Pith Number

pith:WPBBKD2L

pith:2025:WPBBKD2L5QEKOBLE5HDT26JDUT

not attested not anchored not stored refs pending

Fourier frames on smooth surfaces with nonvanishing Gaussian curvature

Bochen Liu, Xinyu Chen

arxiv:2507.05777 v1 · 2025-07-08 · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WPBBKD2L5QEKOBLE5HDT26JDUT}

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	2026-07-05T11:33:36.176441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3c2150f4bec08a70564e9c73d7923a4dd9644a339fc846dfdcea47749a0cd77

Aliases

arxiv: 2507.05777 · arxiv_version: 2507.05777v1 · doi: 10.48550/arxiv.2507.05777 · pith_short_12: WPBBKD2L5QEK · pith_short_16: WPBBKD2L5QEKOBLE · pith_short_8: WPBBKD2L

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/WPBBKD2L5QEKOBLE5HDT26JDUT \
  | 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: b3c2150f4bec08a70564e9c73d7923a4dd9644a339fc846dfdcea47749a0cd77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3877e212c771310efce900de0f6c30940c30f1cb0b4378ad543f0a16a7b8d47",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-07-08T08:31:34Z",
    "title_canon_sha256": "c14e695dd88e7b8e5f92a1d094c47a3682087c3c9c98c314d653c844cdf614df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.05777",
    "kind": "arxiv",
    "version": 1
  }
}