Pith Number

pith:4KFCFLJ4

pith:2025:4KFCFLJ4CQSIRC26I7BHAND23E

not attested not anchored not stored refs pending

The $\pi$-property of a Banach space along a filter

Jaros{\l}aw Swaczyna, Tomasz Kania

arxiv:2508.21242 v1 · 2025-08-28 · math.FA · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4KFCFLJ4CQSIRC26I7BHAND23E}

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	2026-07-05T12:01:30.761962Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e28a22ad3c1424888b5e47c270347ad92f78c40234f9f5fc91ef2042b8429955

Aliases

arxiv: 2508.21242 · arxiv_version: 2508.21242v1 · doi: 10.48550/arxiv.2508.21242 · pith_short_12: 4KFCFLJ4CQSI · pith_short_16: 4KFCFLJ4CQSIRC26 · pith_short_8: 4KFCFLJ4

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/4KFCFLJ4CQSIRC26I7BHAND23E \
  | 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: e28a22ad3c1424888b5e47c270347ad92f78c40234f9f5fc91ef2042b8429955

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef9e0a7414aea951c4e9dae43d040a7af0c8b3fd39117c7b0b9a6fb058cf6257",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-08-28T22:13:11Z",
    "title_canon_sha256": "2faef4384d939e5ca684c59cba56036fe1f7c664a8ee956d534c0433b5698a10"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.21242",
    "kind": "arxiv",
    "version": 1
  }
}