Pith Number

pith:PXWI4CTG

pith:2026:PXWI4CTGFSZ5HUEE7PCMVKX6VJ

not attested not anchored not stored refs pending

Bending the Rules of Propagation: Caustic Beamforming for Next-Generation Wireless Systems

Robert Schober, Shicong Liu, Xianghao Yu

arxiv:2606.12321 v1 · 2026-06-10 · eess.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PXWI4CTGFSZ5HUEE7PCMVKX6VJ}

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	2026-06-11T01:11:01.687969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7dec8e0a662cb3d3d084fbc4caaafeaa57fb9570d06a7eca31f751efb50d1321

Aliases

arxiv: 2606.12321 · arxiv_version: 2606.12321v1 · doi: 10.48550/arxiv.2606.12321 · pith_short_12: PXWI4CTGFSZ5 · pith_short_16: PXWI4CTGFSZ5HUEE · pith_short_8: PXWI4CTG

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/PXWI4CTGFSZ5HUEE7PCMVKX6VJ \
  | 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: 7dec8e0a662cb3d3d084fbc4caaafeaa57fb9570d06a7eca31f751efb50d1321

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4778b731857edd5c7379958f2575a58613cba3ea079f2fc4e11627221f7ffcc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "eess.SP",
    "submitted_at": "2026-06-10T16:55:56Z",
    "title_canon_sha256": "fa15d9e5b8890a41459806a3595e43a8a956ccc882401128ef8e15f08db46543"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12321",
    "kind": "arxiv",
    "version": 1
  }
}