Pith Number

pith:7DZ7SH6I

pith:2026:7DZ7SH6I5KQGLXN3XCHPCSO2TH

not attested not anchored not stored refs pending

On the existence of extremizers for the sum of eigenvalues of Toeplitz operators

Fabio Nicola, Federico Riccardi, Paolo Tilli

arxiv:2607.20965 v1 · 2026-07-23 · 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{7DZ7SH6I5KQGLXN3XCHPCSO2TH}

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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	2026-07-24T01:23:44.559048Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8f3f91fc8eaa065ddbbb88ef149da99fda8628d1e32ae437182763261c988b2

Aliases

arxiv: 2607.20965 · arxiv_version: 2607.20965v1 · doi: 10.48550/arxiv.2607.20965 · pith_short_12: 7DZ7SH6I5KQG · pith_short_16: 7DZ7SH6I5KQGLXN3 · pith_short_8: 7DZ7SH6I

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/7DZ7SH6I5KQGLXN3XCHPCSO2TH \
  | 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: f8f3f91fc8eaa065ddbbb88ef149da99fda8628d1e32ae437182763261c988b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b56d6819bcfd7075957283cdd324665b7b61f02cfb0b5f608ab92cfd52c195bb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-07-23T06:42:34Z",
    "title_canon_sha256": "3cff90099eb5d2b669d80055f7d3e8a3c0728e67188bffad37a203857f9d647e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20965",
    "kind": "arxiv",
    "version": 1
  }
}