Pith Number

pith:NXXBWJCX

pith:2025:NXXBWJCX5PEJKYVFGPV5KMBDWQ

not attested not anchored not stored refs pending

Factorization in independent sums of Haar system Hardy spaces

Konstantinos Konstantos, Thomas Speckhofer

arxiv:2507.18600 v1 · 2025-07-24 · 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{NXXBWJCX5PEJKYVFGPV5KMBDWQ}

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.

Cited by

1 paper in Pith

Primariness and the Primary Factorisation Property

Receipt and verification

First computed	2026-07-05T11:42:50.831402Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6dee1b2457ebc89562a533ebd53023b43ea540045331975b87508103ed6b4dfa

Aliases

arxiv: 2507.18600 · arxiv_version: 2507.18600v1 · doi: 10.48550/arxiv.2507.18600 · pith_short_12: NXXBWJCX5PEJ · pith_short_16: NXXBWJCX5PEJKYVF · pith_short_8: NXXBWJCX

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/NXXBWJCX5PEJKYVFGPV5KMBDWQ \
  | 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: 6dee1b2457ebc89562a533ebd53023b43ea540045331975b87508103ed6b4dfa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83d1583b2643d9ff2208f3eec452c41dd7aa8dc974f72529ba4fe1cfe000e285",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-07-24T17:32:02Z",
    "title_canon_sha256": "c034ca21573ef287422a8391f50782020067ad71d6abeaf991cd2a06192f31d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.18600",
    "kind": "arxiv",
    "version": 1
  }
}