Pith Number

pith:RKJIOJTW

pith:2005:RKJIOJTWOZ4QTJD52NSV2KC2HE

not attested not anchored not stored refs pending

Khintchine type inequalities for reduced free products and Applications

Eric Ricard, Quanhua Xu

arxiv:math/0505302 v2 · 2005-05-14 · math.OA · 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{RKJIOJTWOZ4QTJD52NSV2KC2HE}

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	2026-05-18T01:19:51.185766Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a92872676767909a47dd3655d285a3925b7a1b483da1ee850cf825e8f21c770

Aliases

arxiv: math/0505302 · arxiv_version: math/0505302v2 · doi: 10.48550/arxiv.math/0505302 · pith_short_12: RKJIOJTWOZ4Q · pith_short_16: RKJIOJTWOZ4QTJD5 · pith_short_8: RKJIOJTW

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/RKJIOJTWOZ4QTJD52NSV2KC2HE \
  | 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: 8a92872676767909a47dd3655d285a3925b7a1b483da1ee850cf825e8f21c770

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4abeefad5fcededa6d3e1f34ae1db83c10f6a1d08ed7dfab58ee2034f235632f",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2005-05-14T13:14:27Z",
    "title_canon_sha256": "571a51864efef7a301c290d0c418adae7a8f9cc463d8493181ba3f1c83125f26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0505302",
    "kind": "arxiv",
    "version": 2
  }
}