Pith Number

pith:R3CCRXO5

pith:2015:R3CCRXO52QOFD2MGWIUH6RU2KN

not attested not anchored not stored refs pending

The Dual Form of the Approximation Property for a Banach Space and a Subspace

T. Figiel, W. B. Johnson

arxiv:1508.01212 v1 · 2015-08-05 · 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{R3CCRXO52QOFD2MGWIUH6RU2KN}

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	2026-05-18T01:35:43.148824Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ec428ddddd41c51e986b2287f469a53483cc8f88919c6291ab31fba7f865ce8

Aliases

arxiv: 1508.01212 · arxiv_version: 1508.01212v1 · doi: 10.48550/arxiv.1508.01212 · pith_short_12: R3CCRXO52QOF · pith_short_16: R3CCRXO52QOFD2MG · pith_short_8: R3CCRXO5

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/R3CCRXO52QOFD2MGWIUH6RU2KN \
  | 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: 8ec428ddddd41c51e986b2287f469a53483cc8f88919c6291ab31fba7f865ce8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4af4a47368496e50677f098b57c2b9ce0be300f0fa7bfde58c13a1980a5e53fc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-08-05T20:18:21Z",
    "title_canon_sha256": "6facdb8f84a98066887d503d66089d76e1bf258e8b3fa0653b12ea5804ba451e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.01212",
    "kind": "arxiv",
    "version": 1
  }
}