Pith Number

pith:YDWOGQMB

pith:2026:YDWOGQMBZA7OGCCDCCZYQWFBOR

not attested not anchored not stored refs pending

On the ascent and the angle between the null space and the range of elementary operators

Bojan Kuzma, Hranislav Stankovi\'c, Janko Bra\v{c}i\v{c}

arxiv:2606.18930 v1 · 2026-06-17 · 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{YDWOGQMBZA7OGCCDCCZYQWFBOR}

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	2026-06-19T16:11:52.156591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0ece34181c83ee3084310b38858a174673df909d6277f8ea6923adc6a20088e

Aliases

arxiv: 2606.18930 · arxiv_version: 2606.18930v1 · doi: 10.48550/arxiv.2606.18930 · pith_short_12: YDWOGQMBZA7O · pith_short_16: YDWOGQMBZA7OGCCD · pith_short_8: YDWOGQMB

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/YDWOGQMBZA7OGCCDCCZYQWFBOR \
  | 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: c0ece34181c83ee3084310b38858a174673df909d6277f8ea6923adc6a20088e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f758393ddf2c8d97215427a07b9cc7ee5a3a095d65fffdf36b096f9881596e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-06-17T11:05:24Z",
    "title_canon_sha256": "6d6cfbb4cf422b6a972f5db3e2b22aff1c7d76095224cd6d3acd9e8e6fb6db35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.18930",
    "kind": "arxiv",
    "version": 1
  }
}