Pith Number

pith:W4TGL6TM

pith:2017:W4TGL6TMZBX7TI7OZGWWSDYR7Z

not attested not anchored not stored refs pending

Wallis formula from the harmonic oscillator

Ignacio Cortese, J. Antonio Garc\'ia

arxiv:1709.01214 v2 · 2017-09-05 · math-ph · hep-th · math.MP · quant-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{W4TGL6TMZBX7TI7OZGWWSDYR7Z}

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.

Cited by

3 papers in Pith

Wallis Products from the Four-Dimensional Singular Harmonic Oscillator

Quantum Realization of the Wallis Formula

Emergence of $\pi$ from Equatorial Quantum Localization

Receipt and verification

First computed	2026-05-18T00:21:25.443030Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b72665fa6cc86ff9a3eec9ad690f11fe74a2d6f4fc65a3a1e5da0640a1217e3b

Aliases

arxiv: 1709.01214 · arxiv_version: 1709.01214v2 · doi: 10.48550/arxiv.1709.01214 · pith_short_12: W4TGL6TMZBX7 · pith_short_16: W4TGL6TMZBX7TI7O · pith_short_8: W4TGL6TM

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/W4TGL6TMZBX7TI7OZGWWSDYR7Z \
  | 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: b72665fa6cc86ff9a3eec9ad690f11fe74a2d6f4fc65a3a1e5da0640a1217e3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed3cd8c3f811de184320060aeaf9d45af4da4220951b418793ecbb4afc06d6a3",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2017-09-05T02:02:02Z",
    "title_canon_sha256": "2da5db2bde003729fbb686a099024155787e281dfd93780e58ef503881228fcb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.01214",
    "kind": "arxiv",
    "version": 2
  }
}