Pith Number

pith:DQFNWLDC

pith:2004:DQFNWLDCM3MI7NGFJ37OKBVJ67

not attested not anchored not stored refs pending

A Discrete Fourier Kernel and Fraenkel's Tiling Conjecture

Kevin O'Bryant, Ron Graham

arxiv:math/0407306 v2 · 2004-07-17 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DQFNWLDCM3MI7NGFJ37OKBVJ67}

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	2026-05-18T01:38:27.254816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c0adb2c6266d88fb4c54efee506a9f7db26936a7c0b07e889c47731c5b4a145

Aliases

arxiv: math/0407306 · arxiv_version: math/0407306v2 · doi: 10.48550/arxiv.math/0407306 · pith_short_12: DQFNWLDCM3MI · pith_short_16: DQFNWLDCM3MI7NGF · pith_short_8: DQFNWLDC

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/DQFNWLDCM3MI7NGFJ37OKBVJ67 \
  | 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: 1c0adb2c6266d88fb4c54efee506a9f7db26936a7c0b07e889c47731c5b4a145

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60686ce898a24cada74e4f4fd21a8267ea0910bf94ca8f7d35984802f2d839da",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-07-17T01:00:39Z",
    "title_canon_sha256": "45d2713566d85922c610e853571bfd18139c797aadf8eae0604473729836cafc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0407306",
    "kind": "arxiv",
    "version": 2
  }
}