Pith Number

pith:772TIMS5

pith:2026:772TIMS5FAVUYVT7LRCSOZMIUG

not attested not anchored not stored refs pending

Triebel-Lizorkin spaces and expansive matrices

Jordy Timo van Velthoven, Marcin Bownik

arxiv:2605.13097 v1 · 2026-05-13 · math.FA · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{772TIMS5FAVUYVT7LRCSOZMIUG}

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	2026-05-18T03:08:58.345142Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fff534325d282b4c567f5c45276588a1a5d3d309345c4ffe9fc22eb2c11b9f78

Aliases

arxiv: 2605.13097 · arxiv_version: 2605.13097v1 · doi: 10.48550/arxiv.2605.13097 · pith_short_12: 772TIMS5FAVU · pith_short_16: 772TIMS5FAVUYVT7 · pith_short_8: 772TIMS5

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/772TIMS5FAVUYVT7LRCSOZMIUG \
  | 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: fff534325d282b4c567f5c45276588a1a5d3d309345c4ffe9fc22eb2c11b9f78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "804c807aef65ae930e7079c4ebcde0827c8f33df845bd2f75822f5435c10cde1",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-05-13T07:10:39Z",
    "title_canon_sha256": "009c000418752fa05090c736cd5fa8cc84069be9af2f397cba49e1c9da0e8fff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13097",
    "kind": "arxiv",
    "version": 1
  }
}