Pith Number

pith:WRPI32OF

pith:2026:WRPI32OFFNQUJDFXIK2RO7WRFD

not attested not anchored not stored refs pending

The cosmic tetrarchy: four estimators breaking the assumption degeneracy in cosmological distance tensions

Domenico Sapone, Matteo Martinelli

arxiv:2606.16844 v2 · 2026-06-15 · 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{WRPI32OFFNQUJDFXIK2RO7WRFD}

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	2026-06-30T02:18:09.706132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b45e8de9c52b61448cb742b5177ed128fc142b0b6b73cc88649605ad2be0d428

Aliases

arxiv: 2606.16844 · arxiv_version: 2606.16844v2 · doi: 10.48550/arxiv.2606.16844 · pith_short_12: WRPI32OFFNQU · pith_short_16: WRPI32OFFNQUJDFX · pith_short_8: WRPI32OF

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/WRPI32OFFNQUJDFXIK2RO7WRFD \
  | 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: b45e8de9c52b61448cb742b5177ed128fc142b0b6b73cc88649605ad2be0d428

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ef36364414bc628176f581f44f0ce877381f29a72c282309ecffba068c78535",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2026-06-15T15:22:34Z",
    "title_canon_sha256": "fdf33192432862fdef267a6b40555587a1d1f3d30c1960a82225194463e839a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.16844",
    "kind": "arxiv",
    "version": 2
  }
}