Pith Number

pith:REKW4BH7

pith:2019:REKW4BH7UIAKSCITDFI5VAR23W

not attested not anchored not stored refs pending

Modular symmetry origin of texture zeros and quark lepton unification

Gui-Jun Ding, Jun-Nan Lu, Xiang-Gan Liu

arxiv:1912.07573 v2 · 2019-12-16 · 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{REKW4BH7UIAKSCITDFI5VAR23W}

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	2026-07-05T03:18:23.733552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89156e04ffa200a909131951da823add9af826ed857685a5ca5fb7f42d6b5ac0

Aliases

arxiv: 1912.07573 · arxiv_version: 1912.07573v2 · doi: 10.48550/arxiv.1912.07573 · pith_short_12: REKW4BH7UIAK · pith_short_16: REKW4BH7UIAKSCIT · pith_short_8: REKW4BH7

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/REKW4BH7UIAKSCITDFI5VAR23W \
  | 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: 89156e04ffa200a909131951da823add9af826ed857685a5ca5fb7f42d6b5ac0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bb0a3fd91c1f135cc1d4758f2f668b697357fdc41377635ee38dba6470d9f97",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2019-12-16T18:36:40Z",
    "title_canon_sha256": "e4d4c32c08e8257f8819996f492e17c9ad701492813d15fd00fe1fa862779580"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.07573",
    "kind": "arxiv",
    "version": 2
  }
}