Pith Number

pith:RX7SEAFH

pith:2009:RX7SEAFH256ZX4CFMRHZIOTQPX

not attested not anchored not stored refs pending

Geometric phases in astigmatic optical modes of arbitrary order

Gerard Nienhuis, Steven J. M. Habraken

arxiv:0912.1732 v2 · 2009-12-09 · physics.optics · math-ph · math.MP · quant-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{RX7SEAFH256ZX4CFMRHZIOTQPX}

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	2026-05-18T03:18:06.634132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8dff2200a7d77d9bf045644f943a707dd1e59b4590d80eda8d3219b5287823d6

Aliases

arxiv: 0912.1732 · arxiv_version: 0912.1732v2 · doi: 10.48550/arxiv.0912.1732 · pith_short_12: RX7SEAFH256Z · pith_short_16: RX7SEAFH256ZX4CF · pith_short_8: RX7SEAFH

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/RX7SEAFH256ZX4CFMRHZIOTQPX \
  | 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: 8dff2200a7d77d9bf045644f943a707dd1e59b4590d80eda8d3219b5287823d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fbc2f63ba24656fa47d2bdd3a451ecfff274bf5fdb819160a9142f696081560",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2009-12-09T20:47:31Z",
    "title_canon_sha256": "07c2d8958726295482af7f3e88f1bfeb3c699cba0a5c9135aa6712549780a053"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.1732",
    "kind": "arxiv",
    "version": 2
  }
}