Pith Number

pith:SPF76RPV

pith:2001:SPF76RPVSOM6ODI7XKLS36KPVZ

not attested not anchored not stored refs pending

Commensurate Harmonic Oscillators: Classical Symmetries

Jean-Pierre Amiet, Stefan Weigert

arxiv:math-ph/0111045 v1 · 2001-11-22 · math-ph · math.GR · 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{SPF76RPVSOM6ODI7XKLS36KPVZ}

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	2026-05-18T01:38:34.400041Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93cbff45f59399e70d1fba972df94fae491bc5d30f02b05adb59371044fc92c6

Aliases

arxiv: math-ph/0111045 · arxiv_version: math-ph/0111045v1 · doi: 10.48550/arxiv.math-ph/0111045 · pith_short_12: SPF76RPVSOM6 · pith_short_16: SPF76RPVSOM6ODI7 · pith_short_8: SPF76RPV

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/SPF76RPVSOM6ODI7XKLS36KPVZ \
  | 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: 93cbff45f59399e70d1fba972df94fae491bc5d30f02b05adb59371044fc92c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73d2eb80d658d80c8c25c610f260b05e4ad0544bd36a3ba9d7b3698b87d91880",
    "cross_cats_sorted": [
      "math.GR",
      "math.MP",
      "quant-ph"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2001-11-22T12:16:11Z",
    "title_canon_sha256": "06bc971d1de29a77bef412b3d9c58e8644a7969d6a227f97ed1fa9a65af1fd47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0111045",
    "kind": "arxiv",
    "version": 1
  }
}