Pith Number

pith:4NMLDUZS

pith:2021:4NMLDUZSPRS7C7GXSIN7TONOCH

not attested not anchored not stored refs pending

Modular flavor symmetry and vector-valued modular forms

Gui-Jun Ding, Xiang-Gan Liu

arxiv:2112.14761 v1 · 2021-12-29 · hep-ph · hep-th

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4NMLDUZSPRS7C7GXSIN7TONOCH}

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

Fermion mass relations in one-parameter modular models

Receipt and verification

First computed	2026-07-05T04:13:49.052770Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e358b1d3327c65f17cd7921bf9b9ae11d4a15767410e2ca5b28cd271cf490e2a

Aliases

arxiv: 2112.14761 · arxiv_version: 2112.14761v1 · doi: 10.48550/arxiv.2112.14761 · pith_short_12: 4NMLDUZSPRS7 · pith_short_16: 4NMLDUZSPRS7C7GX · pith_short_8: 4NMLDUZS

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/4NMLDUZSPRS7C7GXSIN7TONOCH \
  | 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: e358b1d3327c65f17cd7921bf9b9ae11d4a15767410e2ca5b28cd271cf490e2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ecb3b09f584c78b27a07c3f9ed7e2efe0da4b2476c3c5e25526cdb82b74f61db",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2021-12-29T18:57:42Z",
    "title_canon_sha256": "fa82473be9f54354c5a71d827e10bf9c7006cc989fb765030dac172008e978fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.14761",
    "kind": "arxiv",
    "version": 1
  }
}