Pith Number

pith:T4RPUPAK

pith:2026:T4RPUPAKXJC3VZCCG54R7Y6YZV

not attested not anchored not stored refs pending

Optimal concentration in the Paley-Wiener space

Lu\'is Daniel Abreu, Michael Speckbacher

arxiv:2607.19192 v1 · 2026-07-21 · math.CA · 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{T4RPUPAKXJC3VZCCG54R7Y6YZV}

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	2026-07-22T01:24:13.559021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f22fa3c0aba45bae44237791fe3d8cd5b52d4dc998851eadcb31ede94224598

Aliases

arxiv: 2607.19192 · arxiv_version: 2607.19192v1 · doi: 10.48550/arxiv.2607.19192 · pith_short_12: T4RPUPAKXJC3 · pith_short_16: T4RPUPAKXJC3VZCC · pith_short_8: T4RPUPAK

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/T4RPUPAKXJC3VZCCG54R7Y6YZV \
  | 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: 9f22fa3c0aba45bae44237791fe3d8cd5b52d4dc998851eadcb31ede94224598

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05c8172dd4077a8befa8622009d4e9637a0209baa15e88cb1fc87f7260b04377",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-07-21T15:28:42Z",
    "title_canon_sha256": "315b2467fe89fe900fe41a77fbd3502f5fe3f55a339227acaca32f1e29783631"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.19192",
    "kind": "arxiv",
    "version": 1
  }
}