Pith Number

pith:7TI7I3E4

pith:2015:7TI7I3E4RCJQ4F75U4E3DTDSO2

not attested not anchored not stored refs pending

Duality on Banach spaces and a Borel parametrized version of Zippin's theorem

Bruno de Mendon\c{c}a Braga

arxiv:1508.02066 v1 · 2015-08-09 · 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{7TI7I3E4RCJQ4F75U4E3DTDSO2}

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	2026-05-18T00:54:10.969695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fcd1f46c9c88930e17fda709b1cc7276be7a6483c43d67f430db54a4f9b2e782

Aliases

arxiv: 1508.02066 · arxiv_version: 1508.02066v1 · doi: 10.48550/arxiv.1508.02066 · pith_short_12: 7TI7I3E4RCJQ · pith_short_16: 7TI7I3E4RCJQ4F75 · pith_short_8: 7TI7I3E4

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/7TI7I3E4RCJQ4F75U4E3DTDSO2 \
  | 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: fcd1f46c9c88930e17fda709b1cc7276be7a6483c43d67f430db54a4f9b2e782

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ece6da57211d9032caaa9c9b4fb37d194a006a12adca249c69b550fb99e6f2c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-08-09T18:27:02Z",
    "title_canon_sha256": "1b91fd35c49ad50be928cbc1597759ce8e66ab3497b20cd8343227b2be57e9cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02066",
    "kind": "arxiv",
    "version": 1
  }
}