Pith Number

pith:PPWX6CEF

pith:2026:PPWX6CEFDV3JE7RX3IKKPACL3J

not attested not anchored not stored refs pending

As Cold as a Black Hole: Extended Photon Spheres

Marcos Riojas

arxiv:2606.30798 v1 · 2026-06-29 · hep-th · 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{PPWX6CEFDV3JE7RX3IKKPACL3J}

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	2026-07-01T00:17:17.216695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bed7f08851d76927e37da14a7804bda7e7d891a7d629786b8395af6956c4709

Aliases

arxiv: 2606.30798 · arxiv_version: 2606.30798v1 · doi: 10.48550/arxiv.2606.30798 · pith_short_12: PPWX6CEFDV3J · pith_short_16: PPWX6CEFDV3JE7RX · pith_short_8: PPWX6CEF

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/PPWX6CEFDV3JE7RX3IKKPACL3J \
  | 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: 7bed7f08851d76927e37da14a7804bda7e7d891a7d629786b8395af6956c4709

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95348794974ffbf7e7d6924d00d42c84d26047fcc6a3c5debcbdd76b10c66750",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2026-06-29T18:21:55Z",
    "title_canon_sha256": "357fac2dcb1439b0e46aef4ea74108aa364d57cefeb1ed3e45fdf2afaa0d6060"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30798",
    "kind": "arxiv",
    "version": 1
  }
}