Pith Number

pith:ZRF2XTPN

pith:2007:ZRF2XTPNSUWC4BK4Z2NVDZELCR

not attested not anchored not stored refs pending

The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature

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

arxiv:0709.2572 v1 · 2007-09-17 · math-ph · math.DG · 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{ZRF2XTPNSUWC4BK4Z2NVDZELCR}

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	2026-05-18T02:25:40.673291Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc4babcded952c2e055cce9b51e48b147c6e71ec89dffae104d6e111cc623f73

Aliases

arxiv: 0709.2572 · arxiv_version: 0709.2572v1 · doi: 10.48550/arxiv.0709.2572 · pith_short_12: ZRF2XTPNSUWC · pith_short_16: ZRF2XTPNSUWC4BK4 · pith_short_8: ZRF2XTPN

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/ZRF2XTPNSUWC4BK4Z2NVDZELCR \
  | 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: cc4babcded952c2e055cce9b51e48b147c6e71ec89dffae104d6e111cc623f73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef56346d3f6b9d9f7fca985c6629d150f126d09e378ba1751be6786e85c0c651",
    "cross_cats_sorted": [
      "math.DG",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2007-09-17T09:55:19Z",
    "title_canon_sha256": "b06eaf92933fd0d0264fa48afd8fec171f3ebcc740f7c2e954d6dd459c6b5a9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.2572",
    "kind": "arxiv",
    "version": 1
  }
}