Pith Number

pith:7R7YSCUE

pith:2026:7R7YSCUEXPI3DE2T3NVK2ZQFLM

not attested not anchored not stored refs pending

A Unified Framework for Virtual Wave Transform: From Generalized Formulation to Excitation-Specific Projection

Julien Lecompagnon, Mathias Ziegler, Pengfei Zhu, Philipp Daniel Hirsch

arxiv:2606.08747 v1 · 2026-06-07 · math-ph · math.MP · physics.app-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7R7YSCUEXPI3DE2T3NVK2ZQFLM}

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	2026-06-09T02:07:36.994419Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc7f890a84bbd1b19353db6aad66055b0915926c34445ceb620fb79fd2c41c5f

Aliases

arxiv: 2606.08747 · arxiv_version: 2606.08747v1 · doi: 10.48550/arxiv.2606.08747 · pith_short_12: 7R7YSCUEXPI3 · pith_short_16: 7R7YSCUEXPI3DE2T · pith_short_8: 7R7YSCUE

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/7R7YSCUEXPI3DE2T3NVK2ZQFLM \
  | 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: fc7f890a84bbd1b19353db6aad66055b0915926c34445ceb620fb79fd2c41c5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "317beb5cc294219d3a41330082cbbe8e209823b8b948fe843aa1dc4e60b8b8bc",
    "cross_cats_sorted": [
      "math.MP",
      "physics.app-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-06-07T17:37:25Z",
    "title_canon_sha256": "a7102ff9d039e54111bc05081aa6e2188fc10517b762246e8531558ba9e8137b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08747",
    "kind": "arxiv",
    "version": 1
  }
}