Pith Number

pith:2UNZQVC2

pith:2014:2UNZQVC2OFGQJS7EYG647EQRY2

not attested not anchored not stored refs pending

Partially strong transparency conditions and a singular localization method in geometric optics

Yong Lu, Zhifei Zhang

arxiv:1412.7787 v4 · 2014-12-25 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2UNZQVC2OFGQJS7EYG647EQRY2}

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	2026-05-18T01:17:53.159812Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d51b98545a714d04cbe4c1bdcf9211c68b5816b3cab8530b945b663b3f6776d7

Aliases

arxiv: 1412.7787 · arxiv_version: 1412.7787v4 · doi: 10.48550/arxiv.1412.7787 · pith_short_12: 2UNZQVC2OFGQ · pith_short_16: 2UNZQVC2OFGQJS7E · pith_short_8: 2UNZQVC2

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/2UNZQVC2OFGQJS7EYG647EQRY2 \
  | 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: d51b98545a714d04cbe4c1bdcf9211c68b5816b3cab8530b945b663b3f6776d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85890ca31c235b6e75585103766fe6ad5351936f133d27c696cddc59c6af7932",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-12-25T05:23:39Z",
    "title_canon_sha256": "66bcc63a8d901f9eaf861ca9338811d8bc200c78b2ec4ee1b4d9ab3a4abb0456"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.7787",
    "kind": "arxiv",
    "version": 4
  }
}