Pith Number

pith:5Z2JKNHG

pith:2026:5Z2JKNHGVVMY6JL72IL2ZA6H5H

not attested not anchored not stored refs pending

Affine Extension of the Free-Particle--Oscillator--Inverted-Oscillator Triangle

Andrey Alcala, Mikhail S. Plyushchay

arxiv:2607.20711 v1 · 2026-07-22 · math-ph · hep-th · 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{5Z2JKNHGVVMY6JL72IL2ZA6H5H}

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	2026-07-24T00:23:30.821843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee749534e6ad598f257fd217ac83c7e9e92173f2a3dacefe939fd5cf2edabb75

Aliases

arxiv: 2607.20711 · arxiv_version: 2607.20711v1 · doi: 10.48550/arxiv.2607.20711 · pith_short_12: 5Z2JKNHGVVMY · pith_short_16: 5Z2JKNHGVVMY6JL7 · pith_short_8: 5Z2JKNHG

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/5Z2JKNHGVVMY6JL72IL2ZA6H5H \
  | 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: ee749534e6ad598f257fd217ac83c7e9e92173f2a3dacefe939fd5cf2edabb75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1dd1dd76169736cbd0b859422fa371b0a12522ae799a02943ffb2aa2bbca405",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-07-22T20:29:40Z",
    "title_canon_sha256": "d7ec5bb19609fe319b71fa7323e0ffdceb58ebdf8b0c0c98ad395181591e3eaa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20711",
    "kind": "arxiv",
    "version": 1
  }
}