Pith Number

pith:K6ZXSE74

pith:2026:K6ZXSE74BU3U4EZIPPWOGDREI4

not attested not anchored not stored refs pending

Geodesic Focusing Conditions in $f(Q)$ Gravity

Chao-Qiang Geng, Chunhui Liu, Jianhui Qiu, Ling-Wei Luo

arxiv:2606.27532 v1 · 2026-06-25 · 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{K6ZXSE74BU3U4EZIPPWOGDREI4}

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	2026-06-29T00:14:09.223349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57b37913fc0d374e13287bece30e244714e3e1ec9cf8cbd21ec1d2335611fe4d

Aliases

arxiv: 2606.27532 · arxiv_version: 2606.27532v1 · doi: 10.48550/arxiv.2606.27532 · pith_short_12: K6ZXSE74BU3U · pith_short_16: K6ZXSE74BU3U4EZI · pith_short_8: K6ZXSE74

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/K6ZXSE74BU3U4EZIPPWOGDREI4 \
  | 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: 57b37913fc0d374e13287bece30e244714e3e1ec9cf8cbd21ec1d2335611fe4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61555949abb3dc5d124b5d51742d449eb9dcffb5c93fc269e693451e7c60edba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-06-25T20:27:44Z",
    "title_canon_sha256": "783c83e0e570dcecb1ba250576f4d749e299b47dd5308c6c99225e3e7296e52a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.27532",
    "kind": "arxiv",
    "version": 1
  }
}