Pith Number

pith:HOOPQ7W7

pith:2026:HOOPQ7W7EFWOYXVRO2FCQC2XCH

not attested not anchored not stored refs pending

Wallis Products from the Four-Dimensional Singular Harmonic Oscillator

Bin Ye, Lei Yin, Ruitao Chen

arxiv:2607.00340 v1 · 2026-07-01 · quant-ph · 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{HOOPQ7W7EFWOYXVRO2FCQC2XCH}

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	2026-07-02T00:18:45.194816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b9cf87edf216cec5eb1768a280b5711d1bf3f902b678af5c9c0d4912a757c3a

Aliases

arxiv: 2607.00340 · arxiv_version: 2607.00340v1 · doi: 10.48550/arxiv.2607.00340 · pith_short_12: HOOPQ7W7EFWO · pith_short_16: HOOPQ7W7EFWOYXVR · pith_short_8: HOOPQ7W7

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/HOOPQ7W7EFWOYXVRO2FCQC2XCH \
  | 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: 3b9cf87edf216cec5eb1768a280b5711d1bf3f902b678af5c9c0d4912a757c3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d51cee866bf04330a5d0532f506ee0f5dc5b48491b8ca1e114c4aad2c888cd33",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-01T02:30:15Z",
    "title_canon_sha256": "e189e8f0d7689af9f0fec31e0c46539009bf25898044777c986644626901d3ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.00340",
    "kind": "arxiv",
    "version": 1
  }
}