Pith Number

pith:XXTCA4KA

pith:2025:XXTCA4KASEBHQ7K6Z3WPUYYS2P

not attested not anchored not stored refs pending

Equivalence of Optical Theorems

Edwin A. Marengo, Mohammadrasoul Taghavi

arxiv:2506.08943 v1 · 2025-06-10 · physics.optics · 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{XXTCA4KASEBHQ7K6Z3WPUYYS2P}

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	2026-07-05T11:19:15.503825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bde62071409102787d5eceecfa6312d3d14f6cda589feed22eb47e7975265906

Aliases

arxiv: 2506.08943 · arxiv_version: 2506.08943v1 · doi: 10.48550/arxiv.2506.08943 · pith_short_12: XXTCA4KASEBH · pith_short_16: XXTCA4KASEBHQ7K6 · pith_short_8: XXTCA4KA

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/XXTCA4KASEBHQ7K6Z3WPUYYS2P \
  | 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: bde62071409102787d5eceecfa6312d3d14f6cda589feed22eb47e7975265906

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb2f21b80628781643f450314ffddf0584621fa8fdede45666d4f022470ef663",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2025-06-10T16:05:37Z",
    "title_canon_sha256": "92cfc5cf7e909ed7166d325a464d0e23b309df22b6040e40c408d3c1a5aaa79d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.08943",
    "kind": "arxiv",
    "version": 1
  }
}