Pith Number

pith:MPW3ECKO

pith:2014:MPW3ECKONIOOZ3WLN6CEQH5FBB

not attested not anchored not stored refs pending

Uniform-to-proper duality of geometric properties of Banach spaces and their ultrapowers

Jarno Talponen

arxiv:1412.1279 v2 · 2014-12-03 · math.FA · math.LO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MPW3ECKONIOOZ3WLN6CEQH5FBB}

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	2026-05-18T01:37:11.220599Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63edb2094e6a1ceceecb6f84481fa5086bd9739dcd5b85e604b623f333c3baad

Aliases

arxiv: 1412.1279 · arxiv_version: 1412.1279v2 · doi: 10.48550/arxiv.1412.1279 · pith_short_12: MPW3ECKONIOO · pith_short_16: MPW3ECKONIOOZ3WL · pith_short_8: MPW3ECKO

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/MPW3ECKONIOOZ3WLN6CEQH5FBB \
  | 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: 63edb2094e6a1ceceecb6f84481fa5086bd9739dcd5b85e604b623f333c3baad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fba0fc1fd7c2b2f1ceb56e48b762120ad6ea9d9ea0a1459029662061ee3e9a9",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-12-03T11:29:58Z",
    "title_canon_sha256": "47d92938703475ed6f445a95f5d6b54f2b54bdc0237ec02ee8ac387bb79fcfa5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.1279",
    "kind": "arxiv",
    "version": 2
  }
}