Pith Number

pith:Y6DIRSUA

pith:2024:Y6DIRSUAJPURIAUTAV2WRQBKXD

not attested not anchored not stored refs pending

The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis

Chen-Kai Qiao

arxiv:2407.14035 v5 · 2024-07-19 · gr-qc · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y6DIRSUAJPURIAUTAV2WRQBKXD}

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.

Cited by

4 papers in Pith

The Flight of the Bumblebee in a Non-Commutative Geometry: A New Black Hole Solution

Photon Spheres and shadow of modified black-hole entropies

Receipt and verification

First computed	2026-07-05T10:18:39.829872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c78688ca804be9140293057568c02ab8ff90ddc405cf3b596e219e546fb27755

Aliases

arxiv: 2407.14035 · arxiv_version: 2407.14035v5 · doi: 10.48550/arxiv.2407.14035 · pith_short_12: Y6DIRSUAJPUR · pith_short_16: Y6DIRSUAJPURIAUT · pith_short_8: Y6DIRSUA

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/Y6DIRSUAJPURIAUTAV2WRQBKXD \
  | 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: c78688ca804be9140293057568c02ab8ff90ddc405cf3b596e219e546fb27755

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d46d44aa4e7d600b92b02a871ed344cccbd7bbc02c6cc1f71c7e125f5080c283",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2024-07-19T05:19:04Z",
    "title_canon_sha256": "4c6487e230bc091ddc056a618acd3db64960b8979d06220c5982e206d818028b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.14035",
    "kind": "arxiv",
    "version": 5
  }
}