Pith Number

pith:I4WTP5H4

pith:2024:I4WTP5H4NTK5NJHDD6AWOLA7WB

not attested not anchored not stored refs pending

Circular reasoning: Solving the Hubble tension with a non-$\pi$ value of $\pi$

Andreas Nygaard, Emil Brinch Holm, Jonas El Gammal, Sven G\"unther

arxiv:2403.20219 v1 · 2024-03-29 · astro-ph.CO · hep-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I4WTP5H4NTK5NJHDD6AWOLA7WB}

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	2026-07-05T08:02:15.859642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

472d37f4fc6cd5d6a4e31f81672c1fb072f778684b85d0e90b47353217cdc882

Aliases

arxiv: 2403.20219 · arxiv_version: 2403.20219v1 · doi: 10.48550/arxiv.2403.20219 · pith_short_12: I4WTP5H4NTK5 · pith_short_16: I4WTP5H4NTK5NJHD · pith_short_8: I4WTP5H4

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/I4WTP5H4NTK5NJHDD6AWOLA7WB \
  | 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: 472d37f4fc6cd5d6a4e31f81672c1fb072f778684b85d0e90b47353217cdc882

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f60755847796753a786f95b33f0ae50d4f6c67fed6bcf8191ec51969160f58bc",
    "cross_cats_sorted": [
      "hep-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2024-03-29T15:00:12Z",
    "title_canon_sha256": "521a4884f179bec50a8222ddab4ab7cdfe687ac6751859b84e99d6949bbef767"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2403.20219",
    "kind": "arxiv",
    "version": 1
  }
}