Pith Number

pith:XJRFTEYR

pith:2025:XJRFTEYRECOHFCTMNSZE6APSLO

not attested not anchored not stored refs pending

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma

Torben C. Frost

arxiv:2508.00624 v1 · 2025-08-01 · 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{XJRFTEYRECOHFCTMNSZE6APSLO}

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	2026-05-21T01:04:15.608887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba62599311209c728a6c6cb24f01f25bb4d9d0a7dc96355c7da81d2dfe783c38

Aliases

arxiv: 2508.00624 · arxiv_version: 2508.00624v1 · doi: 10.48550/arxiv.2508.00624 · pith_short_12: XJRFTEYRECOH · pith_short_16: XJRFTEYRECOHFCTM · pith_short_8: XJRFTEYR

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/XJRFTEYRECOHFCTMNSZE6APSLO \
  | 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: ba62599311209c728a6c6cb24f01f25bb4d9d0a7dc96355c7da81d2dfe783c38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9a128bf5785e99bba48fed2555b580fc36ccb3b3639cf38f39dcb3663004549",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2025-08-01T13:34:43Z",
    "title_canon_sha256": "aa1e2cdcf98b1ae24cf05f6ce31fd8f7522ab2f950760a4d48a5c3f29a533315"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.00624",
    "kind": "arxiv",
    "version": 1
  }
}