Pith Number

pith:VZYMC3IS

pith:2015:VZYMC3ISWPAOCOPSQL6ATVAZ2D

not attested not anchored not stored refs pending

Unbounded composition operators via inductive limits: cosubnormals with matrical symbols

Artur Planeta, Piotr Budzynski, Piotr Dymek

arxiv:1502.01638 v1 · 2015-02-05 · 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{VZYMC3ISWPAOCOPSQL6ATVAZ2D}

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	2026-05-18T00:06:31.658917Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae70c16d12b3c0e139f282fc09d419d0f385ffe16ca1a6bf11e42960a1a40973

Aliases

arxiv: 1502.01638 · arxiv_version: 1502.01638v1 · doi: 10.48550/arxiv.1502.01638 · pith_short_12: VZYMC3ISWPAO · pith_short_16: VZYMC3ISWPAOCOPS · pith_short_8: VZYMC3IS

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/VZYMC3ISWPAOCOPSQL6ATVAZ2D \
  | 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: ae70c16d12b3c0e139f282fc09d419d0f385ffe16ca1a6bf11e42960a1a40973

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2bfc12a94c636c6d30a77a6d3787fb1d70dfdb2b8e827057e9f559fa3a0a14f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-02-05T16:49:36Z",
    "title_canon_sha256": "637a0701eff7960d6c97e2cabbbd3ab6dbe6fa9563032103cc5debefea77a064"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.01638",
    "kind": "arxiv",
    "version": 1
  }
}