Pith Number

pith:D4U3P7VA

pith:2026:D4U3P7VA42Z7PA7CGB7ZEPLUDH

not attested not anchored not stored refs pending

Biased tracers, Hybrid Effective Field Theory and Modified Gravity

Baojiu Li, Guilherme Brando, Kazuya Koyama

arxiv:2606.03860 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{D4U3P7VA42Z7PA7CGB7ZEPLUDH}

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	2026-06-03T02:06:04.490683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f29b7fea0e6b3f783e2307f923d7419f9e3dda0fd13f1620816cf9f47dd4f8a

Aliases

arxiv: 2606.03860 · arxiv_version: 2606.03860v1 · doi: 10.48550/arxiv.2606.03860 · pith_short_12: D4U3P7VA42Z7 · pith_short_16: D4U3P7VA42Z7PA7C · pith_short_8: D4U3P7VA

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/D4U3P7VA42Z7PA7CGB7ZEPLUDH \
  | 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: 1f29b7fea0e6b3f783e2307f923d7419f9e3dda0fd13f1620816cf9f47dd4f8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b9ce402f9f3bf7f073a3602d7e5110c6bf3b94c70eb407ac0ad2ed69f453ce8",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2026-06-02T16:34:38Z",
    "title_canon_sha256": "242b110d8c2ce54a29c25df3070422cea40cdd7d8fd59ae5508737ff579cf306"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.03860",
    "kind": "arxiv",
    "version": 1
  }
}