Pith Number

pith:A3AFD6Z5

pith:2013:A3AFD6Z54XHWZTARGLH5MEYFWP

not attested not anchored not stored refs pending

On the Theory of Self-Adjoint Extensions of the Laplace-Beltrami Operator, Quadratic Forms and Symmetry

Juan Manuel P\'erez-Pardo

arxiv:1308.2158 v2 · 2013-08-09 · math-ph · math.FA · math.MP · math.NA · math.SP · 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{A3AFD6Z54XHWZTARGLH5MEYFWP}

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	2026-05-18T03:13:09.611935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06c051fb3de5cf6ccc1132cfd61305b3f74a2ae36fd095faf20ebd5f931063ad

Aliases

arxiv: 1308.2158 · arxiv_version: 1308.2158v2 · doi: 10.48550/arxiv.1308.2158 · pith_short_12: A3AFD6Z54XHW · pith_short_16: A3AFD6Z54XHWZTAR · pith_short_8: A3AFD6Z5

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/A3AFD6Z54XHWZTARGLH5MEYFWP \
  | 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: 06c051fb3de5cf6ccc1132cfd61305b3f74a2ae36fd095faf20ebd5f931063ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7558850fc3e5e2ebf9b83756f06e205e7ea3ac107d5096d3b791f60d8fe7e11",
    "cross_cats_sorted": [
      "math.FA",
      "math.MP",
      "math.NA",
      "math.SP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-08-09T15:25:53Z",
    "title_canon_sha256": "4eb67365ffdad9447e2f7e6e3ac6fabecb4c2844c5f74d186afc54170e2d270d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.2158",
    "kind": "arxiv",
    "version": 2
  }
}