Pith Number

pith:V6JHZRN5

pith:2015:V6JHZRN5GTLMOQ45RE6SNO2YJ6

not attested not anchored not stored refs pending

Aspherical lens design and imaging

Ahmad Sabra, Cristian E. Gutierrez

arxiv:1507.08237 v2 · 2015-07-29 · math.AP · math-ph · 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{V6JHZRN5GTLMOQ45RE6SNO2YJ6}

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	2026-05-18T01:19:38.674218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af927cc5bd34d6c7439d893d26bb584f83d29143dfc3ec8e66c0153e3f660e27

Aliases

arxiv: 1507.08237 · arxiv_version: 1507.08237v2 · doi: 10.48550/arxiv.1507.08237 · pith_short_12: V6JHZRN5GTLM · pith_short_16: V6JHZRN5GTLMOQ45 · pith_short_8: V6JHZRN5

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/V6JHZRN5GTLMOQ45RE6SNO2YJ6 \
  | 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: af927cc5bd34d6c7439d893d26bb584f83d29143dfc3ec8e66c0153e3f660e27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ed21306799781469438501072afecf1f4a82ad9c4cc931ceb4bbdb9984fa972",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "physics.optics"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-07-29T17:45:50Z",
    "title_canon_sha256": "5bb1d265ff971b4b3314fd96de61f05113faa8f5f309504cde1637c024ebe43f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.08237",
    "kind": "arxiv",
    "version": 2
  }
}