Pith Number

pith:MS5V4J72

pith:2019:MS5V4J72JSQZBNPIWJIXECQHEH

not attested not anchored not stored refs pending

The essential numerical range for unbounded linear operators

Christiane Tretter, Marco Marletta, Sabine B\"ogli

arxiv:1907.09599 v1 · 2019-07-22 · math.SP · math.AP · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MS5V4J72JSQZBNPIWJIXECQHEH}

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	2026-05-17T23:39:52.788523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64bb5e27fa4ca190b5e8b251720a0721fc6afce06a4366bae892cddd2a3a6f77

Aliases

arxiv: 1907.09599 · arxiv_version: 1907.09599v1 · doi: 10.48550/arxiv.1907.09599 · pith_short_12: MS5V4J72JSQZ · pith_short_16: MS5V4J72JSQZBNPI · pith_short_8: MS5V4J72

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/MS5V4J72JSQZBNPIWJIXECQHEH \
  | 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: 64bb5e27fa4ca190b5e8b251720a0721fc6afce06a4366bae892cddd2a3a6f77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9078338ed3c7bd9f9cd0d6674539a776e6a08468f159b3bd438cd00ce4a4d2ed",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2019-07-22T21:55:18Z",
    "title_canon_sha256": "9d52ff1e2fe29ad188872d22348bf1ec8883f3dbc08acf7bdfbb887968fb7936"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.09599",
    "kind": "arxiv",
    "version": 1
  }
}