Pith Number

pith:QVU4ANAE

pith:2014:QVU4ANAEOQRBWSJDJ7ZBO462LR

not attested not anchored not stored refs pending

The angle of an operator and range and kernel complementarity

Dimosthenis Drivaliaris, Nikos Yannakakis

arxiv:1409.4195 v3 · 2014-09-15 · 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{QVU4ANAEOQRBWSJDJ7ZBO462LR}

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	2026-05-18T01:27:05.614666Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8569c0340474221b49234ff21773da5c6166ba1b1e3285ff18787f0c8a748a21

Aliases

arxiv: 1409.4195 · arxiv_version: 1409.4195v3 · doi: 10.48550/arxiv.1409.4195 · pith_short_12: QVU4ANAEOQRB · pith_short_16: QVU4ANAEOQRBWSJD · pith_short_8: QVU4ANAE

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/QVU4ANAEOQRBWSJDJ7ZBO462LR \
  | 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: 8569c0340474221b49234ff21773da5c6166ba1b1e3285ff18787f0c8a748a21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4b7e6983671ee3b7514db0e4b8ef5b20cf4265aa2dbf484c6a88415ad96f0a1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-09-15T09:50:16Z",
    "title_canon_sha256": "1018112d134583f3e614d2d8c13d1f30c36992863e7b035be522a7979e7df6bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.4195",
    "kind": "arxiv",
    "version": 3
  }
}