Pith Number

pith:DUTGKQQY

pith:2012:DUTGKQQYJCWCVGTYY6YNI43GBB

not attested not anchored not stored refs pending

A Tight Upper Bound for the Third-Order Asymptotics for Most Discrete Memoryless Channels

Marco Tomamichel, Vincent Y. F. Tan

arxiv:1212.3689 v3 · 2012-12-15 · 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{DUTGKQQYJCWCVGTYY6YNI43GBB}

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	2026-05-18T03:09:12.972215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d2665421848ac2a9a78c7b0d47366086962c9e31c66b3f2a1742dc54a70aed6

Aliases

arxiv: 1212.3689 · arxiv_version: 1212.3689v3 · doi: 10.48550/arxiv.1212.3689 · pith_short_12: DUTGKQQYJCWC · pith_short_16: DUTGKQQYJCWCVGTY · pith_short_8: DUTGKQQY

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/DUTGKQQYJCWCVGTYY6YNI43GBB \
  | 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: 1d2665421848ac2a9a78c7b0d47366086962c9e31c66b3f2a1742dc54a70aed6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afce79cb89ea108e47436e251f8ab360ace592e0607c1af2b758df7bac3a1e7d",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2012-12-15T14:58:14Z",
    "title_canon_sha256": "34bf5b155c11ee737160932a4babecf322c0c5564f067c890a43a1cace3bb8c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3689",
    "kind": "arxiv",
    "version": 3
  }
}