Pith Number

pith:7NUZYYBB

pith:2026:7NUZYYBB7ILYBVGVQX4JFGHX5J

not attested not anchored not stored refs pending

Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages

Fan Yang, Rui Han

arxiv:2608.08893 v1 · 2026-08-09 · math.CA · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7NUZYYBB7ILYBVGVQX4JFGHX5J}

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	2026-08-11T01:25:38.639603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb699c6021fa1780d4d585f89298f7ea6e47bb6e9ad855bb2e0effe12cee40e9

Aliases

arxiv: 2608.08893 · arxiv_version: 2608.08893v1 · doi: 10.48550/arxiv.2608.08893 · pith_short_12: 7NUZYYBB7ILY · pith_short_16: 7NUZYYBB7ILYBVGV · pith_short_8: 7NUZYYBB

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/7NUZYYBB7ILYBVGVQX4JFGHX5J \
  | 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: fb699c6021fa1780d4d585f89298f7ea6e47bb6e9ad855bb2e0effe12cee40e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3b8155ef65f0b0eb84d019d80d127cb078c23ea34a24828a557845909a620d0",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-08-09T20:14:04Z",
    "title_canon_sha256": "cea2b52e8a4e44950c4e8f40172218e37c7a11bee67bf21d21948165adc0fbae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.08893",
    "kind": "arxiv",
    "version": 1
  }
}