Pith Number

pith:TVBT3TZF

pith:2015:TVBT3TZF3V5HWB7XR6U263MLBA

not attested not anchored not stored refs pending

On the complexity of some inevitable classes of separable Banach spaces

Bruno de Mendon\c{c}a Braga

arxiv:1508.01961 v1 · 2015-08-08 · 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{TVBT3TZF3V5HWB7XR6U263MLBA}

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	2026-05-18T00:54:10.977628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d433dcf25dd7a7b07f78fa9af6d8b082c5710e3eef711160c883b84b7b74645

Aliases

arxiv: 1508.01961 · arxiv_version: 1508.01961v1 · doi: 10.48550/arxiv.1508.01961 · pith_short_12: TVBT3TZF3V5H · pith_short_16: TVBT3TZF3V5HWB7X · pith_short_8: TVBT3TZF

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/TVBT3TZF3V5HWB7XR6U263MLBA \
  | 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: 9d433dcf25dd7a7b07f78fa9af6d8b082c5710e3eef711160c883b84b7b74645

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35c23962bae5fd6b36ff5d3039ea6c97f2321de009c5012f8af3e7ba7d831e00",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-08-08T21:59:01Z",
    "title_canon_sha256": "cd96b479bb5ca54099723bca02bdd24e8efe74ad3c8a8a1ad4fca4a0b428d8d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.01961",
    "kind": "arxiv",
    "version": 1
  }
}