Pith Number

pith:TYQ6VPGH

pith:2019:TYQ6VPGHUSBWYCLIAY5EZRH32H

not attested not anchored not stored refs pending

Type II seesaw models with modular $A_4$ symmetry

Takaaki Nomura, Takashi Shimomura, Tatsuo Kobayashi

arxiv:1912.00637 v2 · 2019-12-02 · 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{TYQ6VPGHUSBWYCLIAY5EZRH32H}

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	2026-07-05T01:30:24.210159Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e21eabcc7a4836c0968063a4cc4fbd1f52d41053b7f0c0dd6302ddef6e6ddca

Aliases

arxiv: 1912.00637 · arxiv_version: 1912.00637v2 · doi: 10.48550/arxiv.1912.00637 · pith_short_12: TYQ6VPGHUSBW · pith_short_16: TYQ6VPGHUSBWYCLI · pith_short_8: TYQ6VPGH

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/TYQ6VPGHUSBWYCLIAY5EZRH32H \
  | 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: 9e21eabcc7a4836c0968063a4cc4fbd1f52d41053b7f0c0dd6302ddef6e6ddca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7bc2b2c09ac4c9b166fa044cdd698351dd1503a961e1ed748eba30d727b72705",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2019-12-02T08:59:02Z",
    "title_canon_sha256": "e13c8187cf11232d725dcff210048b2ef58d473e90d4a0bf0252ef43a7657824"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.00637",
    "kind": "arxiv",
    "version": 2
  }
}