Pith Number

pith:YTLILS2J

pith:2026:YTLILS2JN4KXRRUSITJZKWT6JP

not attested not anchored not stored refs pending

Engineering classical waves with quantized energy spectra in periodic media

Arnaud Lazarus, Georgi Gary Rozenman, John W. M. Bush

arxiv:2606.09695 v1 · 2026-06-08 · 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{YTLILS2JN4KXRRUSITJZKWT6JP}

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	2026-06-09T02:09:04.287960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4d685cb496f1578c69244d3955a7e4be398fbf9494131f82240ecd9af59989f

Aliases

arxiv: 2606.09695 · arxiv_version: 2606.09695v1 · doi: 10.48550/arxiv.2606.09695 · pith_short_12: YTLILS2JN4KX · pith_short_16: YTLILS2JN4KXRRUS · pith_short_8: YTLILS2J

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/YTLILS2JN4KXRRUSITJZKWT6JP \
  | 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: c4d685cb496f1578c69244d3955a7e4be398fbf9494131f82240ecd9af59989f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c733da537f064e3c35e45bfc9c94d4029ecb1fd86b95ce803e607fbda8d0c93b",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-06-08T16:16:53Z",
    "title_canon_sha256": "905713b176e26cae4153f8c7bc916c01cf9d1acfe4dd2aac0570ffbd6f151ef7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.09695",
    "kind": "arxiv",
    "version": 1
  }
}