Pith Number

pith:4KJMDZOW

pith:2026:4KJMDZOWVH4R2Z232SZ6NL6UOY

not attested not anchored not stored refs pending

Nonlinear growth and amplification of phase-transition gravitational waves induced by cosmic expansion

Chi Tian, Csaba Bal\'azs, Xiao Wang

arxiv:2606.31571 v1 · 2026-06-30 · hep-ph · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4KJMDZOWVH4R2Z232SZ6NL6UOY}

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	2026-07-01T01:18:07.986144Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e292c1e5d6a9f91d675bd4b3e6afd47621b85569aac1b9f5358fbe704dca58d9

Aliases

arxiv: 2606.31571 · arxiv_version: 2606.31571v1 · doi: 10.48550/arxiv.2606.31571 · pith_short_12: 4KJMDZOWVH4R · pith_short_16: 4KJMDZOWVH4R2Z23 · pith_short_8: 4KJMDZOW

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/4KJMDZOWVH4R2Z232SZ6NL6UOY \
  | 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: e292c1e5d6a9f91d675bd4b3e6afd47621b85569aac1b9f5358fbe704dca58d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb8d4f8b624b6bf9396638a57a3ef810e1a855e9c0b1dbb9674986ab48afabe1",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2026-06-30T12:29:39Z",
    "title_canon_sha256": "20ddf8919153403ad731fd301a85bc0fd329bf970ea17b8a866ebabd55cfe817"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31571",
    "kind": "arxiv",
    "version": 1
  }
}