Pith Number

pith:4T2F4X4C

pith:2014:4T2F4X4CDMVQI3233VTI6YPCLX

not attested not anchored not stored refs pending

Analytic Solution for $PT$-Symmetric Volume Gratings

Bernard Kress, H. F. Jones, Mykola Kulishov

arxiv:1412.0506 v1 · 2014-12-01 · 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{4T2F4X4CDMVQI3233VTI6YPCLX}

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	2026-05-18T02:32:23.231745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4f45e5f821b2b046f5bdd668f61e25dff255cd23063162e294c086a73c1f334

Aliases

arxiv: 1412.0506 · arxiv_version: 1412.0506v1 · doi: 10.48550/arxiv.1412.0506 · pith_short_12: 4T2F4X4CDMVQ · pith_short_16: 4T2F4X4CDMVQI323 · pith_short_8: 4T2F4X4C

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/4T2F4X4CDMVQI3233VTI6YPCLX \
  | 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: e4f45e5f821b2b046f5bdd668f61e25dff255cd23063162e294c086a73c1f334

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12f46eebf6008234d255399a5ddde7399ad2af2cd7d1782c605d589b943294b3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2014-12-01T15:25:03Z",
    "title_canon_sha256": "406b8a65db2c285aedcc3f0ff910c1a3894878e93e4bc9564ae13fa55641093c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.0506",
    "kind": "arxiv",
    "version": 1
  }
}