Pith Number

pith:Z6AZF4P3

pith:2026:Z6AZF4P3PXYZNO3JRBQYKB5VCI

not attested not anchored not stored refs pending

Constraining Scale-Dependent Growth in $f(R)$ Gravity with Future 21 cm Surveys

Apurba Samanta, Bhuwan Joshi, Jess Worsley, Peter Dunsby, Saikat Chakraborty

arxiv:2606.03729 v1 · 2026-06-02 · 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{Z6AZF4P3PXYZNO3JRBQYKB5VCI}

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	2026-06-03T01:06:05.596166Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf8192f1fb7df196bb6988618507b5120bae578dcff32344dea4e94fe0ab8537

Aliases

arxiv: 2606.03729 · arxiv_version: 2606.03729v1 · doi: 10.48550/arxiv.2606.03729 · pith_short_12: Z6AZF4P3PXYZ · pith_short_16: Z6AZF4P3PXYZNO3J · pith_short_8: Z6AZF4P3

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/Z6AZF4P3PXYZNO3JRBQYKB5VCI \
  | 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: cf8192f1fb7df196bb6988618507b5120bae578dcff32344dea4e94fe0ab8537

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4338152e1891f03637677191a71343bf645f4a3938897bef24ba78c6ab997735",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2026-06-02T14:48:45Z",
    "title_canon_sha256": "4aa64cf090cbbec5cc9758d74a65553f432fc094a35b8a966494b688fc7671e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.03729",
    "kind": "arxiv",
    "version": 1
  }
}