1 · doi: 10.48550/arxiv.hep-ph/0511078 · pith_short_12: M2X2FUF4TYFS · pith_short_16: M2X2FUF4TYFS6MJO · pith_short_8: M2X2FUF4

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/M2X2FUF4TYFS6MJOGMXJYBAKOO \
  | 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: 66afa2d0bc9e0b2f312e332e9c040a73be581dc6341935583be1e2ab95cae1da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "908f7ddbc69dfa0ec5065c4527aa3e7988689c424e64a3d716ac33cbd5f6ff31",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2005-11-07T16:43:21Z",
    "title_canon_sha256": "d6f2c44b930e9b1aef185a67e7e3c3367cf0e0577386e849aa478ee0b6bbbd70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0511078",
    "kind": "arxiv",
    "version": 1
  }
}