Pith Number

pith:J3BLIA7I

pith:2011:J3BLIA7IAY2A5QQZG2UQ4TXCNO

not attested not anchored not stored refs pending

Schrodinger's Hat: Electromagnetic, acoustic and quantum amplifiers via transformation optics

Allan Greenleaf, Gunther Uhlmann, Matti Lassas, Yaroslav Kurylev

arxiv:1107.4685 v1 · 2011-07-23 · math-ph · math.AP · math.MP · physics.optics

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J3BLIA7IAY2A5QQZG2UQ4TXCNO}

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	2026-05-18T01:15:00.649174Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ec2b403e806340ec21936a90e4ee26b868db1ffb267e94b606f2186f9e57f4b

Aliases

arxiv: 1107.4685 · arxiv_version: 1107.4685v1 · doi: 10.48550/arxiv.1107.4685 · pith_short_12: J3BLIA7IAY2A · pith_short_16: J3BLIA7IAY2A5QQZ · pith_short_8: J3BLIA7I

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/J3BLIA7IAY2A5QQZG2UQ4TXCNO \
  | 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: 4ec2b403e806340ec21936a90e4ee26b868db1ffb267e94b606f2186f9e57f4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04ceef107c43b0ea12165e3bdacf9e92c82c2e0ce107674a1866e94923a0b46d",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP",
      "physics.optics"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-07-23T12:26:38Z",
    "title_canon_sha256": "32a37d5a2d68c4c6d72a2f828de8a76b84eb734fe3b8d0974868e4c45d8a74cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.4685",
    "kind": "arxiv",
    "version": 1
  }
}