Pith Number

pith:STPGM7W4

pith:2011:STPGM7W4QXMDWZ44O6DAWQO4AS

not attested not anchored not stored refs pending

Weak randomness and Kamae's theorem on normal numbers

Hayato Takahashi

arxiv:1102.3242 v1 · 2011-02-16 · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{STPGM7W4QXMDWZ44O6DAWQO4AS}

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	2026-05-18T04:28:36.781764Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

94de667edc85d83b679c77860b41dc04a20576ea8f83a24fdf89fce35d2e1c99

Aliases

arxiv: 1102.3242 · arxiv_version: 1102.3242v1 · doi: 10.48550/arxiv.1102.3242 · pith_short_12: STPGM7W4QXMD · pith_short_16: STPGM7W4QXMDWZ44 · pith_short_8: STPGM7W4

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/STPGM7W4QXMDWZ44O6DAWQO4AS \
  | 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: 94de667edc85d83b679c77860b41dc04a20576ea8f83a24fdf89fce35d2e1c99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a41a74de7d44e36c1f2745e79898955e02a6b1cdd633fb6e28e9a0c09c113afc",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2011-02-16T05:25:16Z",
    "title_canon_sha256": "89a055578d6eb6ee2982eb8b75079a8bf7941a18cdbd38c01adafea82e86aedc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.3242",
    "kind": "arxiv",
    "version": 1
  }
}