Pith Number

pith:2VGWE2CM

pith:2026:2VGWE2CMVNMJQEWHJ37VNKLLBP

not attested not anchored not stored refs pending

From Rings to Top-Hat beams

D. S\'anchez-de-la-Llave, F. Soto-Eguibar, H. M. Moya-Cessa, I. Jul\'ian-Mac\'ias, I. Ramos-Prieto, M. A. J\'acome-Silva, U. Ru\'iz-Corona

arxiv:2606.11610 v1 · 2026-06-10 · 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{2VGWE2CMVNMJQEWHJ37VNKLLBP}

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	2026-06-11T01:09:58.935803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d54d62684cab589812c74eff56a96b0bceebffac9f8b530fe7799bd1c9d21973

Aliases

arxiv: 2606.11610 · arxiv_version: 2606.11610v1 · doi: 10.48550/arxiv.2606.11610 · pith_short_12: 2VGWE2CMVNMJ · pith_short_16: 2VGWE2CMVNMJQEWH · pith_short_8: 2VGWE2CM

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/2VGWE2CMVNMJQEWHJ37VNKLLBP \
  | 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: d54d62684cab589812c74eff56a96b0bceebffac9f8b530fe7799bd1c9d21973

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75e9f78aa9d2bb7a49a0a2417254d9bb40b98b4f5d8ad224681e2f9aae8f2ae0",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2026-06-10T03:21:32Z",
    "title_canon_sha256": "43adf435a85858ed1aa8dd2f68faf2440b89b1d61c8f3f426e8065c6711b76ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.11610",
    "kind": "arxiv",
    "version": 1
  }
}