Pith Number

pith:QCBYKDLG

pith:2021:QCBYKDLG77KVHSQC3JYFRN6EAD

not attested not anchored not stored refs pending

The matter density PDF for modified gravity and dark energy with Large Deviations Theory

Alex Gough, Baojiu Li, Catherine Heymans, Christian Arnold, Cora Uhlemann, Matteo Cataneo

arxiv:2109.02636 v2 · 2021-09-06 · 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{QCBYKDLG77KVHSQC3JYFRN6EAD}

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	2026-07-05T04:11:07.308532Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8083850d66ffd553ca02da7058b7c400d2814750f33666b6c6d8a8e5f2fe93e0

Aliases

arxiv: 2109.02636 · arxiv_version: 2109.02636v2 · doi: 10.48550/arxiv.2109.02636 · pith_short_12: QCBYKDLG77KV · pith_short_16: QCBYKDLG77KVHSQC · pith_short_8: QCBYKDLG

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/QCBYKDLG77KVHSQC3JYFRN6EAD \
  | 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: 8083850d66ffd553ca02da7058b7c400d2814750f33666b6c6d8a8e5f2fe93e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd290126758db8dfc6b38334fad659d00b7b48a8d0b052fa9b7ad1c08e7510d8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2021-09-06T17:59:59Z",
    "title_canon_sha256": "62b03d7516d816fafd00418a25726f1bba1ff81cb2b9fa610081eea4055f1f27"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.02636",
    "kind": "arxiv",
    "version": 2
  }
}