Pith Number

pith:PFT5BHZJ

pith:2007:PFT5BHZJYFJKNIBLOVE2PIECZL

not attested not anchored not stored refs pending

Positive Cubature formulas and Marcinkiewicz-Zygmund inequalities on spherical caps

Feng Dai, Heping Wang

arxiv:math/0703768 v1 · 2007-03-26 · math.CA · cs.NA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PFT5BHZJYFJKNIBLOVE2PIECZL}

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	2026-06-03T22:06:22.324284Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7967d09f29c152a6a02b7549a7a082cae79e136ff85c740a5714c60ce2ab8be9

Aliases

arxiv: math/0703768 · arxiv_version: math/0703768v1 · doi: 10.48550/arxiv.math/0703768 · pith_short_12: PFT5BHZJYFJK · pith_short_16: PFT5BHZJYFJKNIBL · pith_short_8: PFT5BHZJ

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/PFT5BHZJYFJKNIBLOVE2PIECZL \
  | 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: 7967d09f29c152a6a02b7549a7a082cae79e136ff85c740a5714c60ce2ab8be9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbbce67b651fb2f7057569c763a59781f2078904b1231691c7e759a9a2fb91f8",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2007-03-26T18:44:05Z",
    "title_canon_sha256": "213825e8f99dbbdae7d2fc42ccb42c1504c3871eb7bf0fa8c796366790cf0236"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703768",
    "kind": "arxiv",
    "version": 1
  }
}