Pith Number

pith:QPNOLUTM

pith:2006:QPNOLUTMTUIHDH322QSXXOQZAZ

not attested not anchored not stored refs pending

A proof of simultaneous linearization with a polylog estimate

Tomoki Kawahira

arxiv:math/0609165 v2 · 2006-09-06 · math.DS · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QPNOLUTMTUIHDH322QSXXOQZAZ}

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	2026-05-18T03:01:56.853397Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83dae5d26c9d10719f7ad4257bba19067700240411d2b08261c24d68b998e3e9

Aliases

arxiv: math/0609165 · arxiv_version: math/0609165v2 · doi: 10.48550/arxiv.math/0609165 · pith_short_12: QPNOLUTMTUIH · pith_short_16: QPNOLUTMTUIHDH32 · pith_short_8: QPNOLUTM

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/QPNOLUTMTUIHDH322QSXXOQZAZ \
  | 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: 83dae5d26c9d10719f7ad4257bba19067700240411d2b08261c24d68b998e3e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7a7b54b951e51d8b26ecb3f241fb921874f39bb748f23938826d0f39a4d5482",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2006-09-06T04:47:44Z",
    "title_canon_sha256": "989b165f472e4e3d172547c6d87e0cd671df7c199282f16ba86743e4373b83fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609165",
    "kind": "arxiv",
    "version": 2
  }
}