Pith Number

pith:GKU2R75P

pith:2017:GKU2R75P4NNTNY2XY6EHNW6V23

not attested not anchored not stored refs pending

Upper Bound on Normalized Maximum Likelihood Codes for Gaussian Mixture Models

Kenji Yamanishi, So Hirai

arxiv:1709.00925 v2 · 2017-09-04 · 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{GKU2R75P4NNTNY2XY6EHNW6V23}

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	2026-05-18T00:00:30.961166Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32a9a8ffafe35b36e357c78876dbd5d6ed04efd91dd176810840ebf63ed30440

Aliases

arxiv: 1709.00925 · arxiv_version: 1709.00925v2 · doi: 10.48550/arxiv.1709.00925 · pith_short_12: GKU2R75P4NNT · pith_short_16: GKU2R75P4NNTNY2X · pith_short_8: GKU2R75P

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/GKU2R75P4NNTNY2XY6EHNW6V23 \
  | 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: 32a9a8ffafe35b36e357c78876dbd5d6ed04efd91dd176810840ebf63ed30440

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f9bd47b40ff6e63a4b0ea2d9cb868ac775303834bac9017c83ee0128d8f5fc3",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2017-09-04T12:41:00Z",
    "title_canon_sha256": "26be1dd1aba268a97a29a94ce791d56270cbddc6626ab20ae02ec404c1444be7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.00925",
    "kind": "arxiv",
    "version": 2
  }
}