Pith Number

pith:PI4FXLFS

pith:2018:PI4FXLFSTB5OULLG6HYREIZ65Y

not attested not anchored not stored refs pending

Rigorous analytical formula for freeform singlet lens design free of spherical aberration

Hector A. Chaparro-Romo, Julio C. Gutierrez-Vega, Rafael G. Gonzalez-Acu\~na

arxiv:1811.03792 v1 · 2018-11-09 · 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{PI4FXLFSTB5OULLG6HYREIZ65Y}

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	2026-05-17T23:49:40.581524Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a385bacb2987aea2d66f1f112233eee086c77c9974ce7b6dab539b11ce89f3c

Aliases

arxiv: 1811.03792 · arxiv_version: 1811.03792v1 · doi: 10.48550/arxiv.1811.03792 · pith_short_12: PI4FXLFSTB5O · pith_short_16: PI4FXLFSTB5OULLG · pith_short_8: PI4FXLFS

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/PI4FXLFSTB5OULLG6HYREIZ65Y \
  | 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: 7a385bacb2987aea2d66f1f112233eee086c77c9974ce7b6dab539b11ce89f3c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc53dea532fd98c5cbde8e23b5a998eb7f8731a1e7066ac13d8f8a60725b8135",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2018-11-09T06:33:40Z",
    "title_canon_sha256": "13711f883b668bd730f5e78459ffa10fc43ee7607f3cc812ceea0d144620863e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.03792",
    "kind": "arxiv",
    "version": 1
  }
}