Pith Number

pith:7PWIGZM4

pith:2015:7PWIGZM4JLNYCSVUTKRFWF2P2X

not attested not anchored not stored refs pending

Perfectly ordered quasicrystals and the Littlewood conjecture

Alan Haynes, Henna Koivusalo, James Walton

arxiv:1506.05649 v3 · 2015-06-18 · math.DS · math-ph · math.MG · math.MP · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7PWIGZM4JLNYCSVUTKRFWF2P2X}

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	2026-05-18T01:32:00.327109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbec83659c4adb814ab49aa25b174fd5c4b053e0c7290d73037b5aee01a1c4b6

Aliases

arxiv: 1506.05649 · arxiv_version: 1506.05649v3 · doi: 10.48550/arxiv.1506.05649 · pith_short_12: 7PWIGZM4JLNY · pith_short_16: 7PWIGZM4JLNYCSVU · pith_short_8: 7PWIGZM4

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/7PWIGZM4JLNYCSVUTKRFWF2P2X \
  | 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: fbec83659c4adb814ab49aa25b174fd5c4b053e0c7290d73037b5aee01a1c4b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2574575c344a502f199b8ee429f7f407d8c069575e727530811dc802bcbc9f09",
    "cross_cats_sorted": [
      "math-ph",
      "math.MG",
      "math.MP",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-06-18T12:38:28Z",
    "title_canon_sha256": "4a47b32a8369cfca0cbc95d4faf4d6f6c46267bcf23e77fede8bc5031a82d875"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.05649",
    "kind": "arxiv",
    "version": 3
  }
}