Pith Number

pith:CIQFGERG

pith:2026:CIQFGERGDL5GT3JV4KG3K4UWD2

not attested not anchored not stored refs pending

Probing Dark Matter Substructure with Wave-Optics Distortions of Strongly Lensed LISA Gravitational Waves

Jieci Wang, Kai Liao, Marek Biesiada, Tonghua Liu

arxiv:2607.22787 v1 · 2026-07-24 · astro-ph.CO · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CIQFGERGDL5GT3JV4KG3K4UWD2}

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	2026-07-28T00:21:54.309700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12205312261afa69ed35e28db572961ebd8b846a20a314642341b91bcda27773

Aliases

arxiv: 2607.22787 · arxiv_version: 2607.22787v1 · doi: 10.48550/arxiv.2607.22787 · pith_short_12: CIQFGERGDL5G · pith_short_16: CIQFGERGDL5GT3JV · pith_short_8: CIQFGERG

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/CIQFGERGDL5GT3JV4KG3K4UWD2 \
  | 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: 12205312261afa69ed35e28db572961ebd8b846a20a314642341b91bcda27773

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ef3c38f3fc1d4268d71f2b9268df065cabade05a09ac58c8d61ecd10fa317b6",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2026-07-24T12:25:13Z",
    "title_canon_sha256": "78c2bdd8fde8a03261f458382c5348d5290cafda83ce7933a924344eec4be7af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.22787",
    "kind": "arxiv",
    "version": 1
  }
}