Pith Number

pith:34GFFXPU

pith:2019:34GFFXPUGQJKZC27WAIWOAT643

not attested not anchored not stored refs pending

Ultra-thin, entirely flat, Umklapp lenses

Gregory J. Chaplain, Richard V. Craster

arxiv:1908.07797 v1 · 2019-08-21 · 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{34GFFXPUGQJKZC27WAIWOAT643}

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	2026-07-05T01:00:33.421588Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df0c52ddf43412ac8b5fb01167027ee6fcf33461def8ca14a35a045ee023aaa9

Aliases

arxiv: 1908.07797 · arxiv_version: 1908.07797v1 · doi: 10.48550/arxiv.1908.07797 · pith_short_12: 34GFFXPUGQJK · pith_short_16: 34GFFXPUGQJKZC27 · pith_short_8: 34GFFXPU

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/34GFFXPUGQJKZC27WAIWOAT643 \
  | 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: df0c52ddf43412ac8b5fb01167027ee6fcf33461def8ca14a35a045ee023aaa9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1353624b812954f16d688cfc09c38a015c6bfed72be2a5a2cb5d9d50ceebc65",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2019-08-21T11:09:27Z",
    "title_canon_sha256": "cd10754b215b9863f6b8e19e179a31147958a37f219fad1013d3591643a7ab77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07797",
    "kind": "arxiv",
    "version": 1
  }
}