Pith Number

pith:TFXKNQSS

pith:2021:TFXKNQSSND7ATUROOWIPTRHHRX

not attested not anchored not stored refs pending

Modular Invariant Dynamics and Fermion Mass Hierarchies around $\tau = i$

Andrea Romanino, Arsenii Titov, Ferruccio Feruglio, Valerio Gherardi

arxiv:2101.08718 v2 · 2021-01-21 · 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{TFXKNQSSND7ATUROOWIPTRHHRX}

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

4 papers in Pith

Fermion mass relations in one-parameter modular models

Finite modular Coleman-Weinberg inflation

Quark hierarchies and CP violation from the Siegel modular group

Predictions of Modular Symmetry Fixed Points on Neutrino Masses, Mixing, and Leptogenesis

Receipt and verification

First computed	2026-07-05T02:43:32.503261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

996ea6c25268fe09d22e7590f9c4e78dfd1f18010265803bc1c8373f0acc3e85

Aliases

arxiv: 2101.08718 · arxiv_version: 2101.08718v2 · doi: 10.48550/arxiv.2101.08718 · pith_short_12: TFXKNQSSND7A · pith_short_16: TFXKNQSSND7ATURO · pith_short_8: TFXKNQSS

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/TFXKNQSSND7ATUROOWIPTRHHRX \
  | 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: 996ea6c25268fe09d22e7590f9c4e78dfd1f18010265803bc1c8373f0acc3e85

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d00fdbfa467c0c37f96ba5e473125b94ab67f855ba4ad71732ea5d54d82e568",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2021-01-21T16:57:33Z",
    "title_canon_sha256": "da370f91d09b9e0375556b2b56c3a4a92d8c205528bab974364e8f4e477499c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2101.08718",
    "kind": "arxiv",
    "version": 2
  }
}