Pith Number

pith:BIWR7WF4

pith:2026:BIWR7WF43UHFO3FTI7BJNWOPSQ

not attested not anchored not stored refs pending

Fermion mass relations in one-parameter modular models

J. T. Penedo, Omar Medina, Salvador Centelles Chuli\'a, Xiang-Gan Liu, Xueqi Li

arxiv:2606.25027 v1 · 2026-06-23 · 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{BIWR7WF43UHFO3FTI7BJNWOPSQ}

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	2026-06-25T00:18:15.219681Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a2d1fd8bcdd0e576cb347c296d9cf940118b1115626c0083f7eb94a23632e39

Aliases

arxiv: 2606.25027 · arxiv_version: 2606.25027v1 · doi: 10.48550/arxiv.2606.25027 · pith_short_12: BIWR7WF43UHF · pith_short_16: BIWR7WF43UHFO3FT · pith_short_8: BIWR7WF4

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/BIWR7WF43UHFO3FTI7BJNWOPSQ \
  | 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: 0a2d1fd8bcdd0e576cb347c296d9cf940118b1115626c0083f7eb94a23632e39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "661a8d640d3504a80c3b1178a8866489edc61fe0fe8866dfe7cfb36122e06183",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2026-06-23T18:00:02Z",
    "title_canon_sha256": "f2ed405c1a17cc1bdfa44582b34329bd358e6666a1b764d3fb14193bb96b9ee2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.25027",
    "kind": "arxiv",
    "version": 1
  }
}