Pith Number

pith:4MXI3SUC

pith:2021:4MXI3SUCCU6QOQJLG35MW24WQF

not attested not anchored not stored refs pending

Endpoint $ \ell ^{r}$ improving estimates for Prime averages

Hamed Mousavi, Michael T. Lacey, Yaghoub Rahimi

arxiv:2101.10401 v2 · 2021-01-25 · math.NT · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4MXI3SUCCU6QOQJLG35MW24WQF}

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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.

Cited by

1 paper in Pith

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

Receipt and verification

First computed	2026-07-05T06:05:24.562029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e32e8dca82153d07412b36facb6b96817d503456a5aa29fbf12b4b5ab579462f

Aliases

arxiv: 2101.10401 · arxiv_version: 2101.10401v2 · doi: 10.48550/arxiv.2101.10401 · pith_short_12: 4MXI3SUCCU6Q · pith_short_16: 4MXI3SUCCU6QOQJL · pith_short_8: 4MXI3SUC

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/4MXI3SUCCU6QOQJLG35MW24WQF \
  | 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: e32e8dca82153d07412b36facb6b96817d503456a5aa29fbf12b4b5ab579462f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff2c2d1cf6a87fa0223c12492b9f9e1946220ba5ab479be8f01c8f6f436e8fae",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-01-25T20:36:23Z",
    "title_canon_sha256": "bacc6ca8e72c8a5b01f0ada8663c80028fe085291b0c00a57ea8c2205ae28ead"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2101.10401",
    "kind": "arxiv",
    "version": 2
  }
}