Pith Number

pith:255UTKAE

pith:2011:255UTKAEZO5K4WLOBTXYTDAQWF

not attested not anchored not stored refs pending

Periodic Riemannian manifold with preassigned gaps in spectrum of Laplace-Beltrami operator

Andrii Khrabustovskyi

arxiv:1105.2431 v2 · 2011-05-12 · math.SP · math-ph · math.AP · math.DG · 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{255UTKAEZO5K4WLOBTXYTDAQWF}

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	2026-05-18T04:09:54.533200Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d77b49a804cbbaae596e0cef898c10b14331c6612cfc496b8f36750d83f67e06

Aliases

arxiv: 1105.2431 · arxiv_version: 1105.2431v2 · doi: 10.48550/arxiv.1105.2431 · pith_short_12: 255UTKAEZO5K · pith_short_16: 255UTKAEZO5K4WLO · pith_short_8: 255UTKAE

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/255UTKAEZO5K4WLOBTXYTDAQWF \
  | 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: d77b49a804cbbaae596e0cef898c10b14331c6612cfc496b8f36750d83f67e06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef2cbe32b7c1148bc797ba1886717644f8372efd2a626a62c64fced2b69cab8a",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-05-12T11:32:35Z",
    "title_canon_sha256": "8e8328c5e4f917e562af623b1393e494e8fd17b82a7b1fee467a3bc5cf0dfd64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2431",
    "kind": "arxiv",
    "version": 2
  }
}