Pith Number

pith:767CMNHT

pith:2013:767CMNHT2AJPRDIQYHTMGX7MJW

not attested not anchored not stored refs pending

On the inverse to the harmonic oscillator

Joachim Toft, Luigi Rodino, Marco Cappiello

arxiv:1306.6866 v4 · 2013-06-28 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{767CMNHT2AJPRDIQYHTMGX7MJW}

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	2026-05-18T02:50:32.455536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffbe2634f3d012f88d10c1e6c35fec4d969094c5b3b3e6655d1e3e55b49869eb

Aliases

arxiv: 1306.6866 · arxiv_version: 1306.6866v4 · doi: 10.48550/arxiv.1306.6866 · pith_short_12: 767CMNHT2AJP · pith_short_16: 767CMNHT2AJPRDIQ · pith_short_8: 767CMNHT

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/767CMNHT2AJPRDIQYHTMGX7MJW \
  | 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: ffbe2634f3d012f88d10c1e6c35fec4d969094c5b3b3e6655d1e3e55b49869eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7ca12079c34e98f8fe2b33661e8e90a01754d9283b9cec19c16c6d993e51d70",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-06-28T15:12:09Z",
    "title_canon_sha256": "3bcd6752fb697f3b15a3202961e0381afc8f4594ec8274be7ec72022e6238c08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.6866",
    "kind": "arxiv",
    "version": 4
  }
}