Pith Number

pith:HSN42SPX

pith:2026:HSN42SPXJX5P7YBVF4AWLN6KGT

not attested not anchored not stored refs pending

Optimal Extrapolation Bounds for Sparse Fourier Sums

Ruizhe Zhang

arxiv:2607.10501 v1 · 2026-07-11 · cs.DS · cs.NA · math.CA · 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{HSN42SPXJX5P7YBVF4AWLN6KGT}

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	2026-07-14T01:21:18.582586Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c9bcd49f74dfaffe0352f0165b7ca34f2492f80d31ce324ea7f8a8fb23ff00d

Aliases

arxiv: 2607.10501 · arxiv_version: 2607.10501v1 · doi: 10.48550/arxiv.2607.10501 · pith_short_12: HSN42SPXJX5P · pith_short_16: HSN42SPXJX5P7YBV · pith_short_8: HSN42SPX

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/HSN42SPXJX5P7YBVF4AWLN6KGT \
  | 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: 3c9bcd49f74dfaffe0352f0165b7ca34f2492f80d31ce324ea7f8a8fb23ff00d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "489c273af69dbb137ad05c45226bb4c7db9106eeb79df4bb976c1479a718c811",
    "cross_cats_sorted": [
      "cs.NA",
      "math.CA",
      "math.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-07-11T22:51:38Z",
    "title_canon_sha256": "6480d369fe202291ec39f23efc7d0eb1ef8380281d3ece33cdaa2aed764b93b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10501",
    "kind": "arxiv",
    "version": 1
  }
}