Pith Number

pith:SXSLXELX

pith:2019:SXSLXELXER2ILPGRKS6J6BKOQ3

not attested not anchored not stored refs pending

On the calculation of exact sum rules of rational order for quantum billiards (spectrum with a null eigenvalue)

Paolo Amore

arxiv:1908.08562 v1 · 2019-08-22 · math-ph · 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{SXSLXELXER2ILPGRKS6J6BKOQ3}

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	2026-07-04T23:59:15.459685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

95e4bb9177247485bcd154bc9f054e86c88b2e29cad10095d1dee636c24f4e1d

Aliases

arxiv: 1908.08562 · arxiv_version: 1908.08562v1 · doi: 10.48550/arxiv.1908.08562 · pith_short_12: SXSLXELXER2I · pith_short_16: SXSLXELXER2ILPGR · pith_short_8: SXSLXELX

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/SXSLXELXER2ILPGRKS6J6BKOQ3 \
  | 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: 95e4bb9177247485bcd154bc9f054e86c88b2e29cad10095d1dee636c24f4e1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53c7eb0ff645626e74724bcc7d7516fbe5a8ec4a990b4b92435f2ce4c296973b",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2019-08-22T18:55:21Z",
    "title_canon_sha256": "828e4ad701f7458c869957373e7fd8ef0e9ff74b3a6b3223c7bfb43719f7cc94"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08562",
    "kind": "arxiv",
    "version": 1
  }
}