Pith Number

pith:UPHSRQ3C

pith:2007:UPHSRQ3CE3KLIJEI5FJ5UO655S

not attested not anchored not stored refs pending

The quantum harmonic oscillator on the sphere and the hyperbolic plane

Jos\'e F. Cari\~nena, Manuel F. Ra\~nada, Mariano Santander

arxiv:0709.0399 v1 · 2007-09-04 · 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{UPHSRQ3CE3KLIJEI5FJ5UO655S}

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	2026-05-18T04:36:41.972838Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3cf28c36226d4b42488e953da3bddec8609ecdceb818b9d97bd65fe659953d7

Aliases

arxiv: 0709.0399 · arxiv_version: 0709.0399v1 · doi: 10.48550/arxiv.0709.0399 · pith_short_12: UPHSRQ3CE3KL · pith_short_16: UPHSRQ3CE3KLIJEI · pith_short_8: UPHSRQ3C

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/UPHSRQ3CE3KLIJEI5FJ5UO655S \
  | 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: a3cf28c36226d4b42488e953da3bddec8609ecdceb818b9d97bd65fe659953d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a838d81fca519b657c217f13379d40617866752483670a8534630c0c2f28d228",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2007-09-04T11:49:23Z",
    "title_canon_sha256": "af5f8e0233d5aaec98b698dc8eb2b76d57ede3b234a0a2aded02454809229695"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.0399",
    "kind": "arxiv",
    "version": 1
  }
}