Pith Number

pith:57VKXJIB

pith:2013:57VKXJIBBFPOW5NTWYUQMDGBFA

not attested not anchored not stored refs pending

Projections in duals to Asplund spaces made without Simons' lemma

Marek Cuth, Marian Fabian

arxiv:1304.1313 v1 · 2013-04-04 · 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{57VKXJIBBFPOW5NTWYUQMDGBFA}

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	2026-05-18T02:38:17.266152Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efeaaba501095eeb75b3b629060cc128026a208caa3c9b33bf5881850b5eadeb

Aliases

arxiv: 1304.1313 · arxiv_version: 1304.1313v1 · doi: 10.48550/arxiv.1304.1313 · pith_short_12: 57VKXJIBBFPO · pith_short_16: 57VKXJIBBFPOW5NT · pith_short_8: 57VKXJIB

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/57VKXJIBBFPOW5NTWYUQMDGBFA \
  | 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: efeaaba501095eeb75b3b629060cc128026a208caa3c9b33bf5881850b5eadeb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b27b62c19feaa5c7a432a267e911771d9af53e52131eb1d07d95a2663422ad67",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-04-04T10:48:27Z",
    "title_canon_sha256": "6c657be4548549c46e549f429b48564ba78024f022cbe8d3a6061ba38a2f37c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.1313",
    "kind": "arxiv",
    "version": 1
  }
}