Pith Number

pith:R72GQM7E

pith:2007:R72GQM7EVVZ2BWJQAPVJ5N3VST

not attested not anchored not stored refs pending

A categorical framework for the quantum harmonic oscillator

Jamie Vicary

arxiv:0706.0711 v2 · 2007-06-05 · quant-ph · math-ph · math.CT · 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{R72GQM7EVVZ2BWJQAPVJ5N3VST}

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	2026-05-18T03:45:11.022292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ff46833e4ad73a0d93003ea9eb77594f8701481857b248cc2498edc990dec94

Aliases

arxiv: 0706.0711 · arxiv_version: 0706.0711v2 · doi: 10.48550/arxiv.0706.0711 · pith_short_12: R72GQM7EVVZ2 · pith_short_16: R72GQM7EVVZ2BWJQ · pith_short_8: R72GQM7E

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/R72GQM7EVVZ2BWJQAPVJ5N3VST \
  | 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: 8ff46833e4ad73a0d93003ea9eb77594f8701481857b248cc2498edc990dec94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c64f5398989ff5a2e9d78efb11cca576ac54ea1e53388c975325520d3f64942",
    "cross_cats_sorted": [
      "math-ph",
      "math.CT",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2007-06-05T18:26:40Z",
    "title_canon_sha256": "240edc573e22ea15ba2e13b4d33cfae05b5d8c84d24c74b41138801949c14722"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0706.0711",
    "kind": "arxiv",
    "version": 2
  }
}