Pith Number

pith:FS7KEZAS

pith:2012:FS7KEZASXXRD2QOM257QOF6MRX

not attested not anchored not stored refs pending

Refinement of the Sphere-Packing Bound: Asymmetric Channels

Aaron B. Wagner, Yucel Altug

arxiv:1211.6697 v1 · 2012-11-28 · 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{FS7KEZASXXRD2QOM257QOF6MRX}

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	2026-05-18T03:39:44.020918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2cbea26412bde23d41ccd77f0717cc8dcf212beb3d1b8057f737a38a5e89b2c0

Aliases

arxiv: 1211.6697 · arxiv_version: 1211.6697v1 · doi: 10.48550/arxiv.1211.6697 · pith_short_12: FS7KEZASXXRD · pith_short_16: FS7KEZASXXRD2QOM · pith_short_8: FS7KEZAS

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/FS7KEZASXXRD2QOM257QOF6MRX \
  | 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: 2cbea26412bde23d41ccd77f0717cc8dcf212beb3d1b8057f737a38a5e89b2c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80a69294a6511fcc066c3ece9d2e6705e6ce96651e3b79532f83c43194892a90",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2012-11-28T18:38:50Z",
    "title_canon_sha256": "b10922e657ad964d0efd8c2989f323bb95350e8fb590e133218d90783dacabcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6697",
    "kind": "arxiv",
    "version": 1
  }
}