Pith Number

pith:NAPUBYBO

pith:2026:NAPUBYBOMJ34RVMVGGBFISYLH3

not attested not anchored not stored refs pending

Freeze-in Warm Dark Matter via Dimension-6 Operators in 3-3-1 Models

Fujun Liu, Fuwei Liu

arxiv:2605.16465 v1 · 2026-05-15 · hep-ph · astro-ph.CO · physics.comp-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{NAPUBYBOMJ34RVMVGGBFISYLH3}

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	2026-05-20T00:02:23.428325Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

681f40e02e6277c8d5953182544b0b3efb4df0caeb0e29f28574910fafbe0035

Aliases

arxiv: 2605.16465 · arxiv_version: 2605.16465v1 · doi: 10.48550/arxiv.2605.16465 · pith_short_12: NAPUBYBOMJ34 · pith_short_16: NAPUBYBOMJ34RVMV · pith_short_8: NAPUBYBO

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/NAPUBYBOMJ34RVMVGGBFISYLH3 \
  | 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: 681f40e02e6277c8d5953182544b0b3efb4df0caeb0e29f28574910fafbe0035

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41d1932b50bfad0e76161b67633979ea7592bee0152307cc023493555757e9d8",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "physics.comp-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2026-05-15T10:37:41Z",
    "title_canon_sha256": "3e2b5fb355f999ab7c56ea23391127a05508620914beba4225c12ba56433e541"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16465",
    "kind": "arxiv",
    "version": 1
  }
}