Pith Number

pith:VP75Z2T5

pith:2026:VP75Z2T5OZZM2K5RI7K7LMPIIM

not attested not anchored not stored refs pending

Spectrally $n$-centered operators. I

Piotr Budzy\'nski

arxiv:2606.24550 v1 · 2026-06-23 · 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{VP75Z2T5OZZM2K5RI7K7LMPIIM}

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	2026-06-24T01:15:33.635495Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abffdcea7d7672cd2bb147d5f5b1e8432cc3d594805776f56e31bc6c97bbc6de

Aliases

arxiv: 2606.24550 · arxiv_version: 2606.24550v1 · doi: 10.48550/arxiv.2606.24550 · pith_short_12: VP75Z2T5OZZM · pith_short_16: VP75Z2T5OZZM2K5R · pith_short_8: VP75Z2T5

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/VP75Z2T5OZZM2K5RI7K7LMPIIM \
  | 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: abffdcea7d7672cd2bb147d5f5b1e8432cc3d594805776f56e31bc6c97bbc6de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b28d25b09a8740294299d1654ce7fb580360e45d126c639ce09723327e2c2d63",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-06-23T13:17:20Z",
    "title_canon_sha256": "f1e70d7723afc4668eae04af901be4b27f16bb8eb90e42e23246bacb9dced0f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24550",
    "kind": "arxiv",
    "version": 1
  }
}