Pith Number

pith:QBI2LBNV

pith:2026:QBI2LBNVVVYCUVFZVOW3ZL7KDN

not attested not anchored not stored refs pending

A model-independent test of the cosmic distance-duality relation using galaxy clusters and Type Ia supernovae matched pairs

Jian Hu, Jian-Ping Hu, Yi Liu, Zhongmu Li

arxiv:2605.16084 v1 · 2026-05-15 · 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{QBI2LBNVVVYCUVFZVOW3ZL7KDN}

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	2026-05-20T00:01:51.968846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8051a585b5ad702a54b9abadbcafea1b64d26d888fabaf7b7a02624a7db55ed0

Aliases

arxiv: 2605.16084 · arxiv_version: 2605.16084v1 · doi: 10.48550/arxiv.2605.16084 · pith_short_12: QBI2LBNVVVYC · pith_short_16: QBI2LBNVVVYCUVFZ · pith_short_8: QBI2LBNV

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/QBI2LBNVVVYCUVFZVOW3ZL7KDN \
  | 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: 8051a585b5ad702a54b9abadbcafea1b64d26d888fabaf7b7a02624a7db55ed0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cbfd6f15090a12eaaa0703577aedfb1dce72ab4bd2b5d19d9204521fa6700487",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2026-05-15T15:45:13Z",
    "title_canon_sha256": "548ceed36e69f4cd2c0c470cb7741a09cbf45a6a8def87a7cecd8e6fcb37015f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16084",
    "kind": "arxiv",
    "version": 1
  }
}