Pith Number

pith:4RRBK5TU

pith:2016:4RRBK5TUXIGKN3BH5XRKSXXXEL

not attested not anchored not stored refs pending

Defects of liquid crystals with variable degree of orientation

Fang-Hua Lin, Onur Alper, Robert Hardt

arxiv:1610.06592 v2 · 2016-10-20 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4RRBK5TUXIGKN3BH5XRKSXXXEL}

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	2026-05-18T00:31:56.100417Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e462157674ba0ca6ec27ede2a95ef722da36626e1c72f8950405fd921e043bd7

Aliases

arxiv: 1610.06592 · arxiv_version: 1610.06592v2 · doi: 10.48550/arxiv.1610.06592 · pith_short_12: 4RRBK5TUXIGK · pith_short_16: 4RRBK5TUXIGKN3BH · pith_short_8: 4RRBK5TU

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/4RRBK5TUXIGKN3BH5XRKSXXXEL \
  | 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: e462157674ba0ca6ec27ede2a95ef722da36626e1c72f8950405fd921e043bd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37dc90b87566539d336b430f38ead2e9e46a413f3e6ac4f5879b637cc606e79e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-10-20T20:08:20Z",
    "title_canon_sha256": "45de770d3d2dc568a19bb620d2f7ef8117dd19ff60c1b0156d90a9ec58a91e9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.06592",
    "kind": "arxiv",
    "version": 2
  }
}