Pith Number

pith:F467Y2RL

pith:2011:F467Y2RLCILCIL72TQ2FL4EPLW

not attested not anchored not stored refs pending

Semiclassical wave functions in billiards built on classical trajectories. Energy quantization, scars and periodic orbits

Jaros{\l}aw Janiak, Stefan Giller

arxiv:1108.2527 v1 · 2011-08-11 · math-ph · 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{F467Y2RLCILCIL72TQ2FL4EPLW}

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	2026-05-18T02:21:42.059718Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f3dfc6a2b1216242ffa9c3455f08f5dbf4df90a73387648761fd0ade8746f37

Aliases

arxiv: 1108.2527 · arxiv_version: 1108.2527v1 · doi: 10.48550/arxiv.1108.2527 · pith_short_12: F467Y2RLCILC · pith_short_16: F467Y2RLCILCIL72 · pith_short_8: F467Y2RL

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/F467Y2RLCILCIL72TQ2FL4EPLW \
  | 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: 2f3dfc6a2b1216242ffa9c3455f08f5dbf4df90a73387648761fd0ade8746f37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "325120179a264f915d58cd2b0ba30e31915c73d141b20967c2052b783343097a",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-08-11T22:01:49Z",
    "title_canon_sha256": "4eef16b639bc5d0de5a80fc7dadd187339ad101af1df4f57c27cacb48a2de000"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.2527",
    "kind": "arxiv",
    "version": 1
  }
}