Pith Number

pith:5WJCNHZG

pith:2026:5WJCNHZGFU46GBTRGXSFROL54K

not attested not anchored not stored refs pending

The 2D Ray Tracing Problem using ABCD Lenses and Mirrors is Turing Complete

Andreas Jakoby, Christian Schindelhauer, Rosemary U. Adejoh, Sneha Mohanty

arxiv:2606.24218 v1 · 2026-06-23 · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5WJCNHZGFU46GBTRGXSFROL54K}

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	2026-06-24T01:14:46.710981Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed92269f262d39e3067135e458b97de294878dda371b972ac2252f795cb0bd8f

Aliases

arxiv: 2606.24218 · arxiv_version: 2606.24218v1 · doi: 10.48550/arxiv.2606.24218 · pith_short_12: 5WJCNHZGFU46 · pith_short_16: 5WJCNHZGFU46GBTR · pith_short_8: 5WJCNHZG

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/5WJCNHZGFU46GBTRGXSFROL54K \
  | 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: ed92269f262d39e3067135e458b97de294878dda371b972ac2252f795cb0bd8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d235f32aec6f3f1965abbc15d63134eecafc4695f87fbb0b6ae2baf8416d39c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2026-06-23T07:06:02Z",
    "title_canon_sha256": "29cc2d65d1729cc4213939b3a7b8e9c1200887b191fc7ceefb1388464a075859"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24218",
    "kind": "arxiv",
    "version": 1
  }
}