Pith Number

pith:CK45EVGX

pith:2015:CK45EVGXR5HCRQ5ISVDFNHK5QH

not attested not anchored not stored refs pending

Direct sums and summability of the Szlenk index

Szymon Draga, Tomasz Kochanek

arxiv:1511.07632 v1 · 2015-11-24 · 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{CK45EVGXR5HCRQ5ISVDFNHK5QH}

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	2026-05-18T01:26:04.122719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12b9d254d78f4e28c3a89546569d5d81ce37789686573302d338f1848507afe9

Aliases

arxiv: 1511.07632 · arxiv_version: 1511.07632v1 · doi: 10.48550/arxiv.1511.07632 · pith_short_12: CK45EVGXR5HC · pith_short_16: CK45EVGXR5HCRQ5I · pith_short_8: CK45EVGX

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/CK45EVGXR5HCRQ5ISVDFNHK5QH \
  | 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: 12b9d254d78f4e28c3a89546569d5d81ce37789686573302d338f1848507afe9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4878066c0265129427965b6a750bf4e4b3dd000fa66d8b00497d523b8e44fc80",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-11-24T10:24:14Z",
    "title_canon_sha256": "4154ba178a482fc78dca17d71119b67de84a02d7c2712869668fe127cf16b264"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07632",
    "kind": "arxiv",
    "version": 1
  }
}