Pith Number

pith:ETPGR2Q4

pith:2014:ETPGR2Q4J6VBSHCOGI5YKMRYZD

not attested not anchored not stored refs pending

Analytic Expressions and Bounds for Special Functions and Applications in Communication Theory

George K. Karagiannidis, Mikko Valkama, Paschalis C. Sofotasios, Steven Freear, Theodoros A. Tsiftsis, Yury A. Brychkov

arxiv:1403.5326 v2 · 2014-03-21 · 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{ETPGR2Q4J6VBSHCOGI5YKMRYZD}

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	2026-05-18T02:14:18.143204Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24de68ea1c4faa191c4e323b853238c8fe8704971a4d8c0083f5462433aafc57

Aliases

arxiv: 1403.5326 · arxiv_version: 1403.5326v2 · doi: 10.48550/arxiv.1403.5326 · pith_short_12: ETPGR2Q4J6VB · pith_short_16: ETPGR2Q4J6VBSHCO · pith_short_8: ETPGR2Q4

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/ETPGR2Q4J6VBSHCOGI5YKMRYZD \
  | 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: 24de68ea1c4faa191c4e323b853238c8fe8704971a4d8c0083f5462433aafc57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09f785b67dc228afb46867ba16c80ba7ff53c74175744a1a902f3931699635bc",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2014-03-21T00:16:17Z",
    "title_canon_sha256": "fa4e6669112ad03040e44b9e38853fdff19ffbb39c19d60fdcba382037b2c6d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.5326",
    "kind": "arxiv",
    "version": 2
  }
}