Pith Number

pith:A3XPVCJX

pith:2025:A3XPVCJXQ6Y2QFSHKIOG5AQT2P

not attested not anchored not stored refs pending

Complex-frequency superlensing faces intrinsic limitations

Philippe Lalanne, Tong Wu

arxiv:2508.10742 v4 · 2025-08-14 · physics.optics · physics.class-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A3XPVCJXQ6Y2QFSHKIOG5AQT2P}

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	2026-05-29T02:05:35.793738Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06eefa893787b1a81647521c6e8213d3febb503477ad4b11ebef5b8b485d781c

Aliases

arxiv: 2508.10742 · arxiv_version: 2508.10742v4 · doi: 10.48550/arxiv.2508.10742 · pith_short_12: A3XPVCJXQ6Y2 · pith_short_16: A3XPVCJXQ6Y2QFSH · pith_short_8: A3XPVCJX

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/A3XPVCJXQ6Y2QFSHKIOG5AQT2P \
  | 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: 06eefa893787b1a81647521c6e8213d3febb503477ad4b11ebef5b8b485d781c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe350b02697597d114c93d9cc504239fe6cab6ee23e2ad0fd05756f4aafea5ca",
    "cross_cats_sorted": [
      "physics.class-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2025-08-14T15:28:02Z",
    "title_canon_sha256": "d264c18ec2cc829154e75aded5cac2fb8c27c12b563bbfcd68b378c08aabb7a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.10742",
    "kind": "arxiv",
    "version": 4
  }
}