Pith Number

pith:H6WICXKV

pith:2026:H6WICXKVWG2S64MEEJOCBM5LXR

not attested not anchored not stored refs pending

Static spheres in black hole spacetimes: pairing, energy conditions, and an upper bound on the innermost radius

Yong Song

arxiv:2607.20850 v1 · 2026-07-23 · 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{H6WICXKVWG2S64MEEJOCBM5LXR}

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	2026-07-24T00:23:38.109096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3fac815d55b1b52f7184225c20b3abbc4b23544034e40726bb9e3daf146a9ffe

Aliases

arxiv: 2607.20850 · arxiv_version: 2607.20850v1 · doi: 10.48550/arxiv.2607.20850 · pith_short_12: H6WICXKVWG2S · pith_short_16: H6WICXKVWG2S64ME · pith_short_8: H6WICXKV

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/H6WICXKVWG2S64MEEJOCBM5LXR \
  | 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: 3fac815d55b1b52f7184225c20b3abbc4b23544034e40726bb9e3daf146a9ffe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fde146fc19c9723f92f1a9e6e572f267613bacbe8c71b603b9cf44a61a847151",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-07-23T02:22:38Z",
    "title_canon_sha256": "36eb07237f27125b6a6fe77a8a29216a20e90628a9299febaed7acf1d5d1ba35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20850",
    "kind": "arxiv",
    "version": 1
  }
}