Pith Number

pith:QQXQYS2O

pith:2026:QQXQYS2OEFQ4LQYLNHIO3PLLZ4

not attested not anchored not stored refs pending

A Separable Banach Space with a Schauder Basis Which Is Not a Lipschitz Retract of Its Bidual

Antonio Acuaviva

arxiv:2607.12935 v1 · 2026-07-14 · 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{QQXQYS2OEFQ4LQYLNHIO3PLLZ4}

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	2026-07-15T01:22:26.069179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

842f0c4b4e2161c5c30b69d0edbd6bcf2db7d724c92e5731187f673f628207de

Aliases

arxiv: 2607.12935 · arxiv_version: 2607.12935v1 · doi: 10.48550/arxiv.2607.12935 · pith_short_12: QQXQYS2OEFQ4 · pith_short_16: QQXQYS2OEFQ4LQYL · pith_short_8: QQXQYS2O

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/QQXQYS2OEFQ4LQYLNHIO3PLLZ4 \
  | 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: 842f0c4b4e2161c5c30b69d0edbd6bcf2db7d724c92e5731187f673f628207de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "daf1237797145794571bb6019c4f5a53ee604f07ca762d482120747dfebe47ec",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-07-14T16:08:57Z",
    "title_canon_sha256": "6eac44f9a21fa9e0d51e3b3a28671aa83d185410914fe23ae194c25856623a1d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12935",
    "kind": "arxiv",
    "version": 1
  }
}