Pith Number

pith:TPZRPCQ3

pith:2026:TPZRPCQ3Z6SZJAFOMYJRJNJCHX

not attested not anchored not stored refs pending

Dark matter imprints on a caustic encounter in an effective spinning black hole binary lens

Mohsen Fathi

arxiv:2607.23300 v1 · 2026-07-25 · gr-qc · astro-ph.HE

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TPZRPCQ3Z6SZJAFOMYJRJNJCHX}

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	2026-07-28T01:22:46.735670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bf3178a1bcfa59480ae661314b5223deeb9aad0038936be73daf8a6162cd2d2

Aliases

arxiv: 2607.23300 · arxiv_version: 2607.23300v1 · doi: 10.48550/arxiv.2607.23300 · pith_short_12: TPZRPCQ3Z6SZ · pith_short_16: TPZRPCQ3Z6SZJAFO · pith_short_8: TPZRPCQ3

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/TPZRPCQ3Z6SZJAFOMYJRJNJCHX \
  | 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: 9bf3178a1bcfa59480ae661314b5223deeb9aad0038936be73daf8a6162cd2d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58db95f8d0d40ce7afd1784005340ec8cee09ebe475e0358d6cd0ead8ef763a1",
    "cross_cats_sorted": [
      "astro-ph.HE"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-07-25T17:21:33Z",
    "title_canon_sha256": "46a0e610ff759366765c74006d27e3da454fd3385f550dc0200786b05d888c5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.23300",
    "kind": "arxiv",
    "version": 1
  }
}