Pith Number

pith:WQR7CD75

pith:2012:WQR7CD75AVAEI2BUA4MPX5ERGA

not attested not anchored not stored refs pending

Restricted Invertibility and the Banach-Mazur distance to the cube

Pierre Youssef

arxiv:1206.0654 v3 · 2012-06-04 · 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{WQR7CD75AVAEI2BUA4MPX5ERGA}

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	2026-05-17T23:53:18.656735Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b423f10ffd05404468340718fbf4913006d33f3f0c047ca7fe713b0e5efbea45

Aliases

arxiv: 1206.0654 · arxiv_version: 1206.0654v3 · doi: 10.48550/arxiv.1206.0654 · pith_short_12: WQR7CD75AVAE · pith_short_16: WQR7CD75AVAEI2BU · pith_short_8: WQR7CD75

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/WQR7CD75AVAEI2BUA4MPX5ERGA \
  | 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: b423f10ffd05404468340718fbf4913006d33f3f0c047ca7fe713b0e5efbea45

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c068824b17c0a8a526bae3a5a50f6c3040b9a6c77268236d08137007209a6c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-06-04T15:41:14Z",
    "title_canon_sha256": "baac68e7eb81f543ea17a1163fe781ffa605b3504c1d63ca4fc07fa42a407540"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0654",
    "kind": "arxiv",
    "version": 3
  }
}