Pith Number

pith:F2ONEUGU

pith:2026:F2ONEUGUKOF4CF4B5BIYB5HPED

not attested not anchored not stored refs pending

Gravitational lensing time delay beyond the Shapiro/geometry split

Kfir Blum, Luca Teodori, Zhaoyu Bai

arxiv:2605.18182 v1 · 2026-05-18 · 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{F2ONEUGUKOF4CF4B5BIYB5HPED}

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	2026-05-20T00:05:49.631853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e9cd250d4538bc11781e85180f4ef20c226903ca3a305daeb78a2066b24c374

Aliases

arxiv: 2605.18182 · arxiv_version: 2605.18182v1 · doi: 10.48550/arxiv.2605.18182 · pith_short_12: F2ONEUGUKOF4 · pith_short_16: F2ONEUGUKOF4CF4B · pith_short_8: F2ONEUGU

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/F2ONEUGUKOF4CF4B5BIYB5HPED \
  | 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: 2e9cd250d4538bc11781e85180f4ef20c226903ca3a305daeb78a2066b24c374

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cfef7ad03e190348a8c1ca41b61c2da0e99220e6410c66efb297fcc22c16cb8f",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2026-05-18T10:24:25Z",
    "title_canon_sha256": "af02be4d74f1d4e9ca7539fecba6d58997e893f8b6acd1beece9adbc88620c0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18182",
    "kind": "arxiv",
    "version": 1
  }
}