Pith Number

pith:5Y4ZMBNI

pith:2025:5Y4ZMBNI7P7JMBU6KNUA3GSFKU

not attested not anchored not stored refs pending

Non-Asymptotic Error Bounds for Causally Conditioned Directed Information Rates of Gaussian Sequences

Andrew Lamperski, Yuping Zheng

arxiv:2512.06238 v2 · 2025-12-06 · cs.IT · math.IT · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5Y4ZMBNI7P7JMBU6KNUA3GSFKU}

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	2026-05-20T00:02:07.940390Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee399605a8fbfe96069e53680d9a4555364817ccc391da91008e698e1f561abe

Aliases

arxiv: 2512.06238 · arxiv_version: 2512.06238v2 · doi: 10.48550/arxiv.2512.06238 · pith_short_12: 5Y4ZMBNI7P7J · pith_short_16: 5Y4ZMBNI7P7JMBU6 · pith_short_8: 5Y4ZMBNI

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/5Y4ZMBNI7P7JMBU6KNUA3GSFKU \
  | 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: ee399605a8fbfe96069e53680d9a4555364817ccc391da91008e698e1f561abe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f703582675f3312d9808738db26a03bbe5f61aba215dd571db4a610a7f29137",
    "cross_cats_sorted": [
      "math.IT",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2025-12-06T01:30:57Z",
    "title_canon_sha256": "f04bf6c559de25926591ebe090048e0b100e10ae7c882b6cfa8a10ed087c19e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.06238",
    "kind": "arxiv",
    "version": 2
  }
}