Pith Number

pith:XF7AES2E

pith:2012:XF7AES2EXA64V3ZQWE66O3PPCW

not attested not anchored not stored refs pending

Three-space property for asymptotically uniformly smooth renormings

G. Lancien, P. A. H. Brooker

arxiv:1209.1567 v1 · 2012-09-07 · 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{XF7AES2EXA64V3ZQWE66O3PPCW}

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	2026-05-18T03:46:04.469646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b97e024b44b83dcaef30b13de76def15bbb3f0dbb979431e41c4c738cc2a855b

Aliases

arxiv: 1209.1567 · arxiv_version: 1209.1567v1 · doi: 10.48550/arxiv.1209.1567 · pith_short_12: XF7AES2EXA64 · pith_short_16: XF7AES2EXA64V3ZQ · pith_short_8: XF7AES2E

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/XF7AES2EXA64V3ZQWE66O3PPCW \
  | 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: b97e024b44b83dcaef30b13de76def15bbb3f0dbb979431e41c4c738cc2a855b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17c04f570b8a922500f1a43049592b00ad5f58a6c6ed48c27ea8167c00a90c29",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-09-07T15:18:19Z",
    "title_canon_sha256": "156eb3ace3550a7829d8fd3eca71bdb6c343c4d2db969672f433e6e6d8619206"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1567",
    "kind": "arxiv",
    "version": 1
  }
}