Pith Number

pith:PWYFMEHF

pith:2025:PWYFMEHFFK37F5ZUZ2YJ7DPPXI

not attested not anchored not stored refs pending

Optimal structured approximation of Fourier subspaces, Toeplitz matrices, and exponential sums

Albert Fannjiang, Weilin Li

arxiv:2511.17239 v2 · 2025-11-21 · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PWYFMEHFFK37F5ZUZ2YJ7DPPXI}

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	2026-07-15T00:21:14.344239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7db05610e52ab7f2f734ceb09f8defba2aa317d00ba49ad9a0af5e1da507f48c

Aliases

arxiv: 2511.17239 · arxiv_version: 2511.17239v2 · doi: 10.48550/arxiv.2511.17239 · pith_short_12: PWYFMEHFFK37 · pith_short_16: PWYFMEHFFK37F5ZU · pith_short_8: PWYFMEHF

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/PWYFMEHFFK37F5ZUZ2YJ7DPPXI \
  | 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: 7db05610e52ab7f2f734ceb09f8defba2aa317d00ba49ad9a0af5e1da507f48c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9914dbb5141881b8b4942bddf5b52bcbead0e1d818693144b9d4cc29c91757a",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2025-11-21T13:33:39Z",
    "title_canon_sha256": "f07ab65f0b9a4a23cf5ff13a59508a49cc556824ef6853981fa302d094612701"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.17239",
    "kind": "arxiv",
    "version": 2
  }
}