Pith Number

pith:D32YZ7W3

pith:2015:D32YZ7W3MA4OKP4J4BD26TWQKL

not attested not anchored not stored refs pending

Deficiency Indices of Some Classes of Unbounded $\mathbb{H}$-Operators

B. Muraleetharan, K. Thirulogasanthar

arxiv:1512.08662 v2 · 2015-12-29 · 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{D32YZ7W3MA4OKP4J4BD26TWQKL}

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	2026-05-18T00:35:49.042606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ef58cfedb6038e53f89e047af4ed052fa5efbf97c885cd7b30a8d20f188b0f1

Aliases

arxiv: 1512.08662 · arxiv_version: 1512.08662v2 · doi: 10.48550/arxiv.1512.08662 · pith_short_12: D32YZ7W3MA4O · pith_short_16: D32YZ7W3MA4OKP4J · pith_short_8: D32YZ7W3

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/D32YZ7W3MA4OKP4J4BD26TWQKL \
  | 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: 1ef58cfedb6038e53f89e047af4ed052fa5efbf97c885cd7b30a8d20f188b0f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5ec78b0778f5975852dc953d5b502f1fcb69373a4e75544e7e32d727248ed62",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-12-29T11:56:19Z",
    "title_canon_sha256": "4ff28641a0f480eefc69e9c0a4619c2d2726929e9a988bb3cbf7165b511a7f94"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08662",
    "kind": "arxiv",
    "version": 2
  }
}