Pith Number

pith:BX4634CF

pith:2018:BX4634CFKZQDPO2GTQEQKZFV45

not attested not anchored not stored refs pending

Approximation of norms on Banach spaces

Richard J. Smith, Stanimir Troyanski

arxiv:1804.05660 v2 · 2018-04-16 · 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{BX4634CFKZQDPO2GTQEQKZFV45}

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	2026-07-05T04:31:09.619536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0df9edf045566037bb469c090564b5e752ef93e6d8bc289de75593ae57985c55

Aliases

arxiv: 1804.05660 · arxiv_version: 1804.05660v2 · doi: 10.48550/arxiv.1804.05660 · pith_short_12: BX4634CFKZQD · pith_short_16: BX4634CFKZQDPO2G · pith_short_8: BX4634CF

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/BX4634CFKZQDPO2GTQEQKZFV45 \
  | 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: 0df9edf045566037bb469c090564b5e752ef93e6d8bc289de75593ae57985c55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "034eb5f49efabcb858b4fefc456df039a80640fa99985922b8a35fd95c5e1a51",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-04-16T13:24:12Z",
    "title_canon_sha256": "d095d31dfdea83d12b51d8d730de4b8bfc19d64dd023f7f830b62d3fa71bf1bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.05660",
    "kind": "arxiv",
    "version": 2
  }
}