Pith Number

pith:W3SEHW6D

pith:2021:W3SEHW6D5N7I27A2W52T3ZGEPO

not attested not anchored not stored refs pending

$(1+)$-complemented, $(1+)$-isomorphic copies of $L_{1}$ in dual Banach spaces

Dongyang Chen, Tomasz Kania, Yingbin Ruan

arxiv:2108.03057 v2 · 2021-08-06 · 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{W3SEHW6D5N7I27A2W52T3ZGEPO}

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	2026-07-05T04:09:14.841410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6e443dbc3eb7e8d7c1ab7753de4c47bb5146c9ff0e66eceb9c7914f68f36d76

Aliases

arxiv: 2108.03057 · arxiv_version: 2108.03057v2 · doi: 10.48550/arxiv.2108.03057 · pith_short_12: W3SEHW6D5N7I · pith_short_16: W3SEHW6D5N7I27A2 · pith_short_8: W3SEHW6D

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/W3SEHW6D5N7I27A2W52T3ZGEPO \
  | 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: b6e443dbc3eb7e8d7c1ab7753de4c47bb5146c9ff0e66eceb9c7914f68f36d76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5237552c8a96b77b6e4d0db385c722b2806a8557f91c17986498392704aaf7fa",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2021-08-06T11:16:39Z",
    "title_canon_sha256": "6e75eca972c9266f07c57b4280c9ffa10465d3f088618b24a063e7b66d7ddafe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.03057",
    "kind": "arxiv",
    "version": 2
  }
}