Pith Number

pith:WPOSPOXM

pith:2010:WPOSPOXMVT2ZKGZSPPRFBNOS7N

not attested not anchored not stored refs pending

On Turing dynamical systems and the Atiyah problem

{\L}ukasz Grabowski

arxiv:1004.2030 v4 · 2010-04-12 · math.GR · cs.CC · math.DS · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WPOSPOXMVT2ZKGZSPPRFBNOS7N}

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	2026-05-18T02:31:27.821817Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3dd27baecacf5951b327be250b5d2fb5026daba7654bc0cd6300e527eb3fbcb

Aliases

arxiv: 1004.2030 · arxiv_version: 1004.2030v4 · doi: 10.48550/arxiv.1004.2030 · pith_short_12: WPOSPOXMVT2Z · pith_short_16: WPOSPOXMVT2ZKGZS · pith_short_8: WPOSPOXM

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/WPOSPOXMVT2ZKGZSPPRFBNOS7N \
  | 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: b3dd27baecacf5951b327be250b5d2fb5026daba7654bc0cd6300e527eb3fbcb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2e4e4da7fb1939b62c76090eef60f23074bf1966c0daf36ff7b1adc9a0f7cf6",
    "cross_cats_sorted": [
      "cs.CC",
      "math.DS",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-04-12T19:26:05Z",
    "title_canon_sha256": "b1dd660c9ddbe23f944bf423e7aee772e12551e6680ad0ab3cda469b8528c854"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.2030",
    "kind": "arxiv",
    "version": 4
  }
}