Pith Number

pith:VJKVZWZ5

pith:2025:VJKVZWZ5LKW2PLNJ77JXYZMKIH

not attested not anchored not stored refs pending

A Fourier analysis approach to disprove the weak Shanks conjecture

Hugo J. Woerdeman, Jeffrey S. Geronimo

arxiv:2508.15938 v1 · 2025-08-21 · math.CV · 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{VJKVZWZ5LKW2PLNJ77JXYZMKIH}

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	2026-07-05T11:57:23.478551Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa555cdb3d5aada7ada9ffd37c658a41ee76939d3f6bc78ada986e08e85ebe2f

Aliases

arxiv: 2508.15938 · arxiv_version: 2508.15938v1 · doi: 10.48550/arxiv.2508.15938 · pith_short_12: VJKVZWZ5LKW2 · pith_short_16: VJKVZWZ5LKW2PLNJ · pith_short_8: VJKVZWZ5

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/VJKVZWZ5LKW2PLNJ77JXYZMKIH \
  | 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: aa555cdb3d5aada7ada9ffd37c658a41ee76939d3f6bc78ada986e08e85ebe2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64ae7850673130c79ba14c6c961226c62f3029ddc38b00e790e96089ab025993",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2025-08-21T20:15:28Z",
    "title_canon_sha256": "8d0a624be2b06efc98bc4807396475f64943af3746360b75385464ddb49f9666"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.15938",
    "kind": "arxiv",
    "version": 1
  }
}